,transcriber's ,note ,the original contains inconsistent hyphenation2 this has been preserved4 ,obvious printer's errors have been corrected2 a full list is available at the end of this book4 - is used for a minus sign4 ,william ,b4 ,white ,theory and ,practice of ,,piano ,,construction ,with a ,detailed1 ,practical ,method for ,tuning ,dover ,publications1 ,inc4 ,new ,york ,published in ,canada by ,general ,publishing ,company1 ,ltd41 #cj ,lesmill ,road1 ,don ,mills1 ,toronto1 ,ontario4 ,published in the ,united ,kingdom by ,constable and ,company1 ,ltd41 #aj ,orange ,street1 ,london ,,wc #b4 ,this ,dover edition1 first published in #aige1 is an unabridged and unaltered republication of the work originally published by ,edward ,lyman ,bill1 ,publisher1 ,new ,york1 in #aijf under the title ,theory and ,practice of ,pianoforte ,building4 ,international ,standard ,book ,number3 #j-dhf-bcaci-i ,library of ,congress ,catalog ,card ,number3 #gd-ghhaa ,manufactured in the ,united ,states of ,america ,dover ,publications1 ,inc4 #ahj ,varick ,street ,new ,york1 ,n4,y4 #ajjad ,,contents4 ,,page ,some ,remarks by the ,publisher #e ,introductory ,remarks #i ,the ,evolution of the ,modern ,pianoforte #ac ,description of the ,modern ,pianoforte #bc ,acoustical ,laws of ,sounding ,strings #bh ,the ,musical ,scale and ,musical ,intonation #cf ,the ,equal ,temperament #dd ,pianoforte ,strings and ,their ,proper ,dimensions #dh ,resonance and the ,resonance-,apparatus of the ,pianoforte #eh ,the ,casing and ,framing of the ,pianoforte #fg ,the ,iron ,frame of the ,pianoforte #gi ,the ,mechanism of ,percussion #ib ,the ,touch ,mechanism #if ,the ,regulation of ,pianoforte ,touch-,mechanism #aac ,tuning and ,tone ,regulation of the ,pianoforte #abb ,the ,draughting of the ,pianoforte ,scale #ace ,conclusion #aci ,appendix ,a--,development of ,player ,piano #add ,appendix ,b--,the ,small ,grand #aec ,,some ,,remarks ,,by ,,the ,,publisher4 ,for many years we have been receiving at the office of ,the ,music ,trade ,review constant inquiries for sources from which information might be gleaned regarding the theory and practice of tone production as applied to the piano4 ,it has therefore been obvious to all who have given this subject the slightest consideration that there has been a lack of book information which should be at the hand of the student and the seeker of knowledge regarding scale draughting and other essentials relating to piano construction4 ,some years ago1 after careful consideration of this subject1 special topics along these lines were assigned to the author of this work1 who was well fitted for the task before him1 and as a result of more than two years of conscientious study and research1 the 8,theory and ,practice of ,pianoforte ,building0 is put forth as representing in a concrete form a work of technical knowledge which hitherto has been unobtainable to the student4 ,the necessity of acquiring some knowledge of the principles of mechanics before proceeding to the study of scale design is admitted4 ,such knowledge1 together with that of the principles of the acoustics as they apply to musical sounds produced by vibrating strings1 is essential to a correct understanding of the fundamental ideas underlying true pianoforte design4 ,to know a piano accurately one must understand the laws governing tone quality1 and how the propagation and transmission of sound is produced as well as the pitch and intensity of sound4 ,and there are thousands of men to-day in the various factories who are anxious to obtain sources of information from which to gain a more correct knowledge of a profession which should take high rank among industrial pursuits4 ,owing to the gradual changes which have been wrought in all industries through the abandonment of the apprentice system1 there is more need for instruction books than ever before4 ,a factory operative1 according to the present plan1 may know thoroughly but one department of the business1 but he can become more useful to himself and his employers when he possesses a knowledge of all branches4 ,in the piano trade particularly there must be a correct knowledge of piano building1 else there can be no advance1 and with our old piano makers rapidly passing away there is need for a healthy school of new inventors1 so that wherever possible1 improvements may be made and defects remedied4 ,these can only be accomplished by the possession of a knowledge of all the intricate principles involved in piano making4 ,we feel that in presenting a work of this kind we are offering a volume which will meet with the approval of those who seek knowledge1 for while there are great trade and technical schools which are the fountains of inspiration for various trades1 the science of piano making is not included as a branch in any of them4 ,it is therefore evident that knowledge must be gained outside1 for piano schools there are none4 ,to every mind seeking information there should be knowledge given1 and we believe that a work of this kind must be of value to an industry wherein there is such a dearth of reliable text books4 ,it will be seen by examination that all of the practical problems which are to be considered by the scale draughtsmen have been fairly treated in this volume and yet the desire of the author has been throughout to avoid tiresome details4 ,condensation is one of the recognized laws of our day1 and in producing this technical work the author has labored to create a volume of convenient size which shall be of service to the student1 and to the advanced thinker as well1 on account of the accuracy with which the subjects are treated4 ,this book is not in the remotest sense a history of piano building or development1 and it should not be so considered2 in fact it has been deemed wise to dip into historical matters only to the extent of showing the application of an enduring principle rather than to give credit to a number of deserving inventors who have worked along special lines4 ,a treatment of worthy inventions would require a much larger volume than this2 and while there are many inventors who have given to the world special devices of value1 it has not been considered timely to describe them in this volume or to enter into an expos of their merits or demerits4 ,we may say that this is not a critical work but rather one which we trust may be eminently practical in its mission as an instructive and an educational force4 ,we may add in closing that the 8,theory and ,practice of ,pianoforte ,building0 is the only work of its kind ever put forth in the ,english language1 and we have every confidence that it will find a growing demand among music trade people everywhere4 ,,edward ,,lyman ,,bill4 ,editorial ,rooms1 ,the ,music ,trade ,review1 ,,new ,,york1 ,may1 #aijf4 ,,theory ,,and ,,practice ,,of ,,pianoforte ,,building4 ,,chapter ,i4 ,,introductory ,,remarks4 ,the development of the modern ,american pianoforte presents a most interesting study to the practical member of the musical industries as well as to the pianist4 ,for it is possible to view the subject with equal facility from the standpoints of both4 ,descended through a clearly defined line of ancestry from the ancient psaltery1 and showing traces of the various steps in its evolution throughout its entire modern form1 the pianoforte of to-day is essentially the product of all the ages4 ,there have not been wanting a sufficient number of writers upon the history and ancestry of the instrument2 but an exposition of the correct principles of design has not hitherto appeared in the ,english language1 at least in a form that possesses permanent value to the ,american manufacturer4 ,the once classic work of ,rimbault is obsolete to-day1 even in ,europe2 while1 on the other hand1 the various ,german treatises have been difficult to obtain and necessarily limited in their appeal to an ,english speaking people1 nor have any satisfactory translations of any of them yet been put forth4 ,furthermore1 the evolution of pianoforte building in this country has proceeded along characteristically ,american lines and has resulted in the existence to-day of a peculiarly national1 advanced and complex type4 ,american pianofortes are universally acknowledged to stand among the highest developments of applied musical craftsmanship1 and artists of every degree have willingly given their assent to every claim that has been made for the instruments4 ,while1 however1 these facts are easily demonstrable1 it would be by no means correct to suppose that the development of the ,american types of pianoforte has been materially assisted by even a respectable minority of those who have been engaged in constructing them4 ,on the contrary1 the magnificent examples of the musical instrument maker's art that grace the homes of musicians and people of culture throughout the ,united ,states owe their present high excellence to the labors and skill of a small band of enthusiastic and clever workers4 ,the names of ,william ,hawkins1 ,jonas ,chickering1 and ,henry ,engelhard ,steinway should be written in letters of gold above the doors of all institutions devoted to the creation of artistic pianofortes4 ,for it is to the earnest labor and untiring enthusiasm of these men and a few others1 working alone and unassisted1 that the modern ,american instrument owes its present proud position4 ,and this state of affairs has continued to exist until the present day4 ,there are1 as there have always been1 a few talented and skilful men who have never been content to rest upon their laurels or to desist from continual labor along the lines of musical and mechanical betterment2 but such as they stand1 and have always stood1 alone4 ,the great majority have been glad to accept the improvements of their preceding or contemporaneous masters after the commercial value of the innovations has been demonstrated2 but they have always lacked the audacity or capability to strike out into new fields and untrodden pathways4 ,we may1 however1 discern a sufficient reason for this timidity on the part of pianoforte makers4 ,the principles that underly the design of the instrument are primarily acoustical4 ,they have never been very easily digested1 either by the mechanic or by the man of affairs4 ,and since a knowledge of acoustics has been profoundly developed only within the last sixty years or so1 it follows that its application to the design of musical instruments has naturally lagged behind the progress of the science itself4 ,pianoforte makers are not usually professing scientists or practical musicians2 and they have discerned little profit in attempting to keep up with the trend of modern acoustical research1 even so far as this has directly affected the principles of musical instrument construction4 ,the development of the pianoforte has1 in fact1 proceeded empirically1 and has been prosecuted inductively rather than from any a priori notions4 ,and while we cannot withhold our admiration from the splendid success that has attended so much of this empirical research1 we cannot be blind to the fact that very many modern pianofortes exhibit clearly the inherent defects of such methods4 ,the practical musical mechanician1 if he possess the requisite knowledge1 is often able to remedy existing faults in tone quality and tone-production4 ,and while studying ways and means for doing this1 he cannot but observe innumerable cases of neglected opportunities1 or even of positive mistakes4 ,the pure empirical method must always produce a large number of failures4 ,yet the application of even the elementary principles of ,applied ,acoustics would frequently prevent the commission of serious sins in design4 ,it is not necessary1 of course1 that every scale draughtsman or designer should have the results of modern acoustical discovery at his fingers' ends2 but it is here insisted that such knowledge1 in so far as it relates to musical instruments1 is essential to the correct construction of pianofortes4 ,tone-production1 otherwise than by the human voice1 implies both scientific and mechanical problems4 ,especially is this true of the pianoforte1 which1 with the exception of the pipe organ1 may properly be considered the most complex of artificial devices for the performance of music4 ,recognition of this truth and a general improvement in the knowledge of the acoustical and musical principles involved cannot fail to exercise a most beneficial influence upon the future of the ,american pianoforte4 ,as has already been remarked1 there is a dearth of convenient treatises in the ,english language that can be said to possess a present value to the earnest student of pianoforte design4 ,the present book is an attempt in the direction of supplying the deficiency4 ,the author has aimed at presenting the various problems pertaining to the art of pianoforte construction with due regard both to their acoustical and mechanical features4 ,no attempt has been made to delve profoundly into the mysteries of sound2 but the elementary and basic principles of tone-production have been stated1 and their true application to the various stages of pianoforte construction explained4 ,each step in the making of a pianoforte from beginning to completion has been subjected to analysis1 and the correct principles pointed out4 ,the author believes that the book may be read and comprehended1 even by one to whom the very term acoustics has hitherto been unfamiliar4 ,while he does not expect that a study of this book can make the novice a full-fledged scale draughtsman1 as it were1 overnight1 he does expect1 on the other hand1 to assist those who have already investigated1 or who intend to investigate the whole problem1 to a clearer and broader comprehension of a beautiful art4 ,if this hope be gratified1 much will have been achieved1 and no one who has at heart the future of musical industry in ,america can fail to be encouraged1 if nothing else1 by the appearance of this condensed work4 ,the general outline of the book can be explained with little detail4 ,recognizing1 as has already been suggested1 the dependence of all right pianoforte making upon the observance of the established principles of acoustics1 the author has thought it well1 after a short historical sketch of the pianoforte1 to make a general statement of the laws that govern the propagation and transmission of sound4 ,it is but a step from this to a concise explanation of the peculiarities of stretched strings and their behavior under varying conditions of excitation1 and differing phases of tension1 etc4 ,this leads us directly to the discussion of pianoforte strings1 their dimensions1 and the manner in which they become the agents of sound-production in the instrument4 ,continuing our investigations1 we pass to the subject of resonance and come naturally to a discussion of the resonating apparatus of the pianoforte4 ,the framing that holds together these two vital elements is next subjected to analysis and explanation1 and finally the mechanisms of percussion and touch are brought under our inquiry and their peculiarities noted and expounded4 ,the remarks upon the draughting of pianoforte scales1 that conclude the volume1 are necessarily broad and general1 since it is quite impossible to indicate with exactitude the actual method to be employed in making mechanical drawings1 at least within the limits that the relative importance of the subject imposes on us4 ,attention has been drawn more particularly to the calculations for shrinkage that are rendered necessary by the vagaries of cast iron1 such as is used in the manufacture of metal frames1 and to the details of hammer-stroke points and string dimensions1 the principles of which have been explained in their proper places within the body of the work4 ,,chapter ,,ii4 ,,the ,,evolution ,,of ,,the ,,pianoforte4 ,while the present work is by no means intended to serve as an elaborate analysis of pianoforte development1 it seems that a proper comprehension of the various principles that are laid down in the course of our argument will be facilitated by a short survey of the evolution of the instrument1 undertaken from an historical viewpoint4 ,as we recognize in the pianoforte of to-day the culmination of the musical-mechanical effort of ages1 and as a complete study of the results that have been achieved can best be introduced by a preliminary knowledge of the manner in which the various steps towards latter-day excellence have been attained1 it seems that we cannot do better than make an attempt to survey the field of pianoforte evolution in a manner broad and general1 though necessarily brief4 ,as was incidentally remarked in the last chapter1 we may properly consider the modern pianoforte as essentially the product of all the ages4 ,the origin of stringed instruments is lost in the mists of antiquity1 but ,greek mythology has supplied us with a most pleasing legend to account for the invention of that pioneer of all stretched-string instruments1 the classic lyre4 ,we are told that ,hermes1 walking one day along the shore1 found lying at his feet the shell of a dead tortoise4 ,the intestines of the animal had been dried in the sun and were stretched along the rim of the shell so that when ,hermes' foot struck against one of them1 a musical sound was given forth and ,lo6 the lyre was born4 ,earlier still are the accounts1 in the shape of cuneiform or other inscriptions1 that show a form of lyre to have been in use among the ,assyrians4 ,the biblical descriptions of various stringed instruments1 such as the psaltery1 or the harp of ,david1 are generally familiar4 ,while doubtless we need not consider it illogical to trace the beginning of modern stringed instruments1 whether they be of the key-board variety or otherwise1 to such misty and vague traditions1 we must look to more modern times for a true understanding of the causes that operated to produce the key-board4 ,this1 the distinguishing feature of the pianoforte family1 first arose through the need for a facile means of accompanying the voice in the then newly beginning art of music which required the simultaneous sounding of different tones4 ,instruments of the organ type were earlier in the field1 for we have accounts of the water-organ in the writings of the historians of the later ,roman ,empire4 ,the earliest form of key-board seems to have been introduced in ,europe in the latter part of the eleventh century ,a4 ,d4 ,at about the same period we hear of a stringed instrument called the organistrum1 having three strings1 one of which was in connection with a number of tangents which were adapted to be pushed in upon it so as to sound different segments and produce different notes4 ,later we find that the ecclesiastical musicians were in the habit of using more or less complicated monochords for the purpose of training their pupils in the plain-chants of the church4 ,these monochords gradually became more complex and finally were mounted on a kind of sound board in groups and thus became no longer monochords but trichords1 tetrachords1 or polychords4 ,the next step was obviously to furnish the instrument with a set of balanced key-levers borrowed from the organ and with tangents to connect the keys with the strings1 these latter coming from the organistrum4 ,thus we have at once the famous clavichord4 ,but this was not the only form of keyed instrument that was thus early devised4 ,we learn that the psaltery had contemporaneously been fitted with keys4 ,there were two forms of this famous instrument1 one trapezoid and one triangular4 ,when both of these had been fitted with keys there were two more distinct forms of keyed instruments2 differences which had a large influence upon the later development of the type4 ,these three instruments were thus developed into the accepted forms that were in general use during the seventeenth century and later2 becoming respectively the clavichord1 harpsichord and spinet4 ,it is from these that the pianoforte is directly sprung4 ,the harpsichord1 as its name implies1 resembled a harp laid on its back and enclosed in a case1 while the strings were plucked1 by quills set on jacks1 mounted on the keys4 ,the natural shape of the harpsichord1 therefore1 was similar to that of the modern grand pianoforte and it derived this form from its direct relationship to the early keyed forms of the triangular psaltery4 ,the harpsichord had been a favorite for a long time when ,bartolomeo ,cristofori1 a maker of ,florence1 completed in #agji the invention of a hammer action to replace the quilled jack at the end of the harpsichord key4 ,thus was made possible the production of dynamic effects1 of which the harpsichord action had never been capable except through the employment of various mechanical devices1 such as swells and double or triple banks of keys with jacks and quills to match4 ,the hammer-action of ,cristofori as completed by him in #agbf shows a remarkable similarity to the mechanisms that are still to be found in certain forms of square pianofortes4 ,he succeeded in producing an acceptable form of escapement and a damping device as well1 although as the date shows1 not until after several years of experimenting and improving upon the original design4 ,examination shows that ,cristofori's action differs in no essential respect from the square pianoforte actions that we have mentioned4 ,there is the upper and under hammer1 the jack working on a groove in the key1 the escapement device to determine the travel of the jack1 the back-check1 and the damper4 ,every feature that is essential to provide escapement1 repetition and damping is found here4 ,cristofori was1 however1 obliged to make many changes in the construction of his 8gravicembalo col piano e forte0 to provide the increased stiffness necessitated by the different manner of exciting the strings4 ,his work1 curiously enough1 was not taken up after his death by any other ,italian harpsichord maker1 and it remained for a ,german to continue his experiments and bring them to a practical and commercial success4 ,only two pianofortes by ,cristofori are known to exist1 and one of these is in the ,metropolitan ,museum of ,art1 ,new ,york4 ,gottfried ,silbermann1 who took up the work of ,cristofori1 built several grand pianofortes towards the end of the first half of the eighteenth century1 and there still exist at ,potsdam some of these that were sold by him to ,frederick the ,great4 ,these instruments appear to be essentially founded upon the work of ,cristofori1 and the superior workmanship and better adjustment of them do not serve to disguise the evident fact that ,silbermann1 while improving in details1 did not discover any new principles either in action or otherwise4 ,somewhat later we hear of ,zumpe1 who was apparently struck with the idea of adapting the pianoforte hammer to the square-shaped clavichord1 which was not deep enough to take the ,silbermann action1 thus producing a veritable square pianoforte4 ,zumpe's device contained no provision for escapement1 which fault was afterwards corrected by the celebrated inventor ,stein4 ,mozart speaks of the merits of ,stein and joyfully describes how his mechanism prevented the blocking of the hammers4 ,mozart used one of ,stein's pianofortes during the rest of his life4 ,the name of ,stein is justly famous among the early pianoforte makers4 ,he was responsible1 with the able assistance of his daughter ,nanette1 for the ,viennese type of pianoforte1 which was for long such a favorite over the heavier and more solid ,english style on account of its surprising delicacy and lightness of touch4 ,after her marriage1 ,nanette ,stein1 in partnership with her husband ,streicher1 made many other improvements1 and her pianofortes were used by ,beethoven and others4 ,the firm of ,streicher still existed in ,vienna a few years ago4 ,at this point1 namely at the beginning of the nineteenth century1 we begin to hear of three revolutionary figures2 a ,frenchman1 an ,englishman and an ,american4 ,these are ,erard1 ,broadwood and ,hawkins4 ,pierre ,sebastian ,erard settled in ,paris during the latter part of the eighteenth century as a maker of harps and harpsichords4 ,shortly before the breaking out of the ,french revolution1 ,erard came to ,london and began to make harps and pianofortes4 ,in the meantime he was continually working to improve his instruments and was responsible for many useful inventions1 such as the up-bearing to the strings by means of the 8agraffe40 ,his chief claim to the consideration of pianoforte makers is due1 however1 to his invention of the 8double repetition0 action which was perfected by him in #ahba1 after many years of unsuccessful experiment4 ,this action1 with slight modification1 is used at the present day in all grand pianofortes1 and its manifold excellences have never been yet surpassed4 ,erard took out a large number of patents1 which were put into use by his successors1 and the house founded by him is still in existence and one of the most famous in ,france or indeed in the world4 ,john ,broadwood1 the great ,english inventor and manufacturer1 who also has his name perpetuated in the continued and flourishing career of the firm that he founded1 was originally a workman in the shop of ,tschudi or ,shudi1 a ,london harpsichord maker4 ,he rose from an apprenticeship to the head of the house of ,shudi and finally turned his attention to the improvement of the pianoforte4 ,he had early been the recipient of the knowledge of ,backers1 the inventor of the so-called ,english action1 and when he came to build pianofortes on his own account1 this experience was made to bear practical fruit4 ,broadwood's first achievement was in the re-designing of the square piano of ,zumpe4 ,about the year #aghj he entirely altered its construction1 set the tuning pins at the back of the case1 and added dampers and pedals4 ,he next set about the improvement of the grand1 and divided the bridge1 giving a separate bass bridge and permitting the striking point of the hammers on the strings to be adjusted with correctness1 something that had never been done before4 ,this completed the divorce of the pianoforte from the harpsichord4 ,with the addition of the action invented by ,backers1 ,broadwood's pianofortes became at once a standard of quality and excellence and until the introduction of iron framing stood alone4 ,we now come to ,hawkins4 ,this remarkable man was an engineer of ,philadelphia1 ,english by birth but ,american by adoption4 ,in the year #ahjj he produced an upright pianoforte1 the first of its kind4 ,this instrument1 though it was not a commercial success1 was remarkable for the fact that ,hawkins in it anticipated so many of the ideas that have since become essential to modern instruments4 ,he had an independent iron frame supporting the sound-board1 a mechanical tuning device1 and metal action frames4 ,his action1 too1 had many features that have since been adopted4 ,unfortunately1 the tone was so poor that the instrument was a failure from the start4 ,his ideas in regard to upright pianoforte construction were not allowed to languish1 however1 and the labors of ,wornum1 who followed ,southwell1 were at last successful in producing1 in #ahbf1 a practical action which at once settled the destiny of the upright4 ,this action had as its peculiar feature the 8bridle tape10 which is now such a necessary element of the upright pianoforte4 ,he also introduced the centre pin and flange4 ,at this point we begin to come to the great dividing line between the early and the modern pianoforte4 ,the introduction of metal framing marks this division and it is from here that the ,american instrument begins its independent and extraordinarily successful career4 ,indeed1 the development of ,american instruments is bound up with the almost concurrent progress of ideas as to metal framing4 ,although the first application of metal to pianofortes1 not considering the unfortunately abortive invention of ,hawkins1 may be credited to ,william ,allen1 an ,englishman1 yet we must look to the ,united ,states for the pioneer in the modern conception of metal bracing4 ,the man in question1 ,alpheus ,babcock1 was a ,boston maker and had been originally an apprentice of ,crehore1 who appears to have made the first ,american pianoforte4 ,babcock applied his invention in ,boston in the form of a cast metal plate for a square pianoforte about the year #ahbb and this date is most memorable in that it marks the epoch of the strictly modern conception of the instrument4 ,continuing the consideration of this ,national school of design1 we find that the celebrated ,jonas ,chickering produced1 in #ahdj1 a cast-iron plate for grand pianofortes1 having the string-plate1 agraffe-bridge and resistance-bars cast solid in one piece4 ,this revolutionary invention unquestionably paved the way for the wonderful ,american productions of later years and at once placed the ,american pianoforte upon a plane of excellence that has never been altogether reached by its competitors in other parts of the world4 ,european makers were at first slow to appreciate the eminently valuable nature of the invention of ,chickering1 and until lately the solid cast plate was not extensively used in ,europe outside of ,germany4 ,the house of ,collard and ,collard1 which had the services of ,stewart1 the assistant of ,chickering for many years1 was1 however1 most progressive in this respect and for long was the only ,london firm which made grand pianofortes with the iron plate cast in one piece4 ,the celebrated house of ,broadwood1 after much experimenting1 produced a form of iron plate for grands that was somewhat different in principle from that of ,chickering4 ,in this type1 the body of the structure was cast complete1 but instead of the multiplicity of braces1 we find only two4 ,one of these runs parallel with the line of the vertically-strung bass strings at the extreme bass end of the instrument1 while the other crosses the plate in a diagonal direction from near the middle of the agraffe-bridge to the point of greatest tension4 ,both of these bars are cast separate from the body of the plate and secured to it by means of bolts and nuts4 ,such a method has usually been characteristic of ,european as opposed to ,american methods1 but the ,broadwoods1 about fifteen years ago1 brought out a decided novelty in their 8,barless ,grand40 ,this remarkable instrument has a plate of cast steel and is entirely without braces or bars of any kind1 the necessary stiffness being gained through the tensile strength of the metal employed and the use of a number of turned up flanges along the sides of the structure1 these being screwed into the case of the pianoforte at equal intervals on its periphery4 ,as to the further development of the grand pianoforte1 we may look to the progress of the ,chickerings and the ,steinways in ,america and to the ,broadwoods in ,england1 the ,erards in ,france and the ,bechsteins and ,blthners in ,germany4 ,these makers are considered here because they have all contributed in no small degree to the development of the instrument as an artistic product and because they have all been responsible for some radical improvement that has later become essential to the make-up of a good pianoforte4 ,we need only mention the ,steinway cupola plate1 fan-like disposition of strings1 overstrung bass1 duplex scale and capo d'astro bar to give the reader some idea of the many inventions that have sprung from the fertile brains of the members of this house4 ,the other houses1 notably that of ,chickering in this country1 and ,broadwood in ,england1 have been prolific in improvements1 and the development of the grand pianoforte has consequently been rapid and successful from the musical and scientific1 no less than from the commercial view-point4 ,the history of the type in more recent years is familiar to all1 however1 and it is unnecessary to enlarge upon it here4 ,if we have seemed1 hitherto1 to have neglected proper consideration of the upright and square forms of pianoforte1 the fault is more apparent than real4 ,for there are two good reasons why discussion of these types should have been delayed4 ,in the first place1 the square is already obsolescent if not obsolete1 while on the other hand the development of the upright into a commercially successful and largely produced instrument has only come about in recent years4 ,this sketch would1 of course1 be incomplete without brief consideration of them and we shall therefore devote some space to this end4 ,as has already been indicated1 the square piano may be considered as having a genesis quite distinct from the grand or upright4 ,it was developed1 as we know1 by ,zumpe1 whose purpose was to fit the hammer action to the body of a clavichord4 ,thus1 when we consider the different roots from which the clavichord and spinet-harpsichord types were themselves evolved1 and the direct descent of the grand pianoforte from the latter1 the entirely separate and distinct growth of the square is easily discerned4 ,this distinction is most interesting at the present day1 when the glory of the square has departed and its days are numbered4 ,the evolution of the square pianoforte in ,america has been recorded with faithful detail by ,spillane in his 8,history of the ,american ,pianoforte10 and the reader will find in that work an abundance of material to satisfy any curiosity that may possess him4 ,incidentally it may be remarked that the idea of cross-stringing the bass had been applied to clavichords as early as the time of ,hndel2 so that the overstringing of the square pianoforte came about quite naturally1 especially after the improvements of ,john ,broadwood the ,first4 ,on the other hand1 this principle was for long overlooked in the design of the other popular types2 so much so1 in fact1 that ,european grands and uprights are still to be found in plenty with straight stringing throughout4 ,the chief reasons for the gradual decline in the popularity of the square may be traced almost as much to social and economic as to artistic and mechanical causes1 although these latter had the greater influence in shaping the ultimate destiny of the type4 ,the square was developed in the ,united ,states until the native ,american product left all imitators and rivals far behind1 but even at that the fundamental defects of construction could never be overcome entirely4 ,the great gap in the middle of the structure1 required for the passage of the hammers1 entailed dangerous weakness1 against which no reasonable weight of iron bracing has ever seemed to prevail4 ,again1 the fact that the bass keys1 where the strength of the blow and the leverage of the action need to be greatest1 were the shortest of all1 while the extreme treble keys were longest1 always tended to destroy the touch proportions and entailed much counter-balancing and other operations which were1 however1 but makeshifts at the best4 ,moreover1 the development of the grand type led to rivalry among those makers who confined themselves chiefly to the square1 with the result that the latter was made more and more heavy and cumbrous in an effort to catch up with the fundamental advantage which the grand pianoforte possessed on account of its superior design4 ,besides1 the square was never a thing of beauty1 and its increasing size was by no means an advantage in this respect1 so that when the rapidly growing population of the great ,american cities began to make living room continually more valuable1 the claims of the small1 powerful1 elegant1 and moderate-priced upright soon were successfully asserted4 ,as a last consideration1 it should be mentioned that the makers of square pianofortes were never able to apply to it a mechanism having the elasticity and rapid repetition that belong to the ,erard grand action or the tape-check device of ,wornum1 which is universal in the upright4 ,in view of all these disadvantages1 it is no longer a matter for wonderment that the upright pianoforte succeeded the square as a bidder for domestic favor1 while the larger and more highly evolved grand remained the choice of professional musicians4 ,the commercial development of the upright pianoforte1 as we have remarked1 began at a comparatively recent period4 ,in this country1 owing to the popularity of the square1 we find that the upright was late in coming into favor4 ,its development1 however1 had been going on in ,europe since the beginning of the nineteenth century4 ,the 8cabinet0 piano of ,southwell and the 8upright grand0 of ,hawkins were examples of early attempts in this line1 but it remained for the genius of ,robert ,wornum to place the upright instrument on a truly practical footing4 ,this was accomplished through his invention of 8the tape-check action10 which at once put the upright pianoforte upon an equal plane of efficiency with the prevailing types and assured its rapid adoption4 ,by the end of the first half of the nineteenth century the upright piano had become firmly established as the home instrument throughout ,europe1 and about the same time began to appear among ,american products4 ,as soon as ,american manufacturers took hold of it1 they set about making vast improvements upon ,european models2 and we may properly date the modern development of the upright from this time4 ,americans were responsible for the adoption of overstrung iron-framed scales1 and for the increase in size and power which now makes our best instruments of this class equal1 if not superior1 to the grands of a few years ago4 ,the later history of the upright1 not less than of the grand1 is a simple record of continuous improvement in details of workmanship and material1 in beauty of case design and in scientific construction of scale4 ,it is not necessary1 for the purpose of this short sketch1 to enter into the familiar modern history of manufacturing the various types of pianoforte1 either in this country or abroad2 but we may note1 incidentally1 that ,european makers have adopted more and more ,american inventions and improvements1 so that the modern1 up-to-date pianoforte owes a great part of its present efficiency to the genius of the great ,american makers1 although these1 of course1 have worked along the great principles that ,broadwood1 ,chickering1 ,steinway1 ,weber1 ,knabe1 ,erard and others laid down4 ,thus we have surveyed1 though truly in a somewhat hurried manner1 the interesting history of the growth and development of the pianoforte of to-day4 ,the reader will forgive the brief and sketchy nature of this bird's-eye view1 when he recollects that our purpose in this book is to lay down the correct principles of modern design1 rather than to analyze those principles from an historical standpoint4 ,some of the laws that we shall have occasion to expound have already been noted here4 ,in the succeeding chapters these and others will be considered in the light of their scientific and practical application4 ,,chapter ,,iii4 ,,description ,,of ,,the ,,modern ,,pianoforte4 ,the pianoforte of to-day is the most complex and ingenious of musical instruments4 ,with the possible exception of the pipe-organ1 there is no existing tone apparatus that combines within itself the product of so many varied industries4 ,both as to the raw material and the finished parts1 this instrument draws its tonal charm1 in the ultimate analysis1 as much from the saw-mill1 the machine shop and the iron foundry as from the forest and the mine4 ,trees of the forest1 ore from the mines--even the wooly coats of the peaceful sheep--alike contribute their share to the completion of the wonderful product of musico-mechanical ingenuity that we recognize in the modern pianoforte4 ,in such circumstances as these1 it is easy to understand that the commercial production of these instruments is a formidable undertaking4 ,to the musical and technical skill that is essential must now be added large capital and a great manufacturing plant4 ,the moderate prices at which it is at present possible to sell pianofortes would not be maintained for a moment without this modern system of productive concentration and distributive expansion4 ,the application of such business systems to the production of an essentially artistic structure has had the double effect of cheapening the selling price and improving the quality4 ,this is not the place to go into details of the organization of a modern pianoforte factory1 but we may very properly devote some moments to a consideration of the main points of construction that are observable in the pianofortes of the day4 ,critical analysis of these points will be in order later on in the course of the present work4 ,for the moment we shall be content with obtaining a bird's-eye view1 as it were1 of that which we are later to dissect and criticise4 ,there are to-day two distinct and prevailing types of pianoforte4 ,these are the 8upright0 and the 8grand40 ,of the once popular 8square0 it is unnecessary here to do more than say that the type has passed into a state of obsolescence and is fast dying out4 ,both structurally and tonally1 it was most defective2 and its popularity was due rather to the imperfect development of the other types during the period of its vogue than to any inherent advantages of its own4 ,it has well and faithfully served its appointed time1 and we may properly leave it to die in peace4 ,for the last thirty years in this country and for considerably longer in ,europe1 the upright1 succeeding the square as a home instrument1 has remained victorious4 ,its small size and great convenience1 together with the surprising tonal capacity that has been developed in it in the ,united ,states1 have universally commended it1 and only the development of the very small grand has lately seemed to be threatening its long unchallenged supremacy4 ,the exterior form of an upright is familiar to all4 ,if we strip from it all the outer appendages1 and then remove the action and keys1 we shall at once see that the instrument consists essentially of a sound-board and a frame1 the latter partly wooden and partly metallic1 upon which are stretched strings of regularly graduated lengths and thicknesses4 ,attached to this framing are two more or less ornate wooden erections which are denominated the 8sides0 of the instrument1 while a horizontal wooden shelf1 called the 8key-bed10 serves to join the sides and support the keys and their frame4 ,the strings of an upright are arranged vertically from the top to the bottom of the framing already described1 with the exception of those which serve the bass notes4 ,these are strung diagonally over the treble strings4 ,it will also be observed that the strings become progressively shorter as the scale ascends until the speaking lengths at the highest notes are two inches or less4 ,the thickness also varies directly as the length4 ,the material of which the strings are made is cast-steel wire1 and the overstrung bass strings are1 in addition1 covered with copper or iron wire4 ,these strings1 in order that they may be maintained at the proper tensions and in the correct positions1 must be supported by suitable framing4 ,the demands of modern construction require that the framing be most massive4 ,we have already cast a hurried glance at it1 and may now proceed to describe it in more detail4 ,first of all1 however1 it is necessary to investigate the apparatus that amplifies the sound waves projected from the strings and transforms them into the pleasing tones of the pianoforte4 ,we must1 in short1 examine the sound-board4 ,we shall have occasion later1 critically to examine and discuss the resonance apparatus of the pianoforte4 ,it is sufficient1 therefore1 that we glance briefly at it here1 so as to familiarize ourselves with its general form and construction4 ,the sound-board is usually constructed of a sheet of spruce fir of varying thickness and arched inwards towards the strings1 the crown of the arch being at its middle portion4 ,it carries wooden bridges1 over which pass the strings and upon which the vibrations of these strings are impressed and which serve to limit their speaking lengths4 ,the side of the sound-board1 remote from the strings1 is strengthened by the addition of a series of strips of hard wood called 8ribs10 which are tightly glued on to it4 ,all of this apparatus is fitted into a wooden frame technically called the 8back40 ,it consists of two horizontal beams1 situated at the top and bottom of the instrument and joined together with a number of vertical wooden posts of great strength4 ,into this structure the sound-board is secured in such a manner as to produce the arched shape above described1 and in such a manner also as to leave nearly the whole of its surface free to vibrate4 ,the top beam of the back is covered with the 8wrest-plank10 a wooden block built up of crossed strips of hard maple into which are driven the tuning pins1 or 8wrest-pins0 as they used to be called4 ,the whole structure is then covered by the 8iron plate10 which is a massive affair cast in one piece and bolted all round to the sides of the sound-board and back1 and to the wrest plank at the top and the bottom beam at the bottom4 ,this plate contains the 8hitch-pins10 over which are looped the waste ends of the strings1 and also the iron bridge1 which limits the upper extension of their speaking lengths4 ,the strings are arranged upon this elaborate foundation1 looped over the hitch-pins1 passed over the sound-board--or 8belly0--bridges1 and thence through the bearing-bar1 up to the tuning-pins4 ,to the sides of this structure are glued the external walls4 ,a wooden bed for the keys is provided1 and the action is secured partly to the iron plate and partly to the key-bed4 ,the pedals are placed upon the bottom board1 which is secured between the external walls or sides1 and the pedals are connected with the proper parts of the action4 ,when this has been done the construction of the instrument is essentially completed4 ,the various kinds of upright pianoforte do not vary greatly in size4 ,in the ,united ,states the popular sizes vary between the extremes of four feet ten inches and four feet in height1 with sufficient width to accommodate the eighty-eight notes that make up the modern compass of seven octaves and a minor third4 ,the multitude of different scale arrangements need not be discussed here at all1 nor is it necessary to enter into any investigation of the various individual arrangements and devices that different manufacturers fit to their instruments4 ,all these things will be treated in their proper order4 ,the grand pianoforte has always been the favorite of the composer and the interpretative artist4 ,in this type alone has it been possible to combine the highest qualities of tonal beauty and mechanical ingenuity4 ,to-day the concert grands of our most eminent makers stand unsurpassed1 both as mechanical structures and as musical instruments4 ,the most obvious dissimilarity between the grand and the upright is1 of course1 seen in the difference of their planes4 ,the grand might properly be called the horizontal pianoforte4 ,its strings are stretched parallel to the plane of the floor and the hammers strike upwards at them from below4 ,the second conspicuous difference is in the function of the exterior casing4 ,we have already noted that this part of the upright is chiefly required to complete the exterior ornamentation of the structure1 and secondarily to support the keys and action4 ,the case of the grand1 on the other hand1 is an essential part of the resonant body of the instrument4 ,it consists of a rim1 bent to suitable shape and built up of continuous veneers1 running all round in one piece and glued together at crossed grain until the desired number of layers and the proper thickness are thus obtained4 ,the whole of what corresponds to the upright back framing1 as well as the sound-board and iron plate1 are rigidly built into this continuous bent rim1 and thus the whole structure forms one complete resonant entity1 entirely unified and interdependent4 ,the rim is made deep enough to permit of the insertion of action and keys in the front portion1 and a gap in the framing is left for the hammers to strike upwards at the strings4 ,the wrest-plank is placed on one side of the gap and the sound-board occupies the remainder of the space on the other side4 ,the iron plate covers the entire structure1 wrest-plank included1 and sustains the same relations to the instrument as in the upright4 ,its shape1 as also that of the sound-board1 is adapted to the peculiar outline of the grand1 which is so aptly implied in the word 8fluegel0 7wing71 used in ,germany to designate the entire grand type4 ,until a comparatively recent period the large concert size grand was practically the only type of these instruments4 ,the revolutionary improvements initiated by the ,steinways in the middle of the nineteenth century paved the way1 however1 for the general introduction of smaller styles4 ,it was found possible to retain the characteristically full and rich tone of the large grand--at least to a great extent--while its inherent advantages in the matter of touch and action all combined to assure the popularity of the smaller instrument among the more critical and discriminating of the public4 ,doubtless1 also1 the remarkable change in the housing of urban populations that has been so conspicuous during the last twenty years had much to do with the general desire for an instrument that should be less common than the ordinary upright and that should at the same time be less cumbersome than the full-sized grand4 ,a powerful incentive was therefore given to manufacturers to strive towards the perfecting of the small types1 and we cannot deny that they have succeeded in a remarkable manner4 ,it is true that there exists today a tendency to cut the size of these small grands down to really impossible proportions4 ,there is a limit to the cutting down process2 and it is apparent to the observer that more than one maker is endeavoring to obtain a true grand tone from a sound-board area and from string lengths that are such as entirely to prohibit the attainment of this desirable goal4 ,of course1 it may be retorted that the term 8true grand tone0 is subject to variations of definition4 ,it may even be plausibly said that tone of any kind is too intangible a thing to be limited by any definitions4 ,nevertheless1 it would seem that there is a very decided limit1 and that when we arrive at the point where it is no longer possible to obtain the fullness1 richness and volume of tone that we are accustomed to accept as the distinguishing characteristic of the grand pianoforte1 then1 indeed1 we no longer have a true grand4 ,other instruments may have the outline and the action of a grand1 but if they have not the proper sound-board area and string length1 then they are merely 7if we may perpetrate a bull7 8horizontal uprights40 ,the very general description that we have thus given of the two prevailing types of pianoforte has not been intended to serve as more than what it so obviously is--a rapid bird's-eye view of the instruments as they appear to the casual observer4 ,the reader may thus prepare himself for the more definite and critical investigation that is now about to be begun4 ,,chapter ,,iv4 ,,acoustical ,,laws ,,of ,,sounding ,,strings4 ,sound is an impression produced upon the brain through the ear by the motion of air particles excited by an external body4 ,in the transmission of sound from the vibrating or 8sonorous0 body to the ear it is motion that is transferred and not the substance of the air itself4 ,in the same way there can be no sensation of sound without the interposition of an elastic fluid such as air or water1 and the production of sound in a vacuum is1 therefore1 impossible4 ,sound1 in short1 has no objective existence4 ,we know it simply as a sensation1 primarily caused by certain physical processes1 the nature of which is comparatively familiar to us4 ,we are aware of all that goes on between a sounding body and the ear1 but we know nothing of the processes whereby these physical motions are transformed until they become1 within the brain1 sensations of musical sound or of noise4 ,while so much of mystery clouds our conception of the nature of sound1 we may take comfort in the knowledge that to penetrate the enigma is by no means necessary4 ,not even the musician requires such transcendent knowledge4 ,to the student of musical craftsmanship it is equally non-essential4 ,it is well1 however1 to recognize the fact that as soon as we leave the sure ground of physical investigation1 we become lost in impenetrable mystery and find ourselves face to face with the ancient1 yet ever new1 questions of our origin and destination4 ,when we reflect upon the essentially spiritual and unearthly influence of music1 we cannot but feel that1 in the making of instruments to serve this art1 we are ourselves assisting1 however blindly1 at a more than ,eleusinian mystery4 ,the ear easily distinguishes between musical and non-musical sounds4 ,nor does it fail to recognize differences in relative loudness or softness of any given musical sound4 ,again1 the relative degree of acuteness or gravity is distinguished1 and1 lastly1 the quality of the same musical note when played upon two different instruments or when sung by two different voices is no less easily observed4 ,now we have first to ask ourselves in what the difference between musical and non-musical sounds consists4 ,we may say that a musical sound is produced by regularly recurring motions of the sounding body communicated to the air2 or1 more technically1 a musical sound may be defined as a sound produced by periodical vibrations4 ,this may be proved by holding a piece of cardboard against a rapidly revolving toothed wheel4 ,as long as the revolutions of the wheel are performed at a comparatively slow speed the noise produced by the impact of the cardboard is broken and disjointed2 but as the wheel is caused to revolve with greater rapidity the noise becomes gradually continuous and assumes a definite pitch4 ,by increasing the speed of the wheel we cause a higher pitched musical sound to be produced4 ,now1 if we arrange a second card and wheel and cause them to be set in motion together with the first we shall find that when the two wheels are revolved at the same speed1 they produce sounds of the same pitch4 ,thus it is apparent that the pitch of a musical sound depends upon the speed of vibration1 or upon the number of vibrations per second4 ,without going too deeply into technicalities it may be said that similar experiments have enabled investigators to determine the behavior of sonorous bodies in reference to all the other conditions that pertain to them4 ,thus1 in the case of strings such as are used in the pianoforte1 we are in possession of facts that make it possible for us to state accurately the pitches that will pertain to strings of given lengths1 densities and thicknesses1 which are stretched at given tensions4 ,it is unnecessary to go into details of the precise methods employed to demonstrate these laws1 and it will be quite sufficient to quote the laws themselves4 ,the reader is therefore invited to note carefully that3 #a4 ,the number of vibrations of a string is inversely proportional to the length of the string4 #b4 ,the pitch of a musical sound is proportional to the number of vibrations per second2 the greater the number of vibrations1 the higher the pitch4 #c4 ,the number of vibrations per second of a string is proportional to the square root of its tension4 ,that is to say1 if a string is stretched with a weight of one pound it will give forth a sound one octave lower than the sound that it would emit if stretched with a weight of four pounds4 #d4 ,the number of vibrations of a string varies inversely as the thickness of the string4 ,so that if there are two strings of the same material and length and subjected to the same tension1 and if the diameter of the first is twice the diameter of the second1 the first will produce one-half as many vibrations as the second4 #e4 ,the number of vibrations per second of a string varies inversely as the square root of its density4 ,thus1 if one string has four times the density of another1 the first will produce one-half as many vibrations as the second4 ,in addition to these valuable laws1 there are certain others which have reference to the actual musical sounds produced by strings4 ,by means of them we know the relative proportions of the strings that will1 other things being equal1 give the various notes of the musical scale4 ,if a perfect musical string be stretched and excited into vibration it will be found that an exact octave above the note that the whole string gives out may be produced by dividing the string at its precise middle point and causing one of the halves to vibrate4 ,now we have already noted that the number of vibrations of a string is proportional to its length1 and it is therefore obvious that the halves of the given string each have double the number of vibrations of the whole1 and that1 consequently1 the octave to a note is produced by either twice or half the number of vibrations that suffice to produce the given note4 ,carrying the experiment further1 we may1 by dividing the given string at other points on its surface1 obtain all the other notes of the musical scale4 ,it will not be necessary to repeat the explanation in each case1 and the reader will have no difficulty in comprehending the following table1 which gives the relative string length required to produce the eight notes of the diatonic scale of ,c major1 taking the length of the complete string that gives the keynote as #a1 and considering all other pertinent conditions to remain equal3 ,c ,d ,e ,f ,g ,a ,b ,c #a #h_/i #d_/e #c_/d #b_/c #c_/e #h_/ae #a_/b ,keynote #b;d #c;d #dth #eth #fth #gth ,octave ,at first sight it might appear that the above data ought to give us all necessary information in regard to the phenomena of vibrating strings4 ,undoubtedly1 the difficulties that surround the pianoforte designer would have little power to cause worry if there were nothing more to learn4 ,our troubles1 however1 are but just now beginning1 and the difficulties that still exist are greater than any that we have yet investigated4 ,these difficulties have their origin in the nature of the sounds that are emitted by musical strings4 ,while we have been investigating the relative vibration speeds and pitches that pertain to the strings under various conditions1 we have not as yet paid attention to any other difficulties that might have their origin under entirely different circumstances4 ,there are1 however1 certain highly important phenomena which are determined by the nature of the strings themselves1 irrespective of all other conditions4 ,these phenomena affect the constitution of such sounds as any musical string may produce4 ,sounds produced through the agency of musical strings are not and cannot be simple sounds4 ,and this peculiarity arises from the fact that such strings in common with most other agencies for the production of musical sounds are incapable of performing perfectly simple vibrations4 ,if a string vibrated as a whole uniformly and all the time1 its motions might be compared to the rhythmic swing of a pendulum1 and the sounds that it emitted would be absolutely simple and absolutely pure4 ,the fact1 however1 is that this never occurs4 ,no string ever vibrates as a whole without simultaneously vibrating in segments1 which are aliquot parts of the whole4 ,these segments1 when thus vibrating1 give out the sounds that pertain to them according to their relative lengths2 while the vibration of the whole length of the string1 at the same time1 causes the production of the sound proper to it1 which is called the 8prime0 or 8fundamental0 tone4 ,the sounds produced by the simultaneously vibrating segments are called 8partial tones0 or 8upper partials40 ,in the case of sounding strings1 such as we are now investigating1 the partials follow each other in arithmetical progression and are produced by the vibrating of segments the proportions of which may be expressed by the harmonic series #a1 #a_/b1 #a_/c1 #a_/d1 #a_/e1 #a_/f1 #a_/g1 #a_/h1 #a_/i1 and so on ad infinitum4 ,now1 if we examine this series we shall see that the lower of the partial tones that are represented by the various fractions must bear distinct harmonic relations to the fundamental tone4 ,it will simultaneously be observed1 however1 that as the series is continued1 the fractional quantities become uniformly smaller1 and the difference between any pair of them 7for the same reason7 is smaller as the position of the given pair is more remote from unity4 ,naturally1 this means that the partial tones represented by such fractional quantities are separated by continually decreasing intervals4 ,if the process is carried far enough1 the time comes when the interval of separation is less than a semitone4 ,clearly1 then1 partial tones in this condition can bear no proper harmonic relation to the fundamental tone4 ,they are1 in fact1 dissonant4 ,here1 then1 we come upon a fact that has a very wide bearing4 ,it is a demonstrated acoustical truth that tone quality depends upon the number and intensity of the partial tones that accompany the fundamental during the sounding of any musical note4 ,if1 through any cause1 these high and dissonant partials are excited into undue prominence1 they may1 and do1 exercise a profound and maleficent influence upon the quality of musical sounds4 ,we shall later have occasion to confirm the truth of this statement1 and we shall learn1 in the course of our investigation1 fully to appreciate its importance in the practical problems of pianoforte design4 ,for the purpose of assisting the reader in the comprehension of the above argument1 the following table is given1 showing the order of succession and pitch of the partial tones of the note ,c 7second line below the staff in the bass clef74 ,taking the pitch of the octave above middle ,c1 for convenience of calculation1 as #eab vibrations per second1 this gives us #fd for the ,c in question4 ,illustration3 ,,name ,,of ,,note ,,order ,,of ,,succession ,,vibration ,,per ,,second ,c#a #a #fd ,c#b #b #abh ,g#b #c #aib ,c#c #d #bef ,e#c #e #cbj ,g#c #f #chd ,b-flat#c #g #ddh ,c#d #h #eab ,d#d #i #egf ,e#d #aj #fdj ,f-sharp#d #aa #gjd ,g#d #ab #gfh ,a#d #ac #hcb ,b-flat#d #ad #hif ,b-natural#d #ae #ifj ,c#e #af #ajbd ,it should be observed that the seventh1 eleventh and fourteenth partials and their multiples cannot more than approximately be indicated in musical notation1 as they do not exactly correspond to the notes that are written to represent them4 ,we are obliged to be content with an approximation to the true pitch of these partials and the notation given here is as near as it is possible to approach4 ,a brief consideration of the facts thus presented will convince the reader that a combination of any fundamental tone with its first eight partials will produce a relatively harmonious effect4 ,at the same time we must observe that this harmoniousness is more and more obliterated as the higher partials are permitted to sound simultaneously with the others4 ,in fact1 it may be said that1 although we can not and must not eliminate the dissonant partials altogether1 we should attempt to cause the strings to vibrate with entire freedom only as far as concerns the first eight partials1 and less freely as far as concerns the others4 ,now1 in what manner can this desirable end be attained8 ,to answer this question we must first discover what pre-disposing causes1 if any1 exist towards the favoring of any combination of partials at the expense of any other4 ,in speaking of the automatic sub-division of a string into vibrating segments1 we omitted1 at the time1 to make mention of a fact which should1 however1 be obvious to the reader2 namely1 that the various points at which the sub-division occur are themselves motionless4 ,it would be more correct1 perhaps1 to say 8apparently motionless02 for1 of course1 if these dividing points or 8nodes10 as they are called1 were entirely without motion1 the formation of the vibrating segments would be impossible4 ,in most cases1 however1 the 8amplitude0 or length of swing of the nodes when in motion is very much smaller than the amplitude of vibration of the segments4 ,consequently1 as the vibration of the segments of a string is itself ordinarily invisible1 the motion of the nodes may be considered as inappreciable4 ,now1 these nodes exercise considerable influence upon the problems that we are considering4 ,for example1 according to the researches of ,young1 it appears that when a string is struck at any point all those partials are obliterated that have their nodes at that point4 ,curiously enough1 however1 it has since been found in the case of the pianoforte1 that those upper partials are not necessarily eliminated that have their nodes at the striking point4 ,undoubtedly1 however1 a properly chosen node provides the best possible striking point1 since its selection permits the operation of its tendency to suppress those particular partials that have their nodes at the same place4 ,a consideration of the phenomena already observed has caused us to perceive that the highest partials of the compound tone produced by a musical string do not bear precise harmonic relations to the prime tone4 ,as the successive sub-divisions of the string approach closer and closer to each other1 the tones thus generated are seen to be distant by proportionately less intervals1 until at length they cease to have a close similarity to any tone of the musical scale4 ,consequently1 as was said before1 they exercise a generally harsh and dissonant influence upon the nature of the compound tone4 ,we have already concluded that1 broadly speaking1 we should aim to eliminate these dissonant partials and1 conversely1 to favor the prominence of those which are more nearly harmonic4 ,the reasoning which has served to lead us to this conclusion may profitably be carried a step further4 ,if the highest partials are non-harmonic1 it is obvious that their presence or absence1 their prominence or the reverse1 must necessarily exercise much influence upon the actual quality of a musical sound2 upon the individual color which different generating agencies impart to the same musical note2 in effect1 upon all the numerous gradations of what we are accustomed to call harshness1 hollowness or mellowness of tonal quality4 ,this inevitable conclusion has been fully substantiated by the results of experiment4 ,the labors of ,helmholtz and ,koenig have demonstrated conclusively that the quality of a musical sound depends upon the number and intensity of the partial tones that accompany the fundamental4 ,thus the mystery of the individual tone coloring that distinguishes the voices of different musical instruments or of different persons is transferred from the realm of psychology to that of science4 ,in fine1 it becomes clear that if we can govern the number of the segments into which a vibrating string divides itself1 and if we can also control the amplitude of vibration of these segments1 we shall find it possible to alter the tone quality of a musical instrument at our pleasure4 ,it has already been observed that the generation of certain partial tones is assisted or retarded as the position of the striking point on a string is changed4 ,it may not be out of place to note that the various other methods of exciting a string1 such as plucking1 bowing1 etc41 permit the production of equally variable effects as the points at which they operate are changed4 ,our inquiry1 however1 is confined to the pianoforte1 and we shall therefore continue to limit ourselves to the cases of pianoforte strings as struck by the usual hammers4 ,the matter of choosing a proper striking point was first systematically investigated by ,john ,broadwood1 founder of the celebrated house of that name1 in the early part of the nineteenth century4 ,until that time the pianoforte makers had1 apparently1 paid no attention to this important problem and had been content to follow in the steps of the builders of harpsichords and spinets4 ,examination of any of the instruments that are direct ancestors of the pianoforte will show that the strings are struck1 indifferently1 at any point from one-tenth to one-half of the speaking length4 ,the only exceptions appear to be those clavichords in which the strings are all of the same length and in which the tangents on the keys impinge upon the strings at different fixed points to give the corresponding notes of the scale4 ,since the time of ,broadwood1 however1 the vast importance of correctness in this particular has come to be recognized with more or less unanimity4 ,the investigations undertaken by this eminent maker convinced him that the ideal striking point lay between one-seventh and one-ninth of the speaking length of the string4 ,now1 our investigations have shown us that the most harmonious and agreeable compound tone is that which is formed by the combination of the first eight partials4 ,it would seem1 therefore1 that one-eighth of the speaking length would be more correct than the approximation that was arrived at by ,broadwood4 ,theoretically1 indeed1 the latter is nearer to the ideal point2 is1 in fact1 the ideal point4 ,for obvious mechanical reasons1 however1 it is usually impossible to hit this point with exactitude1 and the approximation suggested and used by ,broadwood has been proved1 by the practice of the best makers1 to offer the nearest practical solution4 ,we may1 then1 lay it down as a rule to be followed that a point as nearly as possible midway between one-seventh and one-ninth of the speaking length of the string should be chosen and adhered to as the proper place where the blow of the hammer should be struck4 ,if this rule be faithfully followed the greatest obstacle to purity of tone is removed and the most harmonious and agreeable combination of partials is in a fair way to be secured4 ,nevertheless1 it is necessary to make an exception for the highest notes on the piano4 ,practical experience has shown that one-tenth is a better striking point for the very highest and shortest strings4 ,thus we have been able to enunciate and discuss the principal laws that govern the activities of sounding strings1 particularly those of the pianoforte4 ,as the argument is developed1 it will often appear that the theoretical exactitude of the rules here laid down must be modified in practice4 ,such a condition is always inevitable as between a body of laws and the application thereof4 ,it will be found1 however1 that the variations to be recorded are not generally very important1 and the reader will be well advised to make the rules enunciated in this chapter his continual leaning post and guide4 ,the most conspicuous difference is1 perhaps1 that which exists between the theoretical and practical results of halving string lengths to obtain octaves4 ,in practice it is found that pianoforte strings generally sound a little flat of the octave when divided at exactly the middle point4 ,but the variation is the fault of the steel wire and not of the rule4 ,,chapter ,v4 ,,the ,,musical ,,scale ,,and ,,musical ,,intonation4 ,we have now considered as much of the phenomena of musical sounds as may be considered to have a bearing upon the purpose of our investigations4 ,we may then devote some space to the matter of the expression of musical ideas1 and the intonation which has been devised in order to reduce the mental products of composers to the limitations of musical instruments4 ,music is expressed through the medium of a scale of tones1 all of which bear definite relations to each other as to pitch4 ,the 8diatonic scale10 which is the foundation of musical intonation1 is composed of a series of eight tones which are named after letters of the alphabet1 the last tone having the same name as1 and being the octave to1 the first4 ,the frequencies of these tones always bear the same ratios1 one to another1 whatever may be their positions within the compass of any instrument4 ,now1 considering the frequency of the first tone to be unity1 the frequencies of the others are in the following proportions3 ,c ,d ,e ,f ,g ,a ,b ,c #a #i_/h #e_/d #d_/c #c_/b #e_/c #ae_/h #b ,if we now divide these proportionate numbers each by the other we have the proportionate intervals that separate them4 ,doing this1 we have the following result3 ,c ,d ,e ,f ,g ,a ,b ,c #i_/h #aj_/i #af_/ae #i_/h #aj_/i #i_/h #af_/ae ,now1 it will be observed that we have in the above table three different kinds of interval represented by the three ratios1 #i_/h1 #aj_/i and #af_/ae4 ,the first of these is called the major tone and the second the minor tone1 while the third is known as the diatonic semitone4 ,following out these ratios1 we may obtain the frequencies of any diatonic series4 ,we shall choose the scale of which ,c #ebh is the key-note4 ,its frequencies are as follows3 ,c ,d ,e ,f ,g ,a ,b ,c #a #i_/h #e_/d #d_/c #c_/b #e_/c #ae_/h #b_/a #ebh #eid #ffj #gjd #gib #hhj #iij #ajef ,knowing as we do the ratios and frequencies already calculated1 it is obvious that we may similarly calculate the ratios and frequencies for the diatonic scale1 of which any given tone is the tonic or key-note4 ,before doing this1 however1 it is well for us to remember that the diatonic scale is not adequate to all the requirements of music4 ,musicians have found it necessary to interpolate other sounds in between those which form the diatonic progression4 ,the reason for this is that music1 in order that it may have the greatest possible freedom of expression1 must be written in a larger number of keys1 and must contain more distinct sounds than the diatonic scale is able to afford4 ,for these and other cognate reasons the chromatic scale was introduced4 ,the addition of five chromatic semitones1 obtained by taking the difference between a minor tone and a diatonic semitone1 gives the chromatic scale thirteen semitones from key-note to octave4 ,unfortunately1 however1 the same number of keys upon the pianoforte cannot provide us with thirteen pure chromatic sounds in every key4 ,this may be demonstrated as follows3 ,the ratio of a chromatic semitone is #be_/bd4 ,the sharp of ,c #ebh is1 therefore1 #eej4 ,but in the diatonic scale of ,d 7the major second in scale of ,c71 ,c sharp has a frequency of #aaac-c_/d4 ,the octave below this latter sound is the ,c sharp1 which is one chromatic semitone above ,c #ebh4 ,we know the frequency of the latter to be #eej4 ,the frequency of the octave below ,c sharp1 #aaac-c_/d1 ought1 therefore1 to be #eej4 ,but we know that the octave below any given note has a frequency that is one-half that of the given note4 ,now1 one-half of #aaac-c_/d is #eef-g_/h4 ,therefore1 we see that there is a difference of #f-g_/h vibrations per second between the ,c sharp that is a chromatic semitone above ,c #ebh and the ,c sharp that is the octave below the major seventh of the scale of ,d1 and which ought to be the same sound1 as it is in the same position on the key-board as the former4 ,by carrying the same investigation further we are enabled to perceive that sounds of the same name are not identical when played in different keys1 or1 rather1 that the same name does not imply that the sound so denoted means the same thing when it is considered in its relation to any tonic different to that to which it was first related4 ,there is another difficulty also that confronts us in the problem of playing pure sounds upon the pianoforte2 that instrument1 as we know1 does not provide us with different keys for the sharp of one sound and the flat of the sound next above it4 ,there is a general belief that ,c sharp1 for example1 and ,d flat are identical4 ,but this is not so4 ,the flat of ,d is a chromatic semitone below that note1 while the sharp of ,c is the same interval above the latter4 ,by referring to our former calculations it will be seen that the chromatic semitone ratio is #be_/bd4 ,the sharp of ,c is1 therefore1 obtained by multiplying the frequency of ,c by #be_/bd1 and the flat of ,d is likewise evolved by an inverse process1 namely1 by dividing the frequency of ,d by the same ratio4 ,this is equivalent to adding a chromatic semitone to ,c and subtracting the same from ,d4 ,if we take the notes ,c and ,d from the scale of ,c #ebh1 we have the frequencies of ,c and ,d as #ebh and #eid respectively4 ,effecting the multiplication and division as above we see that ,c sharp has a frequency of #eej1 while that of ,d flat is #egj-f_/be4 ,that is to say that these two notes differ by no less than #bj-f_/be vibrations per second4 ,it thus becomes obvious that the expression of all the sounds within the compass of an octave1 in such a manner that absolutely correct sounds in every key may be obtained1 is a problem that calls for more sounds than are provided by the pianoforte4 ,as a correct understanding of this most important subject is essential1 a somewhat elaborate treatment of it will be given here4 ,the reader who takes the pains to master the true inwardness of the problem of musical intonation will have an insight into the matter which few pianoforte makers or musicians possess4 8,just intonation0 is the name given to that system whereby we are enabled to command the expression of all the sounds that are required to be heard within the compass of an octave in order that the degrees of each and every possible scale may be correctly and exactly rendered4 ,it is not difficult to see that performers upon instruments which do not have fixed tones should have no difficulty in adjusting the intonation of every tone to correspond with the variations in pitch required by the different positions in the scale that such tones may occupy4 ,experiments have1 in fact1 been carried out with violinists and it has been shown that artists upon this instrument do naturally play the true diatonic and chromatic intervals when left to themselves and when not forced to adjust their intonation to that of fixed tone instruments4 ,in order to show with accuracy the total number of different sounds that are required to produce 8just intonation0 in every possible key the reader is invited to consider the following table1 which shows the smallest possible number of sounds that will give the true diatonic intervals in twelve keys4 ,the first note in each row is the key-note and the last the octave thereto4 ,the frequencies of those key-notes that are not represented in the first scale 7that of ,c7 have been calculated as follows3 ,the key-note to scale of ,b-flat is the perfect fourth to key-note of scale ,f4 ,the key-note to scale of ,e-flat is the perfect fourth to key-note of scale ,b-flat ,the key-note to scale of ,f-sharp is the octave below major seventh of scale ,g4 ,the key-note to scale of ,g-sharp is the octave below major seventh of scale ,a4 ,the key-note to scale of ,c-sharp is the octave below major seventh of scale ,d4 ,we therefore have the following results3 ,c ,d ,e ,f ,g ,a ,b ,c #ebh #eid #ffj #gjd #gib #hhj #iij #ajef ,c-sharp ,d-sharp ,e-sharp ,f-sharp ,g-sharp ,a-sharp ,b-sharp ,c-sharp #eef-g_/h #fbf-c_/fd #fif-c_/cb #gdb-a_/b #hce-e_/af #ibh-a_/h #ajdd-i_/fd #aaac-c_/d ,d ,e ,f-sharp ,g ,a ,b ,c-sharp ,d #eid #ffh-a_/d #gdb-a_/b #gib #hha #iij #aaac-c_/d #aahh ,e-flat ,f ,g ,a-flat ,b-flat ,c ,d ,e-flat #fbe-d_/i #gjc-de_/gb #gha-cd_/cf #hcc- #ich-a_/ah #ajdb- #aagb- #abej-h_/i #be_/bg #aa_/bg #ei_/gb ,e ,f-sharp ,g-sharp ,a ,b ,c-sharp ,d-sharp ,e #ffj #gdb-a_/b #hbe #hhj #iij #aajj #abcg-a_/b #acbj ,f ,g ,a ,b-flat ,c ,d ,e ,f #gjd #gib #hhj #ich-b_/c #ajef #aagc-a_/c #acbj #adjh ,f-sharp ,g-sharp ,a-sharp ,b ,c-sharp ,d-sharp ,e-sharp ,f-sharp #gdb-a_/b #hce-e_/af #ibh-a_/h #iij #aaac-c_/d #abcg-a_/c #acib-c_/ae #adib ,g ,a ,b ,c ,d ,e ,f-sharp ,g #gjd #gib #hhj #ich #ajef #aagc #acbj #adjh ,g-sharp ,a-sharp ,b-sharp ,c-sharp ,d-sharp ,e-sharp ,fx ,g-sharp #hbe #ibh-a_/h #ajca-c_/d #aajj #abcg-a_/b #acge #aedf-a_/h #afej ,a ,b ,c-sharp ,d ,e ,f-sharp ,g-sharp ,a #hhj #iij #aajj #aagc-a_/c #acbj #adff-b_/c #afej #agfj ,b-flat ,c ,d ,e-flat ,f ,g ,a ,b-flat #ich-b_/c #ajef #aagc-a_/f #abeh-h_/i #adjh #aefd-d_/i #agfj #ahgg-a_/c ,b ,c-sharp ,d-sharp ,e ,f-sharp ,g-sharp ,a-sharp ,b #iij #aaac-c_/d #abcg-a_/b #acbj #adhe #afej #ahef-a_/d #aihj ,in order that the different sounds may more easily be separated1 they have been collated in linear progression1 together with their frequencies and the scales in which they or their octaves appear3 #a4 ,the sound ,c #ebh _/ ,c1 ,f1 ,g1 ,b-flat4 #b4 ,c #eba-aa_/ed ,e-flat #c4 ,c-sharp #eef-g_/h ,a ,d1 ,b1 ,f-sharp1 ,c-sharp #d4 ,c-sharp #eej p ,a1 ,e1 ,g-sharp #e4 ,d #eid p ,c-,g #f4 ,d #ehf-b_/c e ,a1 ,f1 ,b-flat1 ,e-flat #g4 ,d-sharp #fah-c_/d a ,e1 ,b1 ,f-sharp1 ,g-sharp #h4 ,d-sharp #fbf-ca_/fd r ,c-sharp4 #i4 ,e-flat #fbe-d_/i s ,b-flat #aj4 ,e #ffj ,c1 ,g1 ,a1 ,e1 ,b-flat #aa4 ,e #ffh-a_/d i ,d #ab4 ,e-sharp #fif-c_/cb n ,f-sharp1 ,c-sharp #ac4 ,e-sharp #fhg-a_/b ,g-sharp4 #ad4 ,f #gjd t ,c1 ,f1 ,b-flat #ae4 ,f-sharp #gdb-a_/b h ,g1 ,d1 ,e1 ,b1 ,f-sharp1 ,c-sharp #af4 ,f-sharp #gec-a_/c e ,a #ag4 ,g #gib ,c1 ,d1 ,f1 ,g #ah4 ,g #ghb-d_/ac s ,b-flat #ai4 ,g #gha-cd_/cf c ,e-flat #bj4 ,fx #ggc-f_/af a ,g-sharp #ba4 ,g-sharp #hbe l ,a1 ,e1 ,b1 ,g-sharp #bb4 ,g-sharp #hce-e_/af e ,f-sharp1 ,c-sharp #bc4 ,a-flat #hcc-be_/bg s ,e-flat #bd4 ,a #hhj ,c1 ,e1 ,f1 ,a #be4 ,a #hha o ,d #bf4 ,a #hia f ,g #bg4 ,a-sharp #ibh-a_/h ,b1 ,f-sharp1 ,c-sharp1 ,g-sharp #bh4 ,b-flat #ich-b_/c ,f1 ,b-flat1 ,e-flat #bi4 ,b #iij ,c1 ,g1 ,d1 ,a1 ,e1 ,b1 ,f-sharp #cj4 ,b-sharp #ajca-a_/d ,g-sharp #ca4 ,b-sharp #ajdd-h_/fd _/ ,c-sharp ,thus we see that thirty-one different sounds are required to give the true diatonic intervals in only twelve keys4 ,but it is not necessary to remind the reader that there are more keys than these used in music4 ,we have1 in fact1 not yet considered the keys of ,a flat1 ,d flat and ,g flat4 ,the frequencies of the keynotes of these scales have been calculated as follows3 ,a-flat is the perfect fourth to ,e-flat1 which as calculated above #fbe therefore ,a-flat #hcc-be_/bg4 ,d-flat is the perfect fourth to ,a-flat1 which as calculated above #hcc-be_/bg therefore ,d-flat #eee-aed_/afb4 ,g-flat is the perfect fourth to ,d-flat1 which as calculated above #eee-aed_/afb therefore ,g-flat #gda-acj_/dhf4 ,we are therefore able to construct these following additional scales3 ,a-flat ,b-flat ,c ,d-flat ,e-flat ,f ,g ,a-flat #hcc- #ich- #ajdb- #aaaa- #abej- #achi- #aefc- #afff- #be_/bg #bf_/caf #gc_/bcf #gc_/ha #h_/i #ba_/eb #acb_/baf #ej_/ed ,d-flat ,e-flat ,f ,g-flat ,a-flat ,b-flat ,c ,d-flat #eee- #fbd- #fid- #gda- #hcc- #ibf- #ajdb- #aaaa- #aed_/afb #fdj_/abij #cfe_/fdh #acj_/dhf #aej_/afb #bhd_/dhf #ebh_/abif #adf_/aeb ,g-flat ,a-flat ,b-flat ,c-flat ,d-flat ,e-flat ,f ,g-flat #gda- #hbc- #ibf- #ihh- #aaaa- #abhe- #achi- #adhb- #acj_/dhf #cfjj_/chhh #aacf_/aidd #ebj_/adeh #cjh_/def #fej_/adeh #adjh_/cjhh #bfj_/dhf ,by examining the last table the reader will perceive that we have obtained fourteen new sounds4 ,they are shown graphically in this manner3 ,in the scale of ,a-flat the new sounds are ,b-flat1 ,c1 ,d-flat1 ,f and ,g4 ,in the scale of ,d-flat the new sounds are ,e-flat1 ,f1 ,g-flat1 and ,a-flat4 ,in the scale of ,g-flat the new sounds are ,a-flat1 ,c-flat1 ,d-flat1 ,e-flat and ,f4 ,none of these sounds had been obtained in the scales given before and1 consequently1 we have to consider that there are fourteen more sounds to be added to the thirty-one that we have already found4 ,the above calculations would suffice to provide us with the diatonic intervals in all the keys that are used in music4 ,harmony demands1 however1 certain other intervals4 ,these are minor thirds1 minor sevenths1 dominant sevenths and minor sixths4 ,accordingly1 if we desire to probe the matter of just intonation to its depths1 we must calculate the sounds that are required to make up these intervals in such scales as are now without them4 ,examining the tables already prepared1 we find that there are wanting the following members3 ,minor thirds to the key-notes of the scales ,c1 ,d1 ,e-flat1 ,f1 ,g1 ,b-flat1 ,a-flat1 ,d-flat1 ,g-flat4 ,minor sixths to the key-notes of the scale ,c1 ,e-flat1 ,b-flat1 ,a-flat1 ,g-flat1 and ,d-flat4 ,dominant sevenths to the key-notes of the scales ,e-flat1 ,f and ,b-flat4 ,minor sevenths to the key-notes of the scales ,a-flat1 ,d-flat1 and ,g-flat4 ,we shall have no difficulty in calculating the frequencies of the required notes by the same processes that we have followed heretofore4 ,minor ,minor ,dominant ,minor ,key-notes-- thirds-- sixths-- sevenths-- sevenths-- #f_/e ,ratio #h_/e ,ratio #af_/i ,ratio #i_/e ,ratio ,c ,e-flat ,a-flat #ebh #fcc-c_/e #hda-d_/e ,d ,f #eid #gab-d_/e ,e-flat ,g-flat ,c-flat ,d-flat #fbe-d_/i #gej-d_/ee #ajjj-cb_/de #aaaa-hj_/ha ,f ,a-flat ,e-flat #gjd #hdd-d_/e #abea-e_/i ,g ,b-flat #gib #iej-b_/e ,b-flat ,d-flat ,g-flat ,a-flat #ich-b_/c #aabe-aa_/ae #aeja-ac_/ae #affh-bj_/bg ,a-flat ,c-flat ,f-flat ,g-flat #hcc-be_/bg #ajjj-ajf_/ace #ffg-ch_/bgf #gda-fd_/bdc ,d-flat ,f-flat ,b double flat ,c-flat #eee-adf_/aeb #ffg-ff_/haj #hhi-ceh_/haj #ihh-cei_/haj ,g-flat ,b double flat ,e double flat ,f-flat #gda-abd_/dhf #hhi-accj_/bdcj #eic-aj_/bdjj #feh-bijh_/dcgd ,the result of these calculations may now be collated and summarized4 ,we find that there are no less than sixty-six separate sounds required for the production of the necessary intervals in all the possible scales4 ,these sounds are thus classified3 ,different sounds in twelve diatonic scales #ca ,sounds wanting to complete the diatonic scales of ,a-flat1 ,d-flat1 ,g-flat #ad ,minor thirds wanting in scales of ,c1 ,e-flat1 ,f1 ,g1 ,b-flat #f ,minor sixths wanting in scales of ,c1 ,e-flat1 and ,b-flat #c ,dominant sevenths wanting in scales of ,e-flat1 ,f and ,b-flat #c ,minor thirds wanting in scales of ,a-flat1 ,d-flat and ,g-flat #c ,minor sixths wanting in scales of ,a-flat1 ,d-flat and ,g-flat #c ,minor sevenths wanting in scales of ,a-flat1 ,d-flat and ,g-flat #c -- ,total number of sounds in an octave #ff ,now the obvious conclusion to be drawn from this analysis is that the true sounds of the just musical scales are very different from any that we hear upon the pianoforte4 ,indeed1 we may properly carry the reasoning a step further4 ,if the expression of all the degrees of the true musical scales requires this formidable array of sounds1 then surely1 the sounds that are produced upon the piano are not all of the required true sounds1 but are totally unlike any of them4 ,for it is evident that if the sixty-six true sounds within the compass of an octave have to be reduced to the thirteen that are found upon the pianoforte1 the process of compression to which the former must be subjected will force the latter into the position of so many compromises4 ,in fact1 with the exception of the standard tone from which all calculations and all tuning must start1 and its octaves1 there is no tone upon the piano1 as it is now tuned1 which is identical with any sound of the justly tuned scale4 ,the process to which we have alluded1 and which is necessary to secure to the piano and all other instruments with fixed tones the ability to perform music in all keys which are desired for the proper expression of the composers' ideas1 is called temperament4 ,upon the skill and cunning with which this compromise with natural laws is effected depends the whole beauty of1 and the whole of our pleasure in1 music as we are accustomed to hear it4 ,it would be vain to pretend that tempered intonation is preferable to that which is pure and just1 but it is equally vain and foolish to decry the accepted system of temperament until the mechanical skill of manufacturers of musical instruments and the taste of performers have risen to the point of appreciating the beauties of pure intonation and of devising mechanical means of attaining it4 ,until that time arrives we must fain be content to accept what we have and make the best of it4 ,there have1 of course1 been attempts to provide instruments that could be used to give the pure intervals in every key1 but they have been invariably failures4 ,most of them have been forced to depend upon tempered intonation to a certain extent1 while others have been mechanically impossible4 ,in any case we must remember that the pianoforte1 as at present constructed and played1 depends entirely upon an equally tempered intonation4 ,so strongly has the pianoforte entrenched itself in popular favor1 indeed1 that music and tempered intonation have become1 to most people1 exactly synonymous4 ,it is proper that we should be able to draw true distinctions1 however1 as the practical work of piano building ought to be largely guided by the considerations induced from the necessity and fact of temperament4 ,,chapter ,,vi4 ,,the ,,equal ,,temperament4 ,as was suggested in the last chapter1 it becomes necessary to effect a compromise between the demands of true musical intonation and the limitations of musical instruments1 in order that the performance of music may be made practicable4 ,the equal temperament1 now universally employed1 has only risen to its present commanding position within the last century4 ,it seems to have been first used by ,johann ,sebastian ,bach4 ,hndel did not know it1 and it struggled throughout the whole of the eighteenth century with the mean-tone system4 ,temperament systems were1 however1 invented and used long before this period4 ,pythagoras1 the ,greek pre-,christian philosopher1 was one of the earliest experimenters along these lines4 ,the method that he devised has come down to us1 and we are thus able to see wherein lies the difference between it and the modern diatonic scale4 ,without going into too much detail1 we may note that the ,pythagorean system recognizes only two intervals2 namely1 the tone and semitone4 ,the diatonic scale1 as we know1 has a major tone1 a minor tone and a diatonic semitone4 ,the ,pythagorean scale contemplates perfect fifths and sharped thirds1 and is incapable of the effects of modern harmony4 ,the next attempt to adapt the necessary compromise in the interests of practical music was introduced after the modern diatonic scale had become the standard method of octave-division2 that is to say1 some time in the fifteenth century4 ,it has been variously called the 8mean-tone10 8mesotonic0 and 8vulgar0 temperament4 ,in this method the tone is a mean or average between the major and minor tones of the diatonic scale4 ,the fifths are all flattened1 while the thirds are justly tuned4 ,such a system possesses both advantages and disadvantages4 ,on the one hand1 the nearer and more frequently used scales are purer and more agreeable2 on the other hand1 the remoter scales are exceedingly dissonant2 so much so1 in fact1 that they cannot be employed with pleasure to either the performer or the hearer4 ,so long1 however1 as the music is written in the commoner scales the mean-tone temperament1 possessing the great advantage over other methods of having pure thirds1 is far more agreeable to the ear4 ,in fact1 up till a few years ago it was not uncommon to find organs in village churches in ,europe that were still tuned according to this system4 ,the mean-tone system first made harmony1 as we understand it1 practicable1 but as the knowledge and imagination of composers widened1 the desire naturally arose to take advantage of the greater powers for harmony that could alone be afforded by the unrestricted possession of all possible scales4 ,a substitute for the mean-tone system had1 therefore1 to be found1 and thus arose the modern and accepted method1 universally known as the ,equal ,temperament4 ,by this method1 which is at the present time universal1 the octave is divided into thirteen equally distant semitones or half-steps4 ,all distinctions between major and minor tones and diatonic and chromatic semitones are swept away1 and it is assumed that the sound between any two sounds in the scale is equally sharp and flat respectively to the sound immediately preceding and following it4 ,this method1 of course1 implies a rearrangement of the whole scale1 for it is necessary to alter the precise pitch of every sound within the compass of the octave in order that the equalization may be effected4 ,thus it comes about that the equally tempered scale has only one interval tuned purely4 ,this interval naturally is the octave4 ,all the others require to be sharped or flatted in varying degrees4 ,every chord1 every interval1 with one exception1 therefore1 is more or less out of tune4 ,the effect of this system of tempering cannot very well be noted accurately upon the pianoforte1 owing to the evanescence of that instrument's tone2 but the organ often shows the dissonance of certain intervals and chords in a most distressing manner4 ,perhaps the worst of the defects of the ,equal ,temperament are exhibited in the inability clearly to distinguish between true consonances and true dissonances4 ,where the actual distinctions between the true intervals are fused together it is impossible that there should be such distinctions between them as the true scale shows1 and1 consequently1 we often are obliged to miss many delicate shades of comparative consonance or dissonance that would be clearly exhibited in a scale in which the intervals were represented with fidelity4 ,we already know1 however1 that no such method is at present possible1 and we must fain resign ourselves to the compromise that we have1 and hope for better things in the future4 ,but at the same time1 the ,equal ,temperament possesses not a few positive virtues4 ,as explained above1 there can be no difference between the sharp of a given tempered sound and the flat of the tempered sound one whole step above the former4 ,in other words1 the sharp of ,c in the ,equal ,temperament must be the same as the flat of ,d1 for these two sounds are assumed to be equally distant from the sound which is between them1 and the three are simply part of a series of equal semitones4 ,this being the case1 the ambiguity that arises from the identity of these sounds is very often found to be invaluable for the purposes of quick and convenient modulation4 ,there are instances in which the connecting link between two modulations would entirely be lost without the peculiar intonation that is afforded by equally tempered sounds4 ,it seems1 in short1 that the equal temperament1 imperfect and artificial as it is1 cannot easily be replaced in the existing states of our acoustical knowledge and of the mechanical musical industries4 ,in order that the reader may more clearly realize the actual effects of the ,equal ,temperament upon musical intonation1 the following table has been prepared1 showing the differences of frequency between the true sounds of the just chromatic scale and the corresponding tempered sounds3 7,we are already familiar with the identity1 in tempered intonation1 of the sharps and flats of adjacent degrees of the scale47 ,c #ebh 7,philharmonic ,pitch74 ,true ,scale4 ,equally ,tempered ,scale4 ,c #ebh ,c #ebh ,b #die ,b #dih-g_/cb ,b flat #dge-a_/e ,b flat--,a sharp #dgj-g_/bj ,a sharp #deh-a_/c ,a #ddj ,a #ddj ,a flat--,g sharp #dag-a_/bj ,a flat #dbb-b_/e ,g #cia-aa_/bj ,g sharp #dab-a_/b ,g flat--,f sharp #cgc-g_/bj ,g #cif ,f #cdb-d_/aj ,g flat #chj-d_/be ,e #ccb-ag_/bj ,f sharp #cff-b_/c ,e flat--,d sharp #cac-ai_/bj ,f #ceb ,d #bif-g_/bj ,e #ccj ,d flat--,c sharp #bgi-ad_/bj ,e flat #caf-d_/e ,c #bfd ,d sharp #cji-aa_/bd ,d #big ,d flat #bhe-c_/be ,c sharp #bge ,c #bfd ,it would be without the province of our immediate purpose to enter into any special discussion of the possibility of manufacturing pianofortes that shall give pure intonation1 as distinguished from the tempered sounds that we have thus exhibited4 ,we have already had occasion to mention that the ,equal ,temperament has become so strongly and intimately bound up with the performance of music1 that the majority of musicians are probably incapable of distinguishing between the idea of pure as opposed to that of tempered musical sounds4 ,we have already pointed out1 and reference to the various tables will confirm the assertion1 that the ,equal ,temperament imposes excessive roughness of intonation upon very few of the musical intervals4 ,thus the octave is pure1 the fourths and fifths nearly so1 and only the seconds1 thirds1 sixths and sevenths are so rough as to be noticeable to other ears than those of the professional pianoforte tuner4 ,indeed it is very doubtful whether the musical public could ever be universally educated to the point of appreciating the differences between pure and equally-tempered fourths and fifths2 while at the same time it must be remembered that the second and seventh1 at least1 are dissonances whether purely intoned or not4 ,we may properly question the actual advantage that the mechanical attainment of just pianoforte intonation would produce2 we may ask ourselves what would be gained thereby for the cause of art1 and the answer does not appear to be other than that any conceivable benefit must be so slight as to be practically negligible4 ,,chapter ,,vii4 ,,pianoforte ,,strings ,,and ,,their ,,proper ,,dimensions4 ,the strings of a modern pianoforte are made of cast steel and possess a relatively great thickness and stiffness4 ,that is to say1 they enjoy these characteristics to a far greater degree than do the strings of any other musical instruments that employ such agents for the purpose of generating musical sounds4 ,the strings of any member of the viol family1 for example1 are so totally unlike those of the pianoforte that no comparison of their respective behavior when subjected to tension can be of interest to any save the scientist4 ,in dealing with the strings of the pianoforte then1 we face an isolated and unusual problem which we shall have to consider at some length4 ,we shall investigate the peculiar effects produced by the high tension1 great thickness and great stiffness of the strings1 as well as the singular phenomena exhibited in the case of the covered bass strings4 ,we shall note that the strings are responsible for many unpleasant things of which they are seldom accused1 and that their proportions as to length and tension do not comprehend in themselves the whole problem that the scaling of them presents to the designer4 ,this matter of the internal nature of the steel and other wire has not1 unhappily1 received that attention to which its importance justly entitles it4 ,no treatment of the principles of pianoforte design could be considered complete1 however1 without some discussion of the phenomena thus presented4 ,the investigation which we shall undertake will lead us to the development of more of those general principles that we are now engaged in enunciating1 and we shall then be able to formulate certain rules of wide application which may be employed in the practical consideration of the problems with which the whole matter of pianoforte design abounds4 ,as is generally known1 the strings that are charged with the duty of emitting the sounds comprehended within the two lowest octaves on the pianoforte are customarily constructed of a combination of steel wire and some other1 usually copper or iron4 ,the latter is wound over a core of the former wire1 and this winding is graduated1 as to the amount and thickness of the material employed1 according to the pitch to which it is desired that each string shall be tuned4 ,there is an obvious reason for this procedure4 ,for1 as we have already shown1 two strings whose lengths are as #b3a will1 other things being equal1 emit musical sounds separated by the interval of an octave4 ,consequently1 under perfect mechanical conditions1 the length of each string of a pianoforte should conform to the rule thus indicated1 and should be one-half or double the length of that which produces the octave above or below it2 the absolute application of this rule1 however1 being subject to certain practical modifications throughout the entire compass4 ,these will be discussed later4 ,even in the absence of such considerations1 however1 this ideal condition could not be attained4 ,the mechanical difficulties presented would always operate to forbid the carrying out of such an arrangement throughout the whole compass of the instrument4 ,for1 to follow the rule with entire consistency would necessitate a length of #bef inches for the lowest ,c1 on an assumed length of #b inches for the highest note of the same denomination4 ,as this would imply a length or height of the instrument of nearly #bd feet it is not difficult to see that such construction is impossible4 ,furthermore1 evenness of tone quality would be seriously hindered if the lowest strings were of any such dimensions4 ,to secure equality of tonal result it is necessary1 as has been noted above1 that we should be able to equalize1 as far as possible1 the particular forms of vibration that pertain to each string4 ,obviously1 the nature of the blow that would produce a given form of vibration in a string of #bef inches in length must be very different from that which would produce similar forms in a string only one-tenth as long4 ,again1 to maintain such long strings at the required tension involves mechanical problems that savor more of engineering than of pianoforte building4 ,for these and cognate reasons1 therefore1 the practice has arisen of artificially slowing the rate of vibration in the bass strings by wrapping them with brass1 iron or copper wire4 ,naturally1 the form of the vibrations excited in these wrapped strings is entirely different from any that the plain steel wire is capable of producing4 ,the iron or copper wire is itself thrown into vibration both independently of and together with the cord of steel1 so that we have the phenomenon of one string emitting two separate series of vibrations1 with resultant disarrangement of the generated upper partials and concomitant production of beats in a more or less appreciable quantity4 ,now if1 in addition1 the bass strings are not scaled with approximate correctness as to their relative lengths1 thicknesses1 and other dimensions1 it follows that there will be two distinct and different causes of dissonance and unevenness of tone-quality1 either of which is sufficient1 in itself1 to produce very unpleasant tonal results4 ,it is clear1 then1 that particular attention must be paid to the designing of the string arrangement1 if excellence of tone-quality is to be anywhere approached4 ,it is1 fortunately1 possible to give quite precise directions for the calculating of string dimensions4 ,as a preliminary1 we must remind the reader of the rules that were laid down in ,chapter ,,iv1 relating to the behavior of stretched strings4 ,it will be recalled that we had occasion to observe that these rules would require certain modifications in practice1 as they referred only to ideal musical strings which are of perfect flexibility and perfect uniformity1 and are stretched at an absolutely constant tension4 ,the first modification that appears upon investigation has reference to the division of string-lengths4 ,it has already been pointed out that1 in practice1 we cannot obtain the octave above the fundamental tone of a given pianoforte string by dividing it exactly in the middle4 ,conversely1 an exact doubling of the length does not produce the exact octave below the given fundamental tone4 ,this discrepancy occurs on account of the fact that the shortening or lengthening of a given string causes a corresponding change in the tension at which it is maintained and in the density of adhesion of its molecules4 ,now if we double the length of a string in order to obtain the octave below its fundamental tone1 we decrease its tension1 and this causes a slowing of the frequency of vibration4 ,then again1 the increased resiliency of the string brought about by the lengthening tends also to decrease the frequency4 ,the frequencies of vibration of a string vary directly as the square root of the tension1 inversely as the thickness1 and directly also as the stiffness4 ,these axioms being admitted1 we observe that to obtain an octave lower than a given fundamental tone1 we must obtain one-half the frequency that produces the fundamental4 ,therefore1 as we see from above1 the double length must be decreased by one-fourth to allow for the automatic decrease of stiffness which varies directly as the frequency4 ,and this modification must itself be modified to compensate for the increase in frequency produced by the very act of shortening4 ,therefore we must consider the tension1 and we find that to reduce this tends again to decrease the stiffness in exactly the same proportions as it was before increased4 ,but frequency of vibration varies as the square root of the tension2 therefore we take the square root of one-fourth1 which was the fraction first arrived at4 ,this root is one-sixteenth and is the differential factor that must be subtracted from the ideal octave lengths1 in order to obtain the practical lengths4 ,it will be found of course1 as must be apparent to the reader1 that the differential factor here suggested does not provide a complete solution to the problem of allowing for the exhibited differences between theory and practice4 ,it does1 however1 provide a true guide to the lengths4 ,there is of course a difference of produced frequency to be allowed for yet4 ,fortunately1 however1 this is provided for by the graduated thicknesses of pianoforte wire4 ,by taking advantage of this almost geometrically proportioned graduation of diameter we are able to calculate a stringing scale that1 if adhered to1 will give the nearest possible approximation to complete harmony between theory and practice4 ,that is to say1 we can proceed with a string-length calculation based upon the differential factor already obtained1 and then by arranging the distribution of the string thicknesses according to the diameters that are provided by the manufacturers of music wire1 we may obtain a true estimation1 not only as to the thickness of wire to be used at each place1 but also as to the lengths proper to each string4 ,of course the reader will remember that the matter of pitch is of considerable importance in all calculations of this kind4 ,a difference in pitch implies difference of tension when the other factors remain equal1 and we therefore have calculated the following tables on the assumption that the pitch to be used is that known as the ,international or ,c #eag4 ,attention is1 therefore1 directed to the following ,,table ,,showing ,,true ,,lengths ,,of ,,octave ,,strings ,,from ,,the ,,highest ,c ,,string ,,to ,,the ,,last ,c ,,string ,,that ,,is ,,usually ,,left ,,unwrapped4 ,c #b4jdh in4 #b-a_/be 444 ,approx4 ,c #b4jdh #a4icge #c4ifh in4 #c-bd_/be 444 ,c #c4ifh #a4icge #g4fhh in4 #g-ag_/be 444 ,c #g4fhh #a4icge #ad4hge in4 #ad-g_/h 444 ,c #ad4hge #a4icge #bh4hbj in4 #bh-d_/e 444 ,c #bh4hbj #a4icge #ee4hbh in4 #ee-d_/e 444 ,,note4--,the length of the first string is chosen arbitrarily1 but as given is a very close approximation to the practice of the best ,american makers4 ,the vulgar fractions are calculated from the decimals and the error in no case exceed about one-fiftieth of an inch4 ,the differential factor is1 as we know1 #a_/af4 ,therefore we multiply by 7#b - #a_/af7 or #a-ae_/af2 in decimals #a4icge4 ,the above table1 then1 affords us a reliable guide to the scaling of the unwrapped strings4 ,at the same time1 however1 it is not by any means complete1 for the reason that there is no method shown as yet for the calculation of the other and intermediate string-lengths4 ,we are1 however1 able to accomplish this task by the aid of a very ingenious rule proposed by the late ,professor ,pole1 ,f4,r4,s4 ,it is as follows3 ,the proper length of any string may be determined from that of any other string1 provided that the length and frequency of the second string be known4 ,given these factors3 ,then1 7#a7 ,take the logarithm of the length of the known string4 7#b7 ,multiply the number 4#jbejhf by the number of semitones that the sound to be given by the required string length is above or below the sound produced by the given string4 7#c7 ,if the required string is below the given string1 add together the two numbers obtained2 if it be above1 subtract the second number from the first2 the result in both cases is the logarithm of the required length4 ,for example1 we have calculated already the proper length of ,c4 ,in hundredths of an inch this length is expressed as #bhhb4 ,the log4 of this number is #deidc4 7,this may be verified by any table of logarithms47 ,it is required to obtain the length of the string that1 caeteris paribus1 will produce one semitone above ,c4 #deidc log4 of #bhhb #jbejh 7#f7 4#jbejh 7#f7 the number 7#a7 of semitones that required string sounds above given string ------------- ,by subtraction1 #dcdce log4 of #bgah length of required string in hundredths of an inch ,required length for ,c-sharp #bg-ah_/ajj inches ,by reversing the process described above1 and adding instead of subtracting1 the proper lengths for the semitone below and all others in descending progression may be calculated with accuracy4 ,having thus settled the matter of string lengths1 we may proceed to consider the questions of diameter4 ,but it is first of all necessary to warn the reader that the lengths that have here been calculated refer only to such pianofortes as are capable1 by reason of their size1 of taking the ideal string-lengths4 ,very small uprights1 for example1 cannot be brought within that classification1 except as regards the highest of their strings4 ,in all pianofortes1 no matter what their size1 the higher strings are practically identical in length2 but it will be found that shortness of height in an upright or of length in a grand begins1 towards the middle of the scale1 disastrously to affect the string proportions4 ,as already pointed out1 there are only two ways in which these disproportions can be overcome4 ,these are through alterations in the tension or in the thickness4 ,but such alterations necessarily disturb the whole tonal balance2 and here we find a very strong reason for the poor tone that the average atrophied grand or upright possesses4 ,moreover1 it must not be forgotten that disproportionate thickness or unduly slackened tension affect the actual nature of the vibrations that are set up within the string4 ,and the affections are operative both as to frequency and to form4 ,therefore1 naturally1 bad tone and inability to stand in tune4 ,this is not intended as an argument against the small pianoforte2 but it is desired here to show that these little instruments1 whether horizontal or vertical1 must not be expected to perform impossibilities4 ,if we are obliged to build small instruments1 we must revise our calculations and tabulate the string-lengths according to a different basis of apportionment4 ,for the purpose of the present work1 however1 the calculations have been made on the assumption that the standard size of pianoforte is to be designed4 ,turn we then to the consideration of string diameters4 ,the cast steel wire that is used for the pianoforte strings is supplied in definitely numbered and graded thicknesses4 ,the numbers that are used generally run from ,no4 #ac to ,no4 #bd4 ,according to the tests made at the ,chicago ,world's ,fair by the aid of ,riehle ,bros4' testing machine1 the wire of these numbers was of the following diameters and broke at the following strains4 ,the wire manufactured by the firm of ,moritz ,poehlmann1 ,nuremberg1 ,germany1 has been selected from among the various products that were subjected to these tests1 on account of its superior durability and evenness of gradation4 ,number ,diameter in fractions of an inch ,broke at strain of #ac 4#jcj #cbe lbs4 #ad 4#jca #cce #ae 4#jcb #cej #af 4#jce #djj #ag 4#jcg #dae #ah 4#jdj #ai 4#jdb #bj 4#jdd ,now it is a well known fact1 and1 indeed1 obvious from what has already been said1 that the proportional relations as to length1 tension1 diameter and breaking strain do not permit any other arrangement for the scaling of wire than that which is universally accepted by piano makers4 ,that is to say1 the shortest wires are taken from the thinnest numbers1 and vice-versa1 the whole scaling being so arranged as to secure for each tone that its strings shall be stretched at approximately the same tension4 ,experience and the observations of the most eminent manufacturers seem to have established that the strain upon each of the uncovered strings should be maintained1 as nearly as possible1 at #afj lbs4 ,if this be done it will be found that a pianoforte so constructed will produce the proper pitch at each string when the lengths are as calculated in the tables referred to4 ,it will1 of course1 be necessary to arrange with due proportion the number of strings that are to be taken from the wire of each number4 ,it will be found that the best practice takes into account the half sizes not shown here and strings the instrument with an average of five tones to each thickness of wire1 beginning at #ac or #ac-a_/b and continuing down to the end of the unwrapped strings according to the general directions suggested4 ,experience and the individual ideas of the designer1 assisted by such knowledge as this work aims to impart1 are the best guides that can be followed4 ,empirical induction1 based upon observation and experience1 provides the only possible and practical means for arriving at the true and proper arrangements to be made for each individual instrument4 ,this empiricism extends with particular force to all string arrangements and is seen nowhere so conspicuously as in the variety of methods that are adopted by manufacturers in determining the number of strings within the unwrapped sections of the scale4 ,thus1 certain makers carry the wrapping over to the beginning of the treble strings and have two or three string-groups provided with wrapped wire before the overstringing is begun4 ,the idea here is either to correct original defects of scale design or to shade down the break in tone that so often occurs at the point where the overstringing usually begins4 ,from observation of the practice of the best makers1 it may be said that the tone ,c below middle ,c is usually the first overstrung tone4 ,of course1 when the instrument is very small it will often be found that it is impossible to give the last unwrapped strings their proper lengths4 ,in this case these offending strings may either be covered with light wrapping or may be put bodily over into the overstrung portion of the scale1 in which latter case they will be wrapped anyway4 ,supposing then that the matter of the number of overstrung strings has been determined1 we may proceed to the consideration of the dimensions1 number and covering of the strings that are to serve here4 ,we are obliged to confess that the problem of attaining to good tone in the bass is1 indeed1 difficult4 ,it is by no means hopeless1 however1 as the success of more than one eminent maker has already demonstrated4 ,the simplest1 most obvious1 and easiest way out of the inherent difficulties of the scaling of bass strings is to be found in the consideration of their proper lengths4 ,it does not require very much thought to perceive the truth that the longer the strings the less weight need be imposed upon them4 ,if1 in fact1 we make the bass strings to approach as far as may be to the lengths that they would require to have if unwrapped1 we shall be able to reduce proportionally the amount of artificial control that has to be exercised over the vibration speed4 ,not only this1 but the greater length thus attained implies greater tension4 ,that is to say that1 as we saw before1 the tension at which a string is stretched acts to overcome the slowness of vibration-speed induced by its greater length1 and1 consequently1 tends to generate a more regular progression of the upper partials 7as experiment has demonstrated71 with resultant tendency to greater purity of tone-quality4 ,we may1 in fact1 accept it as an axiom that the bass strings should be as long and1 simultaneously1 as lightly weighted as possible1 and that the weight of them should be strictly proportioned to the pitch of the musical tone that they are desired1 at a given tension1 to emit4 ,as far as the second clause of these conditions is concerned it is well to remind the reader that limitations of space within the body of a piano usually determine the possible lengths of the bass strings4 ,so much so is this the case1 indeed1 that it is not often possible to make any great difference in their respective lengths4 ,the best makers appear to be agreed in a method of treating the problem that is at once simple and effective4 ,they recognize the great advantage of scaling the bass strings at the greatest possible length1 and then they take care that the descending increase of length is no greater than to make the lowest bass string one-fifth longer than the highest4 ,at the same time they so graduate the weight of the wrapping material that the same results are attained as would naturally follow if they were as accurately scaled1 in proportionate length1 as are the plain wire strings4 ,this equalization is1 of course1 only approximate4 ,for the forms of vibration excited in two strings of the same pitch will be different whenever the various factors that govern the emission of sound by them are variable4 ,thus when the factor of length is varied1 no counter-adjustment of tension1 thickness or density can restore to the string so modified the exact form of vibration that it may have originally possessed4 ,consequently it becomes impossible to induce from artificially weighted strings precisely the same series of partial tones that a plain wire filament will emit1 even when the tones generated by the two strings are of the same pitch4 ,the lesson of this is plain4 ,as perfection of tonal quality can only be attained in part1 it especially behooves us to pay strict attention to such scaling of the bass strings as will furnish a complement of sound producing agencies that may be relied upon to induce as nearly as possible the same successions of partials as are habitually emitted throughout the higher sections of the piano4 ,thus it becomes evident that the greatest practicable length and the least practicable weight are the chief factors that must govern the designer in laying out the scale for the bass strings4 ,the relative densities of the wrapping material employed in the manufacture of bass strings have been the subject of considerable study4 ,brass1 which was the earliest object of experiment1 has long been superseded by either copper or iron4 ,as to the relative advantages possessed by these two materials1 it can be said at once that the chief and almost the only advantage presented by the latter lies in its relative cheapness4 ,acoustically1 however1 copper forms by all means the most suitable material for the winding of bass strings1 and this for the following reasons3 ,the specific gravity of copper is #h4gh1 while that of iron is but #g4gh4 ,again1 the former metal1 while inferior in tenacity to the latter1 possesses1 on the other hand1 the great advantage of higher ductility1 so that its elastic qualities are very marked4 ,it is thus evident that copper is a more suitable material for the generation of musical sound than is iron1 and the qualities which we have just noted as pertaining to it are precisely those most useful in the production of harmonic progressions of partial tones4 ,it is therefore clear that as between copper and iron all the advantages lie with the former4 ,the thickest wire used for the uncovered strings is generally ,no4 #bd4 ,in beginning the scaling of the bass strings1 however1 we choose ,no4 #ag or ,no4 #ah for the notes nearest to the treble4 ,the covering is usually from ,no4 #be to ,no4 #bh 7standard1 not music1 wire gauge7 according to the size of the piano and the practicable string-length4 ,of course1 longer strings may be covered with lighter wire4 ,the first covered string is generally approximately one-sixth shorter than the string immediately above it4 ,this proportion1 as suggested above1 may1 however1 be profitably disregarded1 if it thereby be possible to lengthen the bass strings4 ,there are always two of these strings to each tone and the thickness of covering wire must be progressively increased as the scale descends4 ,a descending increase of one number in thickness of the covering wire for each pair of strings may properly be allowed1 unless the lengths are too closely alike1 or vice-versa1 in which cases suitable modifications may be made4 ,but assuming that the descending lengths are arranged in arithmetical progression with a mean of #c_/d of an inch1 and supposing the highest covered string to be #de inches long2 then the suggested increase of thickness should under all circumstances hold good4 ,it may often be found1 however1 that the space limitations of an instrument or other practical considerations make it impossible to follow out these rules with exactitude4 ,in any case1 we must remember that all such rules are themselves the fruit of empirical observation and to such observations we must look1 when it becomes necessary to revise them in order to satisfy the requirements of some particular situation4 ,,chapter ,,viii4 ,,resonance ,,and ,,the ,,resonance-,,apparatus ,,of ,,the ,,pianoforte4 ,we have now made a somewhat lengthy and thorough investigation into the nature and behavior of the various materials and substances that are employed in the construction of pianoforte strings4 ,from this inquiry we have been able to deduce a set of rules which1 when practically applied1 will furnish us with a guide to the solution of many perplexing problems which take their root in the conditions imposed upon the designer by the limitations of space and the other mechanical conditions of pianoforte construction4 ,it would not be proper1 however1 to proceed forthwith to the practical questions of support for the strings4 ,for we must still find the correct solutions of another series of problems that spring1 not from the strings themselves1 but from their important and necessary accessories1 the sound-board and belly bridges4 ,the belly-bridge is the medium of connection between the strings and the sound-board4 ,through it the vibrations excited in the strings are conveyed to the freely vibrating surface of the sound-board1 and the sonority of the generated sounds is thereby enormously increased4 ,this is the process in bare outline1 but1 in order to obtain a proper view of the matter under discussion it will be necessary to examine the phenomena to which the juxtaposition of strings1 bridge and sound-board give rise4 ,we must1 in fact1 make another brief excursion into the realms of acoustics4 ,the property which the sound-board possesses of reinforcing and emphasizing the sounds generated by the strings is called 8resonance40 ,important as this property of sonorous bodies is to musicians and the makers of musical instruments1 the fact remains that it is a matter very little understood by the mass of them4 ,this is the more remarkable when one considers that1 without resonant properties1 no musical instruments would be possible4 ,for it is not difficult to perceive that music1 as we know it1 could not exist were the means of expressing it limited to the actual and immediate bodies that perform the motions which are the direct causes of musical sounds4 ,this fact is most clearly illustrated in the case of the pianoforte4 ,the unaided sound of a pianoforte string is ridiculously feeble2 in fact1 it is quite inaudible at the distance of a few feet4 ,yet we are all familiar with the wonderfully harmonious and powerful sounds that the same string will be the means of producing when aided by the sound-board4 ,resonance may be defined as the property which one sonorous body possesses of impressing its vibrations upon another sonorous body4 ,the existence of this power may be demonstrated in a variety of ways4 ,the most simple proofs are afforded by the pianoforte itself4 ,for example1 if we strike any key upon the instrument and at the same time gently press down the corresponding key one octave higher1 so as to raise the damper without at the same time raising the hammer1 we shall find that if the first key be released while the other is held open1 the string corresponding to the latter will continue to give its proper sound4 ,in this case the vibrations excited in the first string travel along the belly-bridge until they reach the nearest open string whose vibration rate is synchronous with that of the original sounding string4 ,when such a string is reached it is immediately impressed with the motions excited in the former string1 with the results above described4 ,this is a case of resonance of two attached bodies4 ,peculiar as it may seem1 however1 it is not essential as a preliminary condition to the existence of resonance between them that two sonorous bodies be tangibly connected4 ,for instance1 the foregoing experiment may be varied by employing two pianofortes and choosing one of the sounds from each4 ,the result will be precisely the same4 ,it will1 however1 be noted that only such sounds as have either synchronous or nearly synchronous rates of vibration will exhibit the phenomena of resonance when separated from each other4 ,where they are connected1 however1 especially when the connecting body is a sound-board prepared for the purpose1 synchronism is not necessary4 ,in fact1 it is a matter of common observation that the sound-board of the pianoforte1 in conjunction with the belly-bridge1 operates to set up more or less intense vibration in every string within the compass of the instrument when the dampers are raised1 even if only one string be struck4 ,when the damper pedal is raised in playing1 every string throughout the instrument is immediately thrown into a state of vibration1 and begins to sound4 ,the result is a large augmentation of the total volume of sound produced4 ,of course1 the sound of any one string thus sympathetically excited is relatively feeble1 but the total volume is considerable1 with especial strength in the particular partials of each string that are more or less synchronous1 as to their vibration rates1 with the sounds originally produced by striking the keys4 ,when the dampers are permitted to rest in their normal positions1 on the other hand1 the sound-board exercises its resonant powers in a different manner4 ,whenever a string or group of strings are struck1 the board is thrown into a state of vibration which affects only itself and not the strings that remain damped4 ,the result of this excitement is to expose a relatively great vibrating surface to the atmosphere1 with the immediate consequence that the quantity of air impelled into a state of periodic motion is multiplied many times4 ,thus the size of the impelled layers of air1 and the resultant sonorous waves is augmented until we obtain sounds of the intensity and richness which we are accustomed to associate with the pianoforte4 ,now1 from what we have already learned of the laws of tone-quality1 it is obvious that the resonant medium must be capable of reinforcing not only the fundamental but the partials of all the tones which it influences4 ,to this end we must provide a substance that combines elasticity with the freedom of vibration that is1 of course1 essential4 ,it is not possible to employ metal on account of its excessive stiffness and consequent resistance to the influence of impressed vibrations2 while on the other hand a wooden body will not be sufficiently stiff and rigid unless artificially strengthened4 ,for this reason it is customary to construct sound-boards of a freely-vibrating wood 7the spruce-fir is generally employed for this purpose7 and to strengthen them by fastening to one side bars of hard wood called 8ribs40 ,in this manner the requisite stiffness is imparted to the board1 which at the same time is sufficiently susceptible to the impressed vibrations from the strings4 ,it is a fact that this accepted and universal form of resonance table is essentially similar to that which was used in the ancient harpsichord and spinet4 ,while there has been much experimentation along these lines1 it does not appear that any lasting improvements have been devised as yet1 at least in the governing principles of sound-board construction4 ,we may then confine ourselves to a description of the accepted styles4 ,the wood used in the construction of sound-boards is the spruce-fir1 which1 as stated above1 has been found to be the best possible for the purpose4 ,it is prepared in a sheet of suitable size1 and is arranged so that the grain runs approximately at right angles to the plane of the belly-bridge4 ,it can easily be understood that the thickness of the board must vary according to the dimensions of the strings that act upon it4 ,in other words1 we can perceive that more resonating power is required for the relatively weaker treble strings than for the relatively stronger bass strings4 ,the actual thicknesses vary with individual makers4 ,from #c_/h inch in the treble to #a_/d of an inch in the bass may be regarded as a fair approximation4 ,nevertheless1 it is necessary to bear in mind that these dimensions are subject to modification according to the variations in the total amount of tension that the instrument is made to bear4 ,other things being equal1 an increased tension load implies a thicker board1 and vice-versa4 ,after the dimensions and material of the board are thus determined1 it remains to consider the bridging1 the reinforcement1 and the adjustment of the board4 ,we shall consider these in their natural order1 as given above4 ,the belly-bridges are placed upon the surface of the board1 as we know1 for the purpose of conveying to the latter the minute blows that are inflicted by the vibrating strings1 in order that the vibrations may be impressed upon the board and there amplified and intensified as described at the beginning of this chapter4 ,a secondary duty is that of delimiting the lower boundaries of the speaking length of the strings4 ,the bridges must naturally be constructed with a curved outline that is determined during the draughting of the scale4 ,the actual shape of this curve has no effect per se1 upon the activities of the bridge1 but has to do entirely with the string lengths4 ,the bridge which carries the overstrung portion of the scale may be considered as being similarly affected1 as to outline1 by the exigencies of the bass string dimensions4 ,the bridges are made of hard wood1 and their sizes are usually from one inch and one-quarter to one inch and one-half high1 and in width about one-eighth of an inch less all round4 ,the variations occur principally on account of the necessity which arises of giving a bearing to the strings as they cross over the bridges4 ,it is necessary that the strings be raised at the bridges in order that they may be firmly held at the points of contact by means of the strain imposed by them on the surface of the bridge when they are stretched at proper tension4 ,of course it is most essential that this bearing be not too high1 as in that case the strain becomes too much for the board to bear with facility and its durability is thereby impaired4 ,the necessary immobility of the portions of the strings that lie upon the bridge is secured by diverting the line of travel1 and causing them to bear against pins placed on either edge of the bridge1 so as to slant the line of the string as it passes over4 ,the waste ends should run parallel to the speaking-length after the bridge has been crossed4 ,it may be further properly remarked that there are interesting and complicated problems to be overcome in choosing the material and the exact method of building the belly-bridges4 ,it is desired to combine extreme facility of vibration with the requisite resisting power4 ,in other words1 the bridge must allow the fullest possible scope to the impressed vibrations from the strings and1 at the same time1 must possess such strength that it can successfully resist the torsions imposed upon it by the pull of the strings4 ,the only method that appears to be thoroughly practical and1 at the same time1 acoustically correct is one which most manufacturers have already had the acuteness to adopt4 ,the bridge1 according to this method1 is built up of a number of layers of hard wood 7generally maple7 which are glued together in such a way that the grain of each layer crosses that of the other4 ,in this way both the requisite strength and more or less facility of vibration are obtained4 ,but it has remained for one distinguished piano maker to go a step further1 and to apply thoroughly scientific methods to the design of the belly-bridges4 ,in the instruments made by him1 he has built the bridges in such a way that the impressed vibrations will travel in the line of the grain instead of across it4 ,the bridges1 in fact1 are built of end-grain and not1 as is general1 of cross-grain wood4 ,this ingenious and simple device facilitates the passage of the impressed vibrations and1 in consequence1 tends to impart a greater clarity to the various partials of the compound tones4 ,some existing pianofortes might be greatly improved as to their clarity of speech if a similar device for increasing the power of resonance were fitted to them4 ,there is another point to be emphasized in reference to the bridges4 ,in some makes of pianos the line of the bridge construction is permitted to be broken wherever there is a corresponding break in the hammer line caused by the interposition of the various braces of the iron frame4 ,the obvious result of such a method of construction is that the resonance of the board is much interfered with and the consequent tonal efficiency of the instrument lessened4 ,for it is easy to see that if the bridge line be broken at any point1 the vibrations that are carried from any sounding string along the bridge to the surface of the sound-board will be stopped at the break and will be unable to reach those parts of the board that are remote from its path1 with rapidity and ease4 ,incontestably1 therefore1 the bridge line should1 if possible1 be continuous4 ,many manufacturers1 however1 while apparently recognizing the force of this proposition1 seem to be afraid to follow it out to its logical conclusion4 ,they are willing to make the line of bridge continuous until the end of the plain wire strings is reached4 ,after that point they seem to think that it is no longer necessary that continuity of communication between the various sounding members of the scale should subsist4 ,this idea is1 of course1 quite fallacious4 ,the bass strings are simply a continuation of the higher ones1 and are1 in fact1 precisely similar except in regard to the details of thickness and length4 ,moreover1 it is quite as important that the portions of the board over which the bass bridge exercises control should be made freely resonant1 as it is that this process should be applied to the others4 ,the bass bridge ought invariably1 therefore1 to be connected with the bridges that serve the rest of the strings4 ,the reinforcement of the board is accomplished by gluing ribs of wood across its back surface in a direction crossing the grain of the board4 ,these ribs are usually made about one inch square in the middle portions4 ,this size is continued until near the edge of the board on each side1 when they are gradually pared down in a graceful curve until at the actual edge the thickness is no more than about one-thirty-second of an inch4 ,according to the most approved modern practice it is found advisable to pocket these ribs into the wooden framing of the instrument1 by continuing them past the edge of the sound board and making suitable apertures in the framing1 into which the extensions are adjusted and fastened4 ,this has the effect of holding the board more firmly in its fastenings and also of preventing the early loosening of the ribs from their places2 an occurrence which causes much rattling1 and complete impairment of tonal quality4 ,it is usual to have twelve ribs upon the surface of the board1 but the number may be varied whenever it is considered necessary4 ,if it is required to give specially ample support to the board on account of unusually great strain1 or for any other reason1 the number may be increased1 but such procedure must be taken with caution1 as too many ribs weight the board to such an extent as to deaden its power of molecular and undulatory vibration4 ,this must at all costs be avoided4 ,it is usual to glue the ribs upon the surface of the board first--that is before the bridges--and good practice dictates that the surface of the board be dried out in a hot-box for at least #bd hours before either of these processes take place4 ,if this be carried out properly1 the resultant shrinking of the wood will be taken up after the board has become thoroughly cooled1 and if the process is repeated when the board is glued into the framing of the instrument1 the result will be to endow it with a natural 8crown10 or arch1 caused by the re-active swelling that takes place after the artificially induced shrinking4 ,although the above methods of ribbing are to be considered the best and as representing the most advanced practice1 yet it will be found that some makers dispose the ribs in a fan-like manner1 having the diverging points of the fan at the upper end of the board1 while others adopt an oblique disposition and arrange them as before described4 ,also1 we find a straight up-and-down arrangement whereby the ribs are glued parallel to the plane of the treble strings4 ,we term these three styles the fan form1 the oblique form1 and the vertical form respectively4 ,as for the comparative advantages of the three types of construction thus described1 it may be said that they all represent individual features that are more or less beneficial4 ,for example1 the fan-like disposition gives a greater number of long ribs1 while the oblique form provides more of separate units4 ,the vertical system may be considered as a mean between the other two4 ,in general1 we shall be well advised in remembering that the prime function of ribbing is to increase the tension of the board and its elasticity1 and thus to promote the power of resonance4 ,a secondary function is that of providing extra resisting power4 ,now it is obvious that both of these duties can be better performed by a multiplicity of ribs1 and consequently a system is to be recommended that permits the employment of the largest total area of ribbing4 ,at the same time unduly long ribs are not good1 for they have a greater tendency to become loose and to spring up from the surface of the board1 with dire results to tone and durability4 ,it would therefore seem that the oblique disposition has more to recommend it than the others1 since it provides enough total ribbing area without imposing inconveniently long ribbing units upon the surface of the board4 ,when the ribbing of the sound-board and the fixing of the bridges has been accomplished1 it remains to adjust the completed structure within the wooden back-framing of the instrument4 ,it is necessary that the board be so secured that it shall acquire a position analogous to that of a stretched membrane--at least as far as concerns the rigidity with which its edges are fixed to the framing4 ,there are several methods for obtaining the required rigidity of the edges of the board4 ,the natural or artificial crowning of the board's surface is best attained through the medium of particularly rigid edge fastening2 and the adoption of a continuous closing rim for the board1 as in certain grand pianofortes1 together with the use of a system of screw compression1 alike indicate the various directions in which the ideas of experimenters have led them4 ,the underlying notion in all these devices is to endow the vibrating surface with both elasticity and durability to an extent that could not be attained with the unaided wood4 ,the gluing of the sound-board to the framing is a process that demands the greatest skill and care4 ,it is essential that the board be warmed1 and that the glue which is used be in just the proper condition2 neither too thick nor too thin1 and1 above all1 boiling hot4 ,if the fastening be done when the board is in the shrunken condition described above1 and with the required skill and care1 it will be found that the fibres of the wood have been squeezed together so as to raise the center part of the board somewhat above the level of the edges4 ,this gives what we have denominated the 8crown10 and is important as affecting the durability and resisting power of the entire board4 ,it must be remembered that by relieving the sound-board of as much as possible of the strain imposed by the strings1 we are able to increase its durability and to preserve its tone-producing quality more surely than is otherwise possible4 ,boards that are not so protected must inevitably become entirely flattened out in the course of a few years4 ,when this happens the level of the belly-bridge sinks and the bearing of the strings upon the latter is destroyed4 ,hence an immediate and inevitable deterioration of tone quality4 ,for the altering of the level in this manner affects the impression of the vibrations of the strings upon the bridges and hence upon the board itself4 ,if the height of the bridges be too great1 the bearing of the strings upon them will likewise be excessive1 and the board will be crushed down in the same manner4 ,if1 however1 the directions as to bridging1 ribbing and adjustment that have been given are followed with discretion1 the troubles outlined here are likely at least to be minimized4 ,of course1 the later care of the pianoforte after it is sold has much to do with the manifold troubles that occur within the entire resonance apparatus4 ,these things cannot be foreseen1 and it is1 therefore1 most essential to guard against them as much as possible by careful attention to the details of construction and adjustment4 ,lastly1 we may observe that the practice of screwing the bridges down on to the board by screws driven in from the rear is to be condemned4 ,while it is undoubtedly advantageous to take some measure to increase the permanency of the fastening1 it will be found that it is far better1 acoustically1 to provide the bridge with wooden dowels and glue these into suitable holes in the board4 ,thus the conducting power of the bridge is increased and the vibrating surface of the sound-board is not broken up by the insertion of foreign metallic substances4 ,another and concomitant advantage is the absence of the wooden washers under the heads of these bridge-screws4 ,such devices are too often1 as they become loose1 a source of rattling and jingling4 ,it is well to be rid of them1 as of all possible things that are likely to be similarly affected by wear or atmospheric conditions4 ,,chapter ,,ix4 ,,the ,,case ,,and ,,framing ,,of ,,the ,,pianoforte4 ,the grand pianoforte is distinguished conspicuously from the upright1 as far as concerns the principles of its construction1 by the different function which its exterior casing exercises4 ,as was stated in ,chapter ,,iii1 the exterior walls of the upright have no part in the bearing or resisting work that the iron and wooden framing performs4 ,they exist chiefly for the purpose of giving support to the key-board and action1 and of affording a foundation whereon may be constructed the elaborate architectural and decorative structure that1 in its entirety1 is denominated the pianoforte case4 ,the synonymous portions of the grand pianoforte1 on the contrary1 have a far more important duty to fulfill4 ,while they are equally charged with the support of the key-frame and action1 they are also an essential part of the wooden framing1 are one and homogeneous with it1 and1 in fact1 occupy much the same position as what is known as the 8back0 of the upright1 as well as being the external and decorative coverings of the instrument4 ,the case of the grand is constructed of a series of continuous veneers1 glued one upon another1 and each extending completely around the periphery of the case4 ,these veneers are glued at cross grain to prevent splitting and are applied to the pianoforte and bent into shape when in a heated state4 ,the complete outline thus obtained is denominated the 8continuous bent rim0 and is a distinguishing feature of the modern grand pianoforte as made in ,america4 ,several eminent ,german makers1 as ,bechstein1 also employ similar means of constructing the external walls4 ,in ,england1 on the contrary1 the case is usually made out of one thickness of wood bent into the required shape by steam and joined in several places4 ,this system provides for separate moldings for the bent and straight sides and for the rear portion4 ,the advantage claimed for the continuous bent rim is that the whole case1 by this means1 becomes so closely bound up with the rest of the structure as to become part of one homogeneous resonant whole1 thus improving the general resonance and imparting a sostenuto and cantabile that can in no other manner be attained4 ,while data are lacking for the precise investigation of this claim1 it is significant that the bent rim method has not only become universal among ,american makers--by one of them it was first devised--but has even made its way into ,european favor4 ,the case1 after it has been bent in this manner into the proper shape1 has to be decoratively veneered according to the style of ornamentation that is intended for it4 ,the work of veneering these cases1 whether for uprights or grands1 need not be gone into here in detail4 ,there are so many specialists in this department who confine themselves to the turning out of such veneered cases1 and the whole matter is so far away from the principles of pianoforte construction1 that it is not considered necessary to go into it here4 ,it is1 of course1 required to provide the case of the grand pianoforte with a system of wooden struts which bind it together and give it strength and resisting power4 ,these struts are set into the case in the general form of the letter ,a1 having the apex at the forward end of the case4 ,at this apex they are crossed by another wooden strut running parallel to the key-board1 which serves to bind them together and to mark the limit of the space to be occupied by the sound-board4 ,these struts are not1 as we may thus see1 carried into the very front of the case1 but are confined to that portion which is directly underneath the sound-board4 ,in front of this space is left the gap through which the action is later to strike1 and underneath is provided a key-bed to carry the action and keys4 ,the key-bed joins the front portions of the bent rim and closes the casing in the front1 thus providing a definite and uniform structure4 ,above the key-bed and in front of the gap is one of the most important parts of the entire instrument4 ,it is called the 8wrest-plank10 and is situated at the foremost portion of the case4 ,this wrest-plank is built of a series of hard wooden layers1 glued together at cross grain and adapted to be bored with holes in which are placed the 8wrest-pins10 or tuning-pins1 that control the tension of the strings4 ,this block or plank must necessarily be of great solidity and be capable of holding the pins frictionally1 so that they will not pull round under the immense strains that are imposed upon them4 ,illustration3 ,,modern ,,method ,,of ,,grand ,,pianoforte ,,case ,,construction4 ,a4 ,continuous bent rim4 ,b4 ,wooden struts4 ,c4 ,iron shoe holding struts and connecting with iron plate4 ,d4 ,main beam4 ,the gap which is necessary in the grand pianoforte between the sound-board and the tuning-pins makes it impossible to join the former to the wrest-plank4 ,this state of affairs undoubtedly constitutes a weakness inherent in the grand and1 besides1 exceedingly unfortunate4 ,for an interruption of the continuity of communication between the various sound-conducting materials of which the instrument is constructed entails a corresponding loss of resonance4 ,the tone of the pianoforte is inevitably fleeting and evanescent2 lack of continuity in the construction only increases this fault4 ,it has somewhere been stated that the construction of the grand pianoforte implies greater resisting strength of the wrest-plank on account of its being entirely supported by the iron frame and not dependent upon a wooden back as in the upright4 ,this view seems to be incorrect4 ,a properly supported back on an upright affords a very strong support to the wrest-plank and in combination with the iron frame supplies all necessary rigidity1 and in a manner more direct and efficient4 ,but the wrest-plank of the grand pianoforte may and should possess a sufficient strength4 ,various makers have adopted several different methods to secure this strength4 ,one very good device supplies a rear truss to the lower surface of the wrest-plank by means of a downward projecting shoulder cast in the iron frame4 ,there are other methods more or less similar4 ,the arrangement of the tuning-pins within the body of the wrest-plank also requires considerable care4 ,of course1 their disposition depends ultimately upon the string arrangement1 but there are problems to be considered in connection with the manner in which they are arranged with relation to their mutual positions as considered apart from the strings4 ,for example1 it is most important that they should be so placed that the strings do no rub against each other in their passage between the pins and the agraffes4 ,the frequent neglect of this matter is a cause for regret4 ,much loss of tonal purity would be avoided and the tuner's work greatly simplified if all designers took the proper amount of care in this important matter4 ,further1 it may be remarked that the best practice accords with this suggestion in every respect4 ,it will also be found that a slight tilting back of the pins in a direction that is remote from the strings tends to lighten the pull of the latter and to assist the resisting power of the wrest-plank4 ,when the iron plate is fastened over the entire structure1 it is fixed on to the wrest-plank by means of heavy iron bolts that should be sufficiently long to go entirely through it and be closed with a nut on the other side4 ,by this means the wrest-plank is secured against lack of rigidity1 and its durability immensely increased4 ,the hardest kind of maple should be used in the construction of the wrest-plank4 ,no other wood appears to have so many of the required qualities1 and its use for this purpose has become1 in ,america at least1 universal4 ,the general details of the external case of the grand pianoforte are not unfamiliar4 ,the standard full size of nine feet and the miniature of six feet or less1 as well as intermediate parlor sizes1 are familiar to all4 ,the shape of the fall-board that covers the keys is well known1 and the design of the lid and supporting legs sufficiently common to make further description superfluous4 ,it is proper1 however1 to note briefly the general change that has come about in the conception of the decorative function of the grand pianoforte case4 ,formerly1 the aim of pianoforte manufacturers was entirely different from that of the early harpsichord and spinet makers4 ,instead of doing their utmost to improve the external sthetic value of their instruments1 they seemed too much occupied in providing means for internal improvement to pay proper attention to appearance4 ,thus we see that the sombre and hideous decorative ideas which prevailed in the furniture of the last generation were long faithfully imitated in the external design of the grand pianoforte4 ,the ugly and cumbersome carved legs1 the inartistic curving of the lid and arms1 and the general look of ponderosity and hugeness all combined to give to the instrument of that era the general appearance of a hypertrophied coffin on legs4 ,modern makers1 however1 animated by a truer appreciation of decorative values1 and recognizing the refining influence of beautiful things1 in themselves1 and apart from their other properties1 have gone far towards consigning the more crude and hideous designs to the limbo of obscurity4 ,it has become generally recognized that the coffin-like look of the concert grand may be largely modified1 if not wholly removed4 ,by altering the design of the legs and by regarding them rather as a part of the case than as mere supports1 it has been possible to combine the proportions of legs and case so as to make them appear one harmonious entity4 ,of course1 the actual method of attaining to this end has varied largely among different makers1 and1 likewise1 the greater number of successful efforts in the direction suggested have been made upon grand pianofortes designed to order to fit the furnishings and decorative schemes of music rooms in the homes of the wealthy4 ,nevertheless it is a healthy sign of the general sthetic development of the ,american people that the number of these specially ordered and designed cases increases yearly4 ,in this way we are going back to the ideals that possessed the ancient makers of the virginals1 clavichords and other instruments1 who were wont to call in the services of the most famous artists in color and the most cunning carvers in wood to compass their beautiful and costly designs4 ,it is true that the stock styles of grand pianoforte cases are usually plain as to contour and decoration1 but no one now can deny to them grace and purity of outline or beauty and richness of material4 ,on the other hand1 the practice increases yearly of keeping in stock cases made in such styles as the ,chippendale1 the ,sheraton and the ,empire1 to say nothing of the perennial and truly ,american ,colonial designs4 ,the fact that these numerous varieties all find purchasers is a striking commentary on the growing taste and refinement of the general public4 ,in considering the case construction of the upright pianoforte1 we are led to observe that this type exhibits1 in these matters1 certain important advantages over the grand4 ,it is true that the case is not so homogeneously fitted into the resonant structure1 and it is equally true that the grand has hitherto had much the better of it in the fight for tonal quality and volume4 ,nevertheless1 considering the upright in the light of its own peculiar fitness for popular use1 we are bound to observe1 in considering the construction of its case and back-framing1 the special advantages over the grand that we mentioned as existing4 ,the chief and most obvious of the inherent advantages of the upright pianoforte lies in the position which the instrument takes up4 ,the hammers strike in front of the strings and tend to force them down upon the bridges1 so that the full energy of the blow is impressed upon them4 ,further1 there is none of that tendency of the strings to fly off from the belly bridge which is always present in the square and to a certain extent in the grand4 ,again the vertical position of the sound-board would seem to be more favorable to the free vibration of the wooden fibres of which it is composed2 while the simplicity of the general outline of the upright permits the employment of a larger sound-board area than is possible with either the square or the small grand4 ,lastly1 the wrest-plank is greatly strengthened by the omission of the gap between it and the sound-board1 which permits the use of lighter framing and a consequent gain in portability4 ,while recognizing these facts1 however1 we are bound to recognize many other features that go far to destroy the great initial advantage here described4 ,it cannot be doubted that today the upright is pre-eminently the popular type4 ,whether this fact is entirely a matter for congratulation is doubtful1 for the upright form lends itself readily to cheap and trashy production4 ,the conditions of modern domestic life are such1 on the other hand1 that the portability and convenience of the popular type1 no less than the possibility of producing it cheaply1 have given it a hold upon the public fancy which its own inherent and undoubted advantages might never have secured for it4 ,the upright form is capable of the highest artistic and mechanical development1 and there is no good reason why it should not be so improved as to produce tones equal in volume1 purity and richness to those of the grand4 ,in considering the details of back and case construction in the upright1 we are compelled to observe instances of faulty method4 ,for example1 it is usual to fasten the sides of the case to the back by gluing after the latter has been fitted with the sound-board1 iron frame and strings4 ,this method is obviously faulty4 ,it is not difficult to understand that1 although the back partially sustains the tensions imposed by the strings1 the sides when glued to the former are constantly subjected to a modification of these tensions4 ,now1 gluing1 while convenient1 is not the best possible process to give to the sides the necessary strength to bear such strains1 for it is a familiar fact that pianofortes that are not of the highest class invariably develop in the course of a few years1 more or less serious cracks and breaks in the continuity of the joins between the glued surfaces4 ,when this happens1 the equilibrium of the instrument is disturbed and its strength diminished4 ,in addition1 the breaks in continuity have1 of course1 a serious effect upon the power of resonance4 ,furthermore1 the glue method is subject to various mechanical defects4 ,it is absolutely necessary that the surfaces that are to be united should be maintained1 during the process of gluing1 at an absolutely uniform temperature4 ,and this temperature must be high4 ,consequently it is not hard to see that in the haste and confusion of construction in the factory1 the large sides and backs may not be so carefully handled as to insure the continual maintenance of the ideal temperature conditions4 ,if1 in short1 the surfaces to be glued together are permitted to become cold1 it is obvious that the adhesion will be imperfect1 that the wear and tear of constant usage will complete what carelessness in the factory began1 and that the value of the instrument will be permanently impaired4 ,before suggesting a remedy for these regrettable conditions1 or a substitute for the faulty methods described1 it will be well to examine carefully the principles that underlie the construction of the upright pianoforte back4 ,it will thus become less difficult to find some better method of uniting the sides and back1 so as better to conserve the strength and durability of the instrument4 ,the back of the upright pianoforte might almost be considered as the foundation of the instrument4 ,indeed1 before the general introduction of iron framing1 this part of the construction deserved such a description4 ,its position1 however1 is now somewhat subordinate1 since the wooden framing of which it is composed is quite inadequate to the task of supporting the tension of the strings4 ,as generally built1 this back consists of a number 7usually six7 of wooden posts arranged in an upright position and joined at the top and bottom by braces1 also of wood and of similar dimensions4 ,thus is provided a compact frame that may be made to possess great strength and resisting power4 ,but1 in order to accomplish properly the duties for which it is designed1 the construction of this frame must be very carefully planned and carried out4 ,at its upper end it must give proper support to the wrest-plank and the sound-board must rest easily and securely within its embrace4 ,the iron frame must then be fastened upon and over the structure4 ,it would be absurd to suppose that the back is not subjected to modifications of the strains imposed upon the sound-board1 wrest-plank1 and iron frame1 and it is equally certain that carelessness in working out the details of construction will tend materially to reduce the coefficient of resistance4 ,an important detail is the joining of the upright posts to the top and bottom rails4 ,if these rails are made continuous and the posts are tenoned into them1 the frame will possess the maximum of strength that is possible to such a structure1 and if1 in addition1 the joints are at all places made more secure by the use of screws and other devices as supplements to the gluing1 then we may consider that we have a properly made back4 ,unfortunately1 however1 examination of any considerable number of pianofortes of various makes will soon convince the reader that these details of construction are seldom given enough attention4 ,many instruments will be found to have the back posts joined at top and bottom by short pieces of wood which do not extend further than the two posts which each unites4 ,such a method of construction1 especially when combined with careless gluing and an absence of other fastenings1 provides a frame that possesses none of the desiderata of homogeneity1 compactness and strength4 ,illustration3 ,,back ,,view ,,of ,,upright ,,pianoforte1 ,,knabe ,,patents1 ,,showing ,,ribbing ,,of ,,sound-,,board ,,and ,,construction ,,of ,,back ,,framing4 ,the upright wrest-plank differs somewhat from the synonymous structure used in the grand4 ,it does not suffer under the disadvantage of an involuntary and inevitable separation from the sound-board and the lower portion of the back1 but1 when constructed with a due regard for correct principles1 forms one homogeneous and uniform structure4 ,the upright wrest-plank should1 therefore1 possess rigidity and resisting power of the highest order1 and should form an unyielding support for the tuning-pins4 ,the general construction of such a wrest-plank will not differ materially from that which has already been discussed in reference to the grand pianoforte4 ,that is to say1 the building up of the body of the structure from crossed layers of hard maple and the bolting of it into the iron frame 7when the latter is made so as to extend over the whole surface of the back frame7 will be done in the same way4 ,but the upright wrest-plank derives from the peculiar form of construction that is proper to the upright pianoforte a further element of strength that is lacking in the grand4 ,for it is in direct and solid connection with the sound-board and the other parts of the back-framing1 and thus obtains a considerable addition of strength4 ,indeed1 the wrest-plank should be so constructed as to form an integral part of the top rail of the back1 and should be1 in fact1 the front portion of this rail4 ,further1 its connection with the rest of the back-frame should be as close and binding as possible1 and it is most essential that a sufficient number of lag screws should be driven into the wrest-plank and through the latter into the further and remote parts of the back-frame top-rail4 ,having thus analyzed the construction of the back in all its parts and divisions1 we may return to the discussion of the sides of the case and the best methods of uniting them with the back4 ,the reader has now a good working knowledge of the construction1 prior to the putting on of the sides1 and he cannot have failed to come to the conclusion that gluing is a poor method for joining heavy sides to the elaborate structure known as the back4 ,nor does there seem to be any good practical reason why some other method should not be substituted for the antiquated gluing4 ,there is no good mechanical reason why a system of screws should not be devised that would not only not mar the outer appearance of the case1 but also afford a more certain and secure manner of uniting the sides to the rest of the instrument4 ,moreover1 such a method would largely increase portability by making possible the removal of the sides when conditions of transport required this4 ,manufacturers might profitably spend a little time in estimating the saving that a detachable side would enable them and the dealers to effect in their annual shipping and trucking bills4 ,the various sizes of upright pianofortes that are customarily found range from nearly five feet in height down to about ten inches less4 ,some very small models are made no more than four feet high4 ,but the public appears to prefer the larger styles1 and in this they are entirely right4 ,for the very small pianofortes1 no matter how cunningly they be scaled1 cannot be equipped with strings of the proper lengths1 nor with sound-boards of sufficient area4 ,hence their tonal possibilities are very limited4 ,the full sized upright1 on the other hand1 approaches closely to the tonal excellence of the grand4 ,the styles of case decoration that are and have been applied to the upright are even more striking and varied than those of the grand4 ,for the upright lends itself more readily to that kind of decorative treatment that considers the whole case as one single entity1 and thus harmoniousness of design and unity of treatment are more easily obtained4 ,at the same time1 we are bound to confess that the outline of the upright is essentially box-like1 and that this defect operates continually to nullify the efforts of the designer to conceal it4 ,it is a fact that over-elaboration of decorative treatment is usually accompanied by most unfortunate effects2 while the larger styles at least are little adapted to sustain the burden of meretricious exterior adornment4 ,in fact1 we may well say that the upright is decoratively at its best in the small sizes4 ,since1 however1 there is a public demand for large models1 which are indeed mechanically and acoustically superior1 we must be content to observe the progress of decorative ideas as applied to the beautifying of these4 ,one of the most striking features of the modern decorative movement1 as applied to furniture1 is seen in the great popularity of rare and beautiful woods4 ,these are much prized1 and it has come to be popular to finish them in such a manner as plainly to exhibit the natural figurings and markings4 ,we have even seen a craze for plain rubbing with wax1 which leaves the wood in absolutely its natural appearance4 ,red and ,white ,mahogany1 ,burled and ,circassian ,walnut1 ,satin ,wood1 ,bird's-,eye ,maple1 ,golden and ,flemish ,oak1 and many other beautiful and costly varieties are constantly made up into rich and elaborate pieces of furniture4 ,in this development the upright has had a large part4 ,while the large size and great first cost of the grand has made the purchasing of specially decorated cases a matter to be avoided by all except the wealthy1 the same obstacle has not so largely existed to frighten away the artistic would-be-purchaser of an upright4 ,in fact1 the decorative movement has shown its best manifestations through the medium of the upright pianoforte1 and this in spite of the unfortunate outline of the instrument that resists all efforts to conceal its excessive crudity4 ,models of the ,english schools have been produced with great success1 and the inlaying of rich woods1 after the manner of ,chippendale1 has resulted in some very beautiful specimens of this particular art4 ,again1 we find the so-called ,renaissance1 the ,colonial1 the ,empire 7more elaborate than the other two71 the ,doric 7severely simple71 and last but not least1 the ,mission4 ,the latter1 extraordinary perversion of the handicraft of the ,spanish fathers as it usually is found to be1 has nevertheless been the cause of one great good4 ,it has begun to popularize the dull finish1 and to teach the public that the high1 glassy1 fragile1 and unreliable varnish finish is not the only possible way of putting a surface upon wood4 ,the ,mission craze has taught many people to admire the natural figure and markings of a fine veneer or piece of lumber1 without regard to the fact that it is or is not covered with a mirror-like finish that cracks as soon as the room becomes cold4 ,in fact we may discern the encouraging signs of a growing sanity and refinement in the demand for1 and production of1 suitable designs for the decorative treatment of pianoforte cases4 ,it has come to be recognized that a truly chaste and beautiful exterior is the fitting complement to richness and nobility of tone4 ,the growth of this feeling deserves the highest encouragement from all4 ,american makers may well congratulate themselves upon being the foremost exponents of this movement4 ,,chapter ,x4 ,,the ,,iron ,,frame ,,of ,,the ,,pianoforte4 ,in the historical portion of the present work1 ample reference has been made to the genesis and early development of metallic framing in the construction of pianofortes4 ,we took occasion to point out that the independent development of the ,american pianoforte is intimately connected with the rise and improvement of the system4 ,it is a matter of no little pride to recall that in the universal recognition of the value of metallic adjuncts to the framing devices of the modern pianoforte1 the ,americans1 as became their traditions1 blazed the trail4 ,it is unnecessary to repeat the observations that were made in ,chapter ,,ii as to the controversies that have raged over the question of priority of invention4 ,it is sufficient to refer the reader back to that portion of the present work where these questions have been treated in a sufficiently copious manner4 ,we may therefore proceed directly to the task of investigating the nature of the universal metallic framing that has been demonstrated to be so essential in modern constructional systems4 ,following the plan that we have adopted throughout1 we shall first consider the nature and application of this kind of framing to the grand pianoforte4 ,as to the form1 then1 of the iron framing1 its weight and size4 ,ever since the first grand pianoforte was produced with an iron plate cast in one piece1 designers have been busy with attempts to improve upon the original invention4 ,they have met with but moderate success4 ,there have been multifarious changes in the details of bracing and of fitting the plate to the case1 but the general form of the original design remains the same4 ,it may be described in general terms as follows3 ,a plate of iron cast in one piece1 which follows the outline of the instrument and is so arranged that it may be secured to the case and to the wooden framing that underlies and knits together the latter and the sound-board4 ,a gap is left in this plate at the point where the hammers strike the strings1 and the resultant weakness is overcome by a system of bracing by means of resistance bars1 also of iron and cast in the same piece with the main body4 ,at its front end1 nearest to the key-board1 the plate is extended so as to cover the wrest-plank in which are driven the tuning-pins2 and at the end remote from the key-board it is provided with a number of hitch-pins1 to which are secured the waste ends of the strings4 ,this plate1 further1 is so arranged that the sound-board is not covered by it except at the edges1 and at the place where the bass bridge is constructed another gap is left in its surface4 ,illustration3 ,,jonas ,,chickering',s ,,full ,,solid ,,cast ,,grand ,,metal ,,plate4 ,the above general description comprehends in bare outline the essential features of the iron framing4 ,there are1 of course1 many variations of detail1 and in seeking for the best methods of designing this important part of the pianoforte we shall have occasion to examine the greater number of these with some care4 ,illustration3 ,,sketch ,,of ,,iron ,,plate ,,for ,,concert ,,grand1 ,,showing ,,general ,,arrangement ,,of ,,braces1 ,,belly-,,bridges ,,and ,,system ,,of ,,bolts ,,for ,,fastening ,,to ,,case4 ,a--,b4 ,hammer line4 #a4 ,body of plate4 #b4 ,bass bridge4 #c4 ,continuous treble bridge4 #d4 ,agraffes4 #e4 ,capo d'astro bar4 ,plate is cast in one piece and scale is overstrung4 ,of the various differences of detail that designers have effected in the construction of iron framing1 one of the most important is presented in the so-called 8cupola0 style of construction4 ,in this form the surface of the plate is raised at the edges of the case in such a manner as to give the general outline of a cupola or semi-dome4 ,the result of this method is to increase the resonance of the framing and1 at the same time1 greatly to enhance the tensile strength of the whole construction4 ,the 8cupola0 style was the subject of a patent by ,steinway ,sons of ,new ,york some years ago1 but has been extensively copied since that time4 ,the same celebrated house was the originator of another variation upon the classic manner of plate building4 ,instead of arranging the strings in the usual manner1 a fan-like disposition was adopted1 with the result of distributing the strain more evenly throughout the entire surface and thus improving the tensile qualities of the whole plate4 ,all these methods of construction1 however1 have failed to avoid that breaking up of the scale which is made necessary by the interposition1 between the string groups1 of bars and bracings4 ,it has appeared impossible to obtain the requisite resisting power without the assistance of a number of heavy iron braces cast into the plate and designed to increase the tensile strength1 which is weakened by the gap at the striking points of the hammers4 ,illustration3 ,,arrangement ,,of ,,iron ,,plate1 ,,braces ,,and ,,scale ,,of ,,parlor ,,size ,,grand ,,pianoforte4 ,there has1 however1 appeared an invention which would seem to overcome1 in an effective manner1 the objections to a multiplication of bracings4 ,the inventor is a member of the celebrated house of ,broadwood1 and his device is called the 8,barless0 or 8open scale0 grand pianoforte4 ,by this invention the barred iron frame is replaced by a plate of mild steel1 which is entirely free from bracings1 is constructed with a continuous turned-up flange and is bolted in the usual manner into the bottom framing4 ,this flange provides the necessary tensile strength and apparently sustains the tension of the strings in a perfectly satisfactory manner4 ,the advantages presented by a method of construction that avoids the breaking up of the string groups into three or four divisions are obvious and need not be explained in detail4 ,it may be stated1 however1 that the principal and conspicuous advantage presented by this method of construction is found in the fact that the absence of the usual barring and bracing tends to subdue the metallic and tinkling quality of tone that is so often found to be induced by the presence of heavy masses of cast iron4 ,at the same time1 the material employed is so much more elastic than iron that there is no perceptible loss of resonance1 nor is the tensile strength lessened to any appreciable degree4 ,no one who has tested the pianofortes thus constructed has failed to be delighted with the singularly beautiful tone-quality and remarkable evenness that is shown throughout the whole compass4 ,it is indeed a most difficult task to overcome the tendency to production of unduly prominent dissonant partials in those parts of the scale where the bracing is especially heavy1 particularly in the lower portions1 and consequently we must regard with admiration so successful an attempt to do away with these difficulties by removing their cause4 ,it may be noted at this point that the eminent firm referred to before as having introduced the 8cupola0 form of construction1 also employ steel in the making of their metal frames1 and it seems curious that this example has not been more generally followed4 ,the two types thus described are the most radical exceptions to the common style of metal framing4 ,it is a matter of regret that manufacturers in general have been content to follow so closely in the footsteps of the pioneers1 and have not experimented more energetically with a view to effecting other improvements in the accepted methods4 ,the problem of sustaining the necessary tensions would undoubtedly be simplified by the adoption1 at least in part1 of the ideas of the eminent firms who have already been mentioned4 ,in order thoroughly to understand the actual advantages and disadvantages of the various styles of framing that have been described1 we must consider how great are the tensions that they are compelled to bear4 ,a concert grand pianoforte of a standard ,american make is so constructed that it bears a total strain1 when tuned at concert pitch1 of not less than #cj tons4 ,the requirements of increased tone and the weight and bulk of strings tend constantly to augment rather than to decrease these tremendous strains1 and at the same time more and more to induce the production of those dissonant partials that have such a maleficent influence upon tone-quality4 ,obviously1 then1 if we are to satisfy the popular demand for greater volume1 and at the same time to maintain the highest standards of quality1 we must seek for some method that will obviate the employment of yet heavier masses of cast iron and at the same time preserve the necessary strength and rigidity4 ,the methods of construction that have been noticed at some length above seem to present manifold advantages over the older styles4 ,steel has greater tensile strength than iron1 and consequently a smaller bulk of it is required4 ,again1 its elasticity is higher and the vibrations impressed upon it traverse its surface with greater facility and in a shorter period of time4 ,whether1 therefore1 we prefer the barless or the cupola style of construction1 we must recognize the fact that steel is a better material than iron in any form4 ,foremost among the requirements of a successful framing system are that it shall sustain its burden with such rigidity that the strings shall stand in tune and the wooden case of the instrument shall not be twisted out of shape4 ,even if the material be the best possible1 a faulty method of securing the metal frame to the case will not only prevent the consummation of these desires1 but will tend to weaken the sound-board and hasten its splitting4 ,it is essential1 in fact1 that the board should be relieved of strain1 and great care must therefore be exercised in fitting the framing4 ,the approved method is as follows3 ,the framing is connected with the system of wooden posts that extend below the sound-board and bind together the sides of the case4 ,the latter connection is made by means of long bolts that extend through the bracings of the frame and are sunk into the posts at convenient places4 ,the sound-board is secured to the sides of the case by means of its ribs1 which are continued beyond its edges and pocketed into the sides and the posts1 and also by being glued to the bottom surface of the case and to the system of posts4 ,lastly1 the frame is connected both with the board and the posts1 by a series of heavy screws that pass through the board and into the posts at regular intervals along its outer edges4 ,this method of securing the frame and sound-board to the case ensures that the former shall be incorporated within the body of the instrument as rigidly as is possible1 and that the latter shall have the fullest protection against those twisting strains that the metal frame alone ought to bear4 ,with such a method as has been described we can find no great fault4 ,it should be noted1 however1 that in the barless or open scale construction the bolts that were described as passing through the braces into the posts below are omitted1 and the whole frame is supported within the case by a series of bolts driven through the turned-up steel flange at equal intervals in its surface4 ,having thus considered the forms of framing that are employed by various makers we may turn our attention to the matter of suspending the strings across the frame and over the sound-board4 ,the upward stroke of the hammer of the grand pianoforte tends to drive the string away from its bridge and thus to lessen the energy with which the vibrations imparted to the string are impressed upon the latter4 ,we may note that all makers are agreed in giving to the strings of a grand pianoforte an upward thrust or 8bearing0 in order that the blow of the hammer may throw the strings against the upper surface of the bearing-bridge instead of away from it4 ,there are two devices that are generally employed for this purpose4 ,they are known as the 8agraffe0 and the 8capo d'astro bar40 ,the first of these was the invention of the celebrated ,erard of ,paris4 ,it consists of a brass stud screwed into the iron framing 7or into the wrest-plank where the plate does not extend over the latter71 at the beginning of the speaking length of each string or group of strings4 ,this stud is bored with the required number of holes--one for each string in the group4 ,these holes are bored at such an angle that the ends nearest to the tuning-pins are higher than the other ends1 while the pins are placed at a higher elevation than the agraffes4 ,in this manner the string is given an upward thrust as it proceeds toward the tuning-pin1 and the blows of the hammer force it against the upper surface of the agraffe1 which1 being solid1 conveys the impressed vibrations through the medium of its own surface to the framing4 ,the 8capo d'astro bar0 performs the same functions in a slightly different manner4 ,it is practically a continuous 8agraffe10 and consists of a metal bar which is cast into the metal frame at the beginning of the speaking length of the strings4 ,it is fitted1 according to the best practice1 with an under edge of tool steel1 and the strings are caused to pass underneath it on their way toward the tuning-pins1 which are higher than the bar1 as before4 ,the up-bearing is thus imparted to the strings in a manner similar to that which is followed in the case of the agraffes4 ,as to the advantages of the two systems1 it may be said that the 8capo d'astro0 undoubtedly overcomes those objections to agraffes which are based upon their tendency to pull out from their places4 ,it provides an absolutely rigid resistance1 and is therefore stronger and more reliable4 ,on the other hand1 however1 the mass of metal employed is considerably greater than in the 8agraffe0 method1 and the resultant influences upon tone-quality are clearly disadvantageous4 ,further1 the work of tuning is rendered more difficult by reason of the fact that the strings cannot so readily and correctly be pulled through the space intervening between the bar and the tuning-pin4 ,it is debatable whether the greater rigidity and resonance offered by the 8capo d'astro0 method are not too dearly bought at the cost of inconvenience in tuning and deterioration of tone-quality4 ,it is noteworthy that most manufacturers confine the 8capo d'astro0 bar to the high treble register of their instruments1 where brilliancy and a somewhat metallic quality of tone are a desideratum4 ,the iron framing of an upright piano follows the same general lines of construction as have already been noted in the previous discussion of the grand4 ,the functions of the frame are precisely the same and its construction differs outwardly but little4 ,there are1 however1 certain divergencies from the grand forms that must be noted carefully4 ,for example1 it will be remembered that the form of the upright pianoforte is such that the framing has no direct and positive connection with the outside case4 ,it is thus impracticable to consider the sides of the iron plate as homogeneous with the sides of the case1 nor is it possible to give to it that consistency of form that1 in the grand1 results from the shaping of the plate to correspond with the curved outline of the case4 ,this1 however1 is no reason why the upright iron plate should not be as strong and secure as that of the grand4 ,illustration3 ,,iron ,,plate ,,for ,,upright ,,pianoforte ,,fitted ,,with ,,capo ,d',,astro ,,bar4 ,among the various differences of detail that we observe to exist between these two forms of plate is the device adopted to secure the bearing and rigidity of the strings at their upper end deserves notice4 ,the practice is entirely different in this respect as regards the upright1 and we are therefore introduced to a new feature3 the 8pressure bar40 ,this device has superseded both the old-fashioned pinned bearing bridge and the later agraffe forms4 ,it consists1 essentially1 of a bar of heavy metal that is screwed into the wrest-plank through the metal plate and is placed so that the strings pass under it on the way to the tuning pins4 ,in fact it occupies the same position as do the agraffes or capo d'astro bar on the grand4 ,its function is also similar2 namely1 accurately to delimit the speaking lengths of the strings at the upper end and to assist in the formation of a thrust or bearing whereby the latter may more advantageously be secured4 ,illustration3 ,,iron ,,plate ,,for ,,upright ,,pianoforte ,,with ,,agraffes 7,,mehlin ,,patents74 ,this form of building the bearing bridge possesses important advantages4 ,it does not require to be cast into the plate1 nor is it weakened1 as in the agraffe system1 by being broken up into a large number of units4 ,moreover1 the bearing for the strings is formed much more smoothly and easily between the pressure bar and its attendant ribs on the plate than is possible when either the agraffes or the capo d'astro bar are used4 ,this is an important point1 for such construction tends to make the task of tuning much more rapid and correct4 ,there are1 however1 several points to be considered in the designing of pressure bars4 ,as a general thing1 it is impracticable to apply this form to the bass strings on account of the fact that the overstringing requires of them a slanting direction4 ,on this account the pressure bar cannot be made properly to maintain the obliquely-running strings in their respective places4 ,it is therefore usual to build the bass bridge after the old pinned type and thus to secure the bass strings by much the same device as is employed in the belly bridges4 ,as far as the designing of pressure bars is concerned1 it will be found that care should be exercised in arranging the space that the bar must occupy and its position with regard to the scale ribs that are placed on each side of it and that support the strings before and after their passage under it4 ,in general it may be said that the pressure bar must be screwed in such a position that its lower curved surface is lower than the upper surfaces of the scale ribs by about one-half of the height of the latter4 ,it must also describe a curve that corresponds to the dip or angle of the scale and must be secured by enough screws 7one between each three string-groups is usual71 to ensure that the pull of the strings will have no injurious effect upon its rigidity4 ,it is also essential that the curve into which the string is bent during its passage under the pressure-bar and over the scale-ribs be not too deep or sudden4 ,the bearing surface of the bar should be gently rounded until very near its middle point where the string exercises its greatest pulling strain4 ,here the surface must be curved a little more sharply4 ,the iron plate of the upright is the chief supporter of the strains imposed upon the structure by the strings4 ,it is necessary1 as in the grand1 that it should be built so as to have absolute rigidity under these strains1 and that it should be always capable of withstanding any others that may by any chance be imposed upon it4 ,remembering this1 what shall we say of the designs that we sometimes see where the iron is cut and shaved away at every possible point in order to save a few pounds of weight8 ,there are pianofortes in existence where the iron framing is so much cut down that the treble can never be depended upon to stay in tune for a reasonable length of time1 and where the unevenness of the distribution of metal throughout the body of the frame has caused a warping of the whole instrument out of its proper shape4 ,all this is unnecessary1 but it will continue so long as manufacturers are willing to effect small savings at the expense of the future reliability of their product4 ,it is certainly much better to have the plate of the upright pianoforte so arranged that the total volume of iron1 if it is to be decreased1 may have this process applied evenly and all through4 ,the most correct design would consider a moderately heavy plate of iron1 or better1 of steel4 ,this plate would be so arranged that the hitch-pin plate 7the portion which carries the hitch-pins7 covers the entire surface of the instrument at its bottom end and is bolted into the back with as many and as heavy bolts as are employed at the other end4 ,the upper portion of the proposed plate need not extend over the surface of the wrest-plank1 for such a construction can add little to the resisting power of the frame1 while it inevitably tends1 for reasons that have already been described1 to the production of dissonant partials and the consequent emission of a metallic tone4 ,if it is desirable1 for any reason1 to cut down the weight of a frame1 it can better be done at the upper end than at the lower1 where diminution of the resisting power of the frame is most severely felt4 ,we may1 then1 contemplate a form of iron frame which covers that portion of the back-framing whereon the edges of the sound-board are glued1 and that is not continued up and over the wrest-plank4 ,it will be cut away in the centre1 as in the grand1 and will thus expose a large part of the sound-board to view4 ,it will be provided with a certain number of bracings for the purpose of taking up the strains that are imposed upon the structure at the points of greatest resistance1 such as those where the over-stringing begins and ends1 and those around the middle registers of the scale4 ,there must not be more of these bracings1 however1 than is necessary1 as it is very important that the scale should be broken up into the least possible number of divisions4 ,the bracings will be so designed that no one of them interferes with the true curve of the belly-bridge4 ,the whole structure will be solidly bolted into the back-framing through the sound-board by a series of long and heavy screws and bolts that will be inserted at frequent intervals along the edges4 ,we cannot conclude this survey of plate-construction without taking note of a property that is common to all cast-iron structures4 ,we refer to shrinkage4 ,the calculations of the designer1 no matter how carefully worked out1 must take into consideration the fact that cast-iron shrinks largely in the cooling4 ,it must be noted that the design for the iron plate is the chief portion of the work of scale draughting4 ,as will be explained later on1 this work is first done on paper and then transferred to a wooden pattern4 ,from this pattern the casting is made4 ,after the first casting is thus completed it is taken in hand by the designer1 who marks and punches it for the boring and pinning and corrects it where necessary4 ,the corrected casting is then used as a model for the future plates that are to be turned out for the same scale4 ,but these also shrink2 so that we are compelled to take into account both shrinkages1 and allow for each4 ,fortunately1 however1 there is no difficulty in arranging this4 ,the method is as follows3 ,after the string-lengths have been calculated and the size of the iron plate thus determined1 a complete drawing is made1 showing the exact dimensions1 shape1 and other features of the proposed plate4 ,this is to be used as the guide for the wooden templet4 ,but this difference exists between the two paper drawings2 namely1 that the second is multiplied as to every dimension of the plate by a quantity that represents the amount of shrinkage that is known to occur in the two castings4 ,the average shrinkage of cast-iron in the form of pianoforte plates is estimated at about one per cent4 ,consequently to account for the double shrinkage it becomes necessary to multiply by the square of #aja_/ajj2 that is approximately #ea_/ej4 ,a great deal of trouble will be avoided if the shrinkage is carefully worked out in this manner4 ,every dimension of the plate is affected1 and the greatest care must be taken to ensure that the corrected calculations are accurate4 ,only thus will it be possible for the ideas of the designer to be brought out in the completed instrument as he expects to see them4 ,,chapter ,,xi4 ,,the ,,mechanism ,,of ,,percussion4 ,the pianoforte hammer is perhaps the most striking of the many and various features of that instrument4 ,although it is a comparatively simple device1 its historical and musical interest is supreme4 ,for while the strings1 the framing1 and even the action that we see in the instruments of today are but the modern developments of their clavichord and harpsichord ancestors1 the hammer1 on the contrary1 is the one revolutionary device that1 at a single step1 separated the pianoforte from all other stringed instruments and endowed it with its own peculiar and powerful attributes4 ,it was the hammer1 in fact1 that made the pianoforte4 ,as soon as it was fitted into a harpsichord1 the pianoforte was born1 and no refinement of stringing or framing could have effected the fundamental nature of key-board instruments in the same manner4 ,for we must recognize the fact1 sometimes overlooked1 that the pianoforte is essentially an instrument of percussion4 ,it is necessary that there be a more or less violent blow from the hammer to excite the sound-producing vibrations of the strings4 ,the tone of the instrument1 under the most favorable circumstances1 cannot fail to partake of the character peculiar to sounds produced in this manner4 ,the importance of the hammer as a tone-producer cannot1 then1 be underestimated4 ,it stands upon a plane of importance equal to that occupied by the scale-designing1 the stringing and the resonance apparatus4 ,we are therefore justified in devoting space to consideration of the construction of this essential feature4 ,we cannot say with absolute surety what was the nature of the material with which the hammers of ,cristofori's original invention were covered4 ,but we may presume that it was leather4 ,we know that the hammers were exceedingly small and apparently all of the same size4 ,neither ,silbermann nor ,zumpe can be said to have perfected any special improvements in the form of hammer construction1 and we find that the revolutionary genius1 ,john ,broadwood the ,first1 and also ,sebastian ,erard1 were the pioneers in the work of adapting the hammers to the more strenuous styles of playing that the improved touch mechanism invented by them permitted and encouraged4 ,broadwood1 who first perceived the necessity of adopting a scientifically correct striking point1 likewise began to fit his pianofortes with hammers graduated in size1 and under him the leather-covered hammer arrived at its full development4 ,but leather as a covering material soon began to be decried4 ,it was discovered that the kind of tone demanded by the rising pianoforte masters could not be obtained from such material4 ,after much experiment on the part of pianoforte makers1 the ,german-,frenchman1 ,pape1 of ,paris1 tried the use of felt4 ,his success was immediate and conspicuous1 and it was discovered that not only did this kind of covering produce finer tone quality1 but there was little difficulty in regulating that quality through the hammers within certain well-defined limits4 ,nevertheless1 we find square pianofortes to-day in which the felt covering upon the higher hammers is overlaid with strips of buckskin4 ,this practice1 however1 represented the last dying struggles of the leather-covered hammer1 and now we use it no longer4 ,it is true that the use of felt is not unattended with conspicuous disadvantages4 ,it wears out rapidly1 and unless constantly kept in good condition by use of the felt-needles1 the iron1 and the sand-paper file1 soon comes to produce a harsh and unpleasant tone-quality4 ,this defect arises from the fact that as usually constructed1 the continual pounding of the hammer head upon the strings causes the felt on the crown of the hammer head to become tightly packed and compressed1 and the shaping of the head to be lost4 ,as will be explained later1 this change in the manner in which the head is originally made up causes a modification in the nature of the vibrations set up in the strings1 and1 as we have already learned1 this change in the nature of the produced excitement is the cause of unpleasant tone-quality4 ,nevertheless1 and in spite of these real disadvantages1 the use of felt as a covering material for pianoforte hammers is now universal4 ,nor does it seem at present that we are very likely to find a superior substitute4 ,as we shall shortly see1 however1 a simple change in the manner of securing the felt to the wooden foundation of the hammer-head may be depended upon to add largely to the durability and efficiency of the whole structure1 both as a tone-producing medium and as a mechanical device4 ,as will be surmised by the reader1 early covering of pianoforte hammers with felt was a tedious operation4 ,the material was cut up separately for each hammer1 and glued on to the wooden head by hand4 ,but this method suffered under the grave disadvantage of affording no correct guide to the true thicknesses and no means other than furnished by hand-cutting1 of graduating these thicknesses with exact evenness4 ,it remained for an ,american 7or ,americanized ,german7 inventor to devise a machine that should glue up and finish an entire set of hammers from one continuous sheet of felt1 of which the thickness was graduated in the making and which could be relied upon to contain the correct amount of felt1 of any desired total weight1 the whole graduated with great evenness4 ,not merely was this so1 but the methods of manufacturing felt for other special purposes connected with the manufacture of pianofortes has been entirely revolutionized1 so that today we have dampers1 punchings1 and many other parts of the mechanism of pianofortes successfully manufactured out of various kinds of felt1 which vary greatly in consistency1 thickness1 and other properties4 ,to return1 however1 to the special case of hammer-felt4 ,we find that the original methods of working together the layers of carded wool has been much improved1 chiefly through the efforts of the inventor mentioned above4 ,it is now a matter of slight difficulty to turn out sheets of felt for the making of piano hammers that shall have any desired weight1 size and graduation of thickness4 ,the weight of the sheets of felt varies largely according to the nature of the hammers that are to be produced4 ,thus it is customary1 as may be guessed1 to provide full-size concert grands with hammers of greater thickness1 while the smaller styles of instrument have progressively smaller hammers4 ,the actual weights vary according to the caprice or calculation of manufacturers and designers4 ,an average weight of felt for hammers suitable to be placed in a nine-foot concert grand is from #af to #ah lbs4 per sheet4 ,this does not include the 8underfelt10 which is glued directly to the wooden head of the hammer and is used to give greater resiliency to the lower hammers4 ,it is generally omitted at the higher treble end4 ,upright pianofortes frequently are hammered with felt weighing not more than #h lbs4 to the sheet1 but this seems to be too light for really efficient results4 #aj lbs4 is quite light enough in most cases4 ,as has already been indicated1 the foundation of the hammer is a wooden molding4 ,over this is glued1 in the machine1 a strip of 8underfelt10 which is long enough to cover about five and a half or six octaves of hammers1 counting from the bass end upwards4 ,the main felting is then laid over this1 the thickest end being at the lowest bass4 ,by means of the machines1 now so generally used1 it is possible to glue the entire underfelt and also the topfelt1 in one piece4 ,the moldings are then separated and the operation is complete4 ,it is customary to insert a small piece of wire1 doubled over in a loop1 through each hammer1 in order to ensure further strength to the fastening4 ,as may well be imagined1 the details of manufacture1 of the quality of the felting1 and of the dimensions of the completed hammers1 require much care in their execution4 ,long practice1 study1 and experience have combined to render the specialists1 who devote themselves to the preparation of hammers and hammer-felt1 most excellently fitted to place upon the market the very finest productions of this kind4 ,there have been attempts made at various times to provide a hammer head1 and a method of felting it1 that would obviate the somewhat rapid deterioration caused by the pounding of the glued and compressed felt against the stiff steel wire strings4 ,the felt1 which requires to be compressed before it is glued on to the wooden molding1 rapidly becomes altogether too hard4 ,moreover1 the fastening of the felt to the molding is by no means really permanent4 ,it has been suggested that the felt might properly be contained within a wooden shell which would extend as far along the sides of the felt as the wooden molding now reaches within it4 ,the compressed sheet of felt would be forced into this shell and fastened therein so that it would always be protected by an outer wooden covering4 ,thus1 not only would the fastening of the felt to the wood be reduced more secure1 but the pounding upon the strings would not so rapidly assure the undue hardening of the felt4 ,for there would not be the hard wooden base between which the strings and the felt is continually subjected to compression4 ,the idea is good and undoubtedly will yet be recognized4 ,details of the adjustment of the hammers to the rest of the action and of the preparation of them by the tone-regulator1 for the better production of good and even tone1 will be dealt with in the chapters upon action-and tone-regulating4 ,,chapter ,,xii4 ,,the ,,touch ,,mechanism4 ,as the hammer-idea evolved itself in the mind of ,cristofori and the other experimenters who were contemporaneously bending their efforts towards the improvement of the dynamic possibilities of keyed instruments1 we may be certain that much perplexity was caused them by the problem of providing some mechanism that should form the connecting link between the hammer and the key4 ,we may understand how the ingenious ,italian must have labored1 with the picture of the dulcimer and its player continually in his mind1 to obtain an efficient mechanical substitute for the uncertain stroke of the hand operated dulcimer-hammer1 as well as the dynamically incapable harpsichord jack and quill4 ,it is surprising to note1 indeed1 how early the present ruling principles of action-mechanism were elaborated by these pioneer workers4 ,cristofori1 as we have already mentioned1 obtained1 ere he died1 a complete check to the rebound of the hammer and a form of escapement that may be seen unaltered in essentials in surviving square pianofortes of the 8,english action0 variety4 ,we may further reflect that the invention of ,backers1 as improved by ,john ,broadwood the ,first1 remains today the approved mechanism of many ,english and other ,european grands4 ,not only is this so1 but until the general adoption of the ,steinway overstrung model1 there existed ,german makers who were content to fit their moderate priced grands with a slightly modified form of the ,viennese action invented by that remarkable woman ,nanette ,stein1 afterwards ,madame ,streicher1 the conspicuous feature of which was the mobility of the hammer-butt and the stationary condition of the jack4 ,the fact that these early mechanisms remained satisfactory to performers until recent years is the best proof of the thorough and sure mechanical basis upon which they were designed4 ,it is not necessary to go into elaborate detail in describing these early actions4 ,reference to the accompanying cuts will be sufficient to lay bare their actuating principles4 ,we may1 however1 observe that the radical difference of touch between the ,viennese 7,streicher7 models and those of ,broadwood 7known as the ,english grand action7 continued to be a source of annoyance to performers until the increasing technical demands of the modern virtuoso school and the improvements in wire-drawing and iron casting made inevitable the supersession of the very light ,streicher action by the heavier1 more durable and more efficient ,broadwood ,english model1 which continued in favor until within recent years4 ,illustration3 ,,cristofori',s ,,action ,,in ,,its ,,final ,,form4 #a4 ,key4 #b4 ,jack4 #c4 ,jack-operating spring4 #d4 ,cushion limiting rebound of jack4 #e4 ,under-hammer4 #f4 ,hammer-butt4 #g4 ,hinge of hammer-butt4 #h4 ,hammer-shank4 #i4 ,hammer head4 #aj4 ,check4 #aa4 ,damper-lifter4 #ab4 ,damper-head4 #ac4 ,action-beam4 #ad4 ,wrest-plank4 #ae4 ,tuning pins4 #af4 ,bearing-bridge4 #ag4 ,string4 ,illustration3 ,,action ,,by ,,andreas ,,and ,,nanette 7,,stein71 ,,streicher ,,viennese ,,escapement 7#agid74 #a4 ,key4 #b4 ,jack4 #c4 ,jack-operating spring4 #d4 ,cushion limiting rebound of jack4 #e4 ,button and screw regulating escapement of hammer4 #f4 ,hammer-butt and operating face4 #g4 ,hammer-butt pivot4 #h4 ,hammer-shank4 #i4 ,hammer-head4 #aj4 ,check4 #aa4 ,damper-lifter4 #ab4 ,damper-head4 #ac4 ,action-rails4 ,illustration3 ,,english ,,direct ,,lever ,,grand ,,action1 ,,developed ,,by ,,broadwood ,,from ,,backers 7#ahhd74 #a4 ,key4 #b4 ,jack4 #c4 ,jack operating spring4 #d4 ,rail and cushion limiting travel of jack4 #e4 ,button and screw regulating escapement of hammer4 #f4 ,hammer-butt with operating notch4 #g4 ,hammer-butt flange4 #h4 ,hammer-shank4 #i4 ,hammer-head4 #aj4 ,check4 #ac4 ,action-rails4 ,illustration3 ,,double ,,repetition ,,action ,,of ,,sebastian ,,erard ,,as ,,used ,,by ,s4 ,p4 ,,erard1 ,,paris4 #a4 ,key4 #b4 ,wippen4 #c4 ,jack4 #d4 ,escapement lever4 #e4 ,hammer-shank4 #f4 ,roller4 #g4 ,hammer-head4 #h4 ,jack regulating button4 #i4 ,regulating button to limit rise of escapement lever4 #aj4 ,hammer-butt4 #aa4 ,check4 #ab4 ,felt cushion to engage with check4 #ac4 ,sticker connecting key and wippen4 #ad4 ,action-rails4 #ae4 ,damper-head4 #af4 ,damper operating device4 #ag4 ,device to limit travel of jack4 #ah4 ,string4 #ai4 ,spring 7v-shaped7 for escapement lever and jack4 ,shortly before the general adoption of the ,broadwood model1 however1 there was brought forward a new type of grand action1 which was destined in its turn entirely to supersede the then favorite ,english type4 ,this was the invention of ,sebastian ,erard1 of ,paris1 founder of the still existing house of ,s4 ,p4 ,erard4 ,his new action was termed the 8double repetition action10 and it fully deserves the name4 ,by the use of this device the leverage that exists between the hammer and the key is so manipulated that the very slightest touch upon the keys is sufficient to cause the hammer to deliver a blow4 ,it will be observed by reference to the cut that the ,erard action differs very largely from that of ,broadwood4 ,in the first place1 we observe that the hammer heel is no longer provided with a notch in which the jack works1 but that this heel is reduced to the smallest dimensions and acts merely as a pivot4 ,upon the shank of the hammer is fastened a felt-covered roller4 ,the jack acts upon this roller4 ,between the jack and the roller1 however1 we observe a long lever1 one end of which has a slot through which the jack passes1 while the other end is pivoted on to a rail projecting from the wippen4 ,this is the 8escapement0 or repetition lever1 and forms the main improvement of ,erard4 ,it will be observed that the repetition lever bears against the roller1 and indeed lifts it before the jack can come into engagement with it4 ,the jack1 working through the slotted portion of the lever1 is not brought into play until the lever has raised the hammer a little way4 ,the long1 double spring that acts both upon the lever and the jack gives them their motions1 and the result of the depression of the key is that the repetition lever is always in engagement1 and when the angular key-motion is not sufficient to bring the jack into play1 the work will be done by aid of the lever4 ,furthermore1 the lever operates to maintain the hammer-shank in precisely the proper position for striking1 at all times1 and without reference to the angular position of the key4 ,it can easily be understood that such a vital change in action mechanism did not become popular at once4 ,many pianists objected to double escapement4 ,notable among these were ,chopin and ,kalkbrenner2 these two being the greatest pianists of their day in ,paris4 ,chopin preferred pianofortes fitted with the ,broadwood action4 ,illustration3 ,,the ,,erard ,,grand ,,action ,,modified ,,by ,,herz4 #a4 ,key4 #b4 ,wippen4 #c4 ,jack4 #d4 ,escapement lever4 #e4 ,hammer-shank4 #f4 ,hammer-butt notch4 #g4 ,hammer-head4 #h4 ,jack regulating button4 #i4 ,regulating button to limit rise of escapement lever4 #aj4 ,hammer-butt4 #aa4 ,check4 #ab4 ,molded tail of hammer-head to engage with check4 #ac4 ,capstan-screw connecting key and wippen4 #ad4 ,action-rails4 #ae4 ,damper-head4 #af4 ,damper-operating device4 #ag4 ,device to limit travel of jack4 #ah4 ,regulating device for escapement lever4 #ai4 ,springs 7#b7 for escapement lever and jack4 #bj4 ,string4 #ba4 ,flange4 ,nevertheless1 the merits of ,erard's invention continued to impress themselves upon the musical world1 although ,pierre ,erard1 who had patented his uncle's invention in #ahba1 was obliged to obtain an extension of the ,english patent in #ahce1 on the ground of the loss occasioned in working it4 ,it did not become generally adopted1 even after the expiration of the extended patent1 until modified and simplified by ,henri ,herz1 the famous pianist and pianoforte manufacturer4 ,then its merits1 in the modified form1 were so generally recognized that it is now in use by ,steinway1 ,chickering1 ,knabe and all manufacturers of grand pianofortes in the ,united ,states2 by ,broadwood1 ,collard ,collard1 ,brinsmead1 and others in ,england2 by ,bechstein ,bluthner in ,germany1 and by most ,french makers of eminence with the sole exception of the house of ,erard itself4 ,this eminent firm continues to employ the pure and original form of action as patented in #ahba1 with improvements only in details of workmanship and material4 ,whatever we may say as to the general adoption of the ,erard action only after it had been considerably modified1 we must not withhold admiration from the ,erards1 whose genius and courage gave to us the enduring double-escapement principle that has never yet been superseded4 ,the main features of the ,herz-,erard mechanism may be seen at a glance4 ,the roller is replaced by the notch1 once more restored to favor1 and the repetition lever is made more effective by being pivoted centrally with two free ends1 and by having means provided to limit its up and down motion4 ,moreover1 the wippen is shortened and made straight1 the single spring is replaced by two1 and the damper is once more permitted to fall down on the strings by its own weight without recourse to artificial springs4 ,the ,herz-,erard action has been taken up by ,american makers1 but we find that they have modified it again1 after their own ideas4 ,for example1 if we look at the accompanying cut showing a modern ,american grand action of the highest class1 we shall observe that the original roller of ,erard is restored1 the damper mechanism simplified and additional means of controlling the movements of the jack introduced4 ,these two latter improvements combine to make the present ,american grand action most perfect1 and the achievements of the specialist action makers must ever command our respectful admiration4 ,the reader has now been able to take a comparatively complete survey of the progress of invention in grand pianoforte action mechanism4 ,we shall therefore turn to a critical examination of the modern standard grand action here illustrated1 in order that the adjustment of it within the instrument may be understood4 ,illustration3 ,,standard ,,modern ,,american ,,grand ,,action4 #a4 ,key4 #b4 ,wippen4 #c4 ,jack4 #d4 ,escapement lever4 #e4 ,hammer-shank4 #f4 ,roller4 #g4 ,hammer-head4 #h4 ,jack-regulating button4 #i4 ,regulating button to limit rise of escapement lever4 #aj4 ,hammer-butt4 #aa4 ,check4 #ab4 ,molded tail of hammer-head to engage with check4 #ac4 ,key-rocker and sticker connecting wippen and key4 #ad4 ,action-rails4 #ae4 ,damper-head4 #af4 ,damper operating device4 #ag4 ,device to limit travel of jack4 #ah4 ,regulating device for escapement lever4 #ai4 ,separate springs for jack and escapement lever4 #bj4 ,string4 #ba4 ,flanges4 ,it will be observed that the key 7#a7 is supported upon a key-frame1 part of which is clearly shown in the drawing4 ,this frame is provided with a cloth strip at its rear end1 also shown1 and with a 8balance rail0 upon which the key is pivoted by means of a pin4 ,the position of this balance rail must be such that the divisions of the key thus made are to one another as #c3b4 ,the part nearest to the player's finger is the longer4 ,but such a proportion as this holds good only for the actual operative lengths of the keys from the front to the point where the sticker1 or capstan screw is placed4 ,for otherwise we have a distinct change in the mechanical relations of the parts of the lever-system1 and this1 of course1 entails a corresponding change in the forces that are brought into operation4 ,it is therefore necessary to have a standard length of key1 as between the points mentioned1 and this length is placed at #ae-c_/d inches4 ,but1 in order to maintain the mechanical relations between the dimensions of the lever we must also consider the depth to which the key sinks in front1 and also the height to which it rises at the back4 ,if1 then1 we arrange that the depth in front shall be #c_/h-;inch full and the rise in the rear #a_/d-;inch full1 we shall be able to maintain the position of the balance pin as already calculated4 ,such a proportion supplies the very best arrangement4 ,in order to fix the proportions in the reader's mind we repeat them in tabular form1 as follows3 ,inches ,length between front of key and balance pin #i-i_/bj ,length between balance pin and capstan or sticker #f-c_/aj ,total length of key between front and capstan or sticker #ae-c_/d ,depth of fall of front portion of key #c_/h full ,height of rise of back portion of key #a_/d full ,the front portion of the key is mounted upon a rail of the key-frame which is provided with a pin4 ,this pin works in a mortise cut in the bottom of the front portion of the key and bushed with cloth4 ,the pin is oval in form and adapted to be turned so as partially to increase the amount of space occupied by it whenever wear or age tend unduly to enlarge the size of the mortise4 ,the exact size of all the various action parts that are mounted above and in connection with the keys depends largely upon the exact interior dimensions of the grand pianoforte case4 ,so that it becomes necessary carefully to measure the height from the key-bed to the level of the strings1 and also the distance from the front of the keys to the line of damper lifter wires1 and from there to the extreme rear end of the key-bed4 ,likewise the exact position of the middle string of each three-string group1 the middle point of each two-string group and the position of each single string must be marked upon a stick for the guidance of the action-maker4 ,the latter will then be able to effect the correct alignment of the hammers1 the rise of the escapement lever and jack1 and the exact position1 in reference to these1 of the other parts of the action4 ,it will1 of course1 be understood that the proportionate dimensions of all the action parts depend upon the measurements that we mentioned just now1 as well as upon the dimensions of the keys4 ,the greatest care is therefore necessary in making these measurements4 ,illustration3 ,,grand ,,pianoforte ,,action ,,with ,,metallic ,,action ,,and ,,damper ,,frames1 ,,sostenuto ,,pedal ,,device ,,and ,,hammer ,,swinging ,,soft ,,pedal ,,attachment4 #bb4 ,sostenuto pedal-rod4 #bc4 ,attachment to damper-lever engaging with sostenuto pedal-rod4 #bd4 ,metallic action and damper-brackets4 #be4 ,hammer swing-rail and cushion4 #bf4 ,hammer swing-rail rod4 #bg4 ,hammer swing-rail lifter4 #bh4 ,lifter-rod4 #bi4 ,lost motion compensating levers4 #cj4 ,lost motion compensating levers4 ,the junction of these parts with the damper mechanism lies within the province of the action finisher and regulator and will therefore be treated in the chapter on action regulation4 ,it will be observed then1 to return to the consideration of the action in its actual movements1 that the depression of the key causes the wippen to rise at its forward end4 ,this brings the escapement lever 7#d7 to bear upon the roller 7#f71 with which it is in continual contact1 and raises the hammer-shank and hammer-head 7#e7 and 7#g74 ,at the same time the jack 7#c7 is raised and its tail end is brought nearer to the button 7#h71 which it finally touches4 ,as soon as this happens the jack is tripped up and its head comes out of contact with the roller4 ,the latter in the meantime1 having been raised away from the escapement lever by the action of the jack1 falls back into contact with the former and is then borne up on the lever so that the hammer is maintained in position near to the strings4 ,the result of this is that so long as the finger is held on the front of the key1 the whole action is continually in proper position to actuate the hammer4 ,the jack is not permitted to fall away1 for the roller is maintained in the right place by the escapement lever and it thus happens that a very small angular motion of the key obtained by slightly raising and depressing the finger1 is sufficient to cause the whole action to be set in motion1 and the operation of actuating the hammer to be gone through as often and as rapidly as required4 ,the pedal motions of the grand action are simple4 ,the whole action and keys1 as we know1 are mounted upon the key-frame together1 and thus form a homogeneous structure4 ,the 8piano0 pedal is caused to shift this frame so that the hammers each strike only two of the members of each three-string group and only one of each two-string group4 ,this is effected by the use of a heavy spring that is set in the side of the interior case and bears against the key-frame1 and by a lever that operates from a hole cut in the bottom of the key-bed and engages with one of the bars of the key-frame4 ,the pedal is connected with this iron lever so as to shift the key-frame1 and the spring operates to push the key-frame back into place whenever the foot-pressure is removed from the pedal4 ,the 8forte0 pedal simply pushes up the whole line of damper levers 7#af7 each of which is pivoted on flanges 7#ba7 for that purpose4 ,the lifting is effected by means of a rod connecting with the pedal which is projected through the bottom of the key-bed and engages with a rail set under the line of damper levers and adapted to raise them when operated by the pedal-rod4 ,there are1 however1 two variations to the pedal mechanism of grand pianofortes that require some attention on account of their mechanical interest4 ,these are clearly illustrated and described in the cut and specifications shown on adjoining page4 ,the working of the sostenuto pedal and of the new soft pedal device will be readily comprehended by reference to the cut4 ,it will be noted1 in the first place1 that the metallic action brackets which were omitted in the previous drawing for the sake of exhibiting the working parts more clearly1 are now shown4 ,the 8sostenuto pedal0 is devised to permit the sustaining of a chord while the fingers of the performer1 for the purpose of continuing the melody1 are withdrawn from the keys4 ,it will be observed that the action is provided with a rod 7#bb7 which is connected with a pedal and is adapted to be brought into contact with an additional damper-lever 7#bc74 ,this additional lever is provided with a tongue of felt1 and when the rod is turned on its axis1 this tongue engages with a similar metallic device on the rod1 thus holding the damper up as long as the rod is kept in the position of contact4 ,when the key is pressed down1 the damper rises to clear the string1 and brings the additional lever up with it1 so that1 if the rod is now caused to revolve1 the tongues on each engage one with another and the damper is held up as long as the pedal is pressed down and irrespective of the position of the key4 ,provided that the keys are first depressed1 the pedal will always hold up as many of the dampers as are thus raised4 ,the result is to sustain the sound of the strings after the hand has been removed from the key4 ,this gives a more permanent character to the harmonization of a melody1 without the dissonance that comes from the releasing of all the dampers by the ordinary 8forte0 pedal4 ,the 8sostenuto pedal0 is generally situated between the others in the lyre or pedal case at the level of the player's feet4 ,the second device is also most interesting4 ,it consists of a method for softening the sound of the string1 by a method similar to that which is employed in the upright4 ,it is claimed1 and with some justice1 that the use of the shifting key-frame is attended with various complications1 and that the motion tends to hinder the adjustment of the action to the strings4 ,moreover the hammers become unevenly worn by being continually caused to strike two1 instead of three1 strings and this operates to cause loss of directness in the hammer-strokes4 ,in this new device1 the hammer is provided with a swing-rail 7#be71 having a cushion for the hammer-rebound similar to the ordinary cushion that is supported upon the wippen in most actions1 and a rod 7#bf7 for pivoting it to the metallic action frame 7#bd74 ,the swing-rail also is fitted with a lifter 7#bg71 which is operated by the soft pedal through a lifter-rod 7#bh74 ,so far the process is simple4 ,the effect of the motion of the swing-rail is to bring the hammer closer to the string and to soften the tone4 ,but this is only accomplished at the cost of lost motion between the capstan-screw and the key4 ,to avoid the loss of touch thus brought about1 the lifter-rod is connected with two compensating levers 7#bi7 and 7#cj71 which are so adjusted that they form a continuous link between the parts where the lost motion would occur1 and thus preserve the continuity of touch and the weight that is lost by the different actuating positions of the hammer4 ,the ingenuity of this device commends it to the student of pianoforte mechanism1 and the makers are entitled to great praise for the successful achievement of this important modification4 ,we may conclude our survey by giving a list of the materials of which grand actions are constructed4 ,various ,woods-- ,pear tree ,damper heads4 ,holly ,jacks and other small parts4 ,sycamore ,jacks and other small parts4 ,ebony ,tops of black keys4 ,maple ,hammer moldings and shanks4 ,mahogany ,hammer moldings1 buttons1 etc4 ,white pine ,key-frames4 ,felts and ,cloths-- ,baize ,on key-frames1 hammer-rails1 etc4 ,baize ,punchings4 ,flannel cloth ,bushing centre pin holes1 damper lifter holes1 etc4 ,tone felt ,upper and under felt for hammer4 ,hard felt ,bass damper wedges4 ,soft felt ,treble dampers1 etc4 ,flannel ,sundry action parts4 ,leathers and ,skins-- ,doeskin ,buckskin ,various parts of action1 operating faces of ,elkskin hammer-butts1 etc4 ,ivory ,tops of white keys4 ,celluloid ,fronts of white keys4 ,graphite ,lubrication of working parts4 ,iron ,action frames1 screws1 etc4 ,brass ,centre pins1 springs1 pedal-feet1 etc4 ,illustration3 ,,standard ,,american ,,upright ,,action4 #a4 ,key-rocker4 #b4 ,abstract4 #c4 ,abstract-lever4 #d4 ,flange4 #e4 ,action-rail4 #f4 ,wippen4 #g4 ,jack4 #h4 ,jack-spring4 #i4 ,check4 #aj4 ,check-wire4 #aa4 ,bridle-wire4 #ab4 ,tip of bridle-tape4 #ac4 ,bridle-tape4 #ad4 ,back-stop4 #ae4 ,regulating rail4 #af4 ,regulating button4 #ag4 ,regulating screw4 #ah4 ,hammer-butt4 #ai4 ,hammer-shank4 #bj4 ,hammer-molding4 #ba4 ,hammer-head4 #bb4 ,hammer-rail4 #bc4 ,hammer-butt spring4 #bd4 ,hammer-spring rail4 #be4 ,damper-spoon4 #bf4 ,damper-lifting rod4 #bg4 ,damper-lever4 #bh4 ,damper-lever spring4 #bi4 ,damper-wire4 #cj4 ,damper-block4 #ca4 ,damper-head4 #cb4 ,string4 #cc4 ,continuous brass hammer-butt flange4 ,we are now able to turn our attention to the action mechanism of the upright pianoforte4 ,the historical chapter of this work contains a short description of the early history of the upright form4 ,of course1 it will at once be seen that the only real mechanical difficulty in designing a vertical type of pianoforte was to be found in the department of touch-mechanism4 ,the problem was indeed primarily of the action4 ,as such it is interesting to note the efforts of ,hawkins1 ,southwell and ,loud1 to produce an action that would approach in efficiency that of the grand4 ,it was ,robert ,wornum1 however1 who found the solution1 though not until nearly the end of the first quarter of the nineteenth century4 ,the principle applied by ,wornum possessed such value that it has never been superseded1 and remains today the distinguishing feature of the upright action4 ,we refer1 of course1 to the tape4 ,as applied to the action of uprights1 this device has become universal1 and all upright actions in consequence have for years been everywhere similar as to general design4 ,thus we do not find those radical differences of actuating principle that to this day distinguish ,american from certain ,european grand pianofortes4 ,this is partly due to the fact that the great battles had already been fought out when the first successful upright actions were made4 ,at present1 the only remaining types of the ancient 8sticker0 leather-hinged action are to be found in old-fashioned and obsolete ,european pianofortes of the cheaper grade4 ,none are made now1 however1 except in the case of a very few worthless commercial ,english instruments4 ,in the ,united ,states the 8sticker0 action has hardly been heard of4 ,thus it seems unnecessary to give detailed drawings of any but the accepted type of upright action4 ,the reader's attention is immediately called1 therefore1 to the drawing herewith given4 ,the method of operation may be seen very clearly4 ,depression of the key1 to which is screwed the key-rocker 7#a71 causes the ,abstract 7#b7 and the ,wippen 7#f7 to rise4 ,this brings the ,jack 7#g7 to bear against the butt 7#ah71 which is raised1 forcing the hammer 7#bj7 and 7#ba7 through the shank 7#ai7 against the string 7#cb74 ,as the hammer strikes1 the rise of the jack has brought its tail against the regulating-button 7#af71 which trips it up so that it falls towards the back-stop 7#ad74 ,the butt1 being thus left free1 drops back1 assisted by the pull of the tape 7#ac71 until the back-stop is caught and held by the check 7#i71 thus leaving time for the jack to get back under the hammer butt through the aid of the spring 7#h74 ,repetition of the hammer is thus assured1 and while the rapidity of stroke cannot be so great as that of the grand1 it is sufficiently so to satisfy ordinary users4 ,sometimes a spring is fastened to the front of the jack in connection with a silk loop and cord which stretches back and engages with the hammer spring 7#bc74 ,the latter is then fastened to the hammer butt instead of to a rail 7#bd74 ,this arrangement gives a far more rapid repetition to the action and causes it to approach the delicacy of the double escapement of the grand4 ,illustration3 ,,upright ,,action ,,showing ,,lost-,,motion ,,device1 ,,metallic ,,regulating ,,rail ,,support1 ,,capstan ,,screw1 ,,jack ,,regulating ,,rail ,,and ,,metallic ,,action ,,brackets4 #cd4 ,hammer-rail lifter-wire4 #ce4 ,hammer-rail swing-lever4 #cf4 ,hammer-rail lifter rod4 #cg4 ,lifter-rod lever4 #ch4 ,compensation-lever4 #ci4 ,capstan-screw4 #dj4 ,rail for limiting return movement of jack4 #da4 ,metallic regulating rail support4 ,the pedal mechanism is the same as in the grand4 ,the 8piano0 effect is obtained by pushing forward the hammer-rail 7#bb71 so that the hammers approach nearer to the strings4 ,the 8forte0 pedal effect is obtained by use of the damper lifting rod 7#bf7 which is turned rearwards and forces back the whole line of damper heads so that they leave the strings4 ,the lost motion that occurs in the action when the 8piano0 pedal is used has been overcome in a most ingenious manner1 and by means similar to those already described in the discussion of the grand action4 ,the trouble to be overcome is the same1 namely the lifting up of the abstract from the rocker or capstan screw caused by the forcing of the hammers towards the strings4 ,this causes loss of touch and is very irritating to the performer4 ,the drawing given herewith also shows the metallic action bracket for supporting the action and the capstan screw that is used as an alternate to the key-rocker4 ,the lost motion attachment operates through the rod 7#cf7 which lifts the hammer rail and at the same time brings into play the compensation lever 7#ch71 which takes up the space between the abstract and the key that would otherwise intervene4 ,thus the touch remains true irrespective of the position of the hammer4 ,the materials that are required for the manufacture of the upright action do not differ from those1 which we have already classified as pertaining to the grand4 ,the adjustment of the upright action requires that the same precautions be taken in the measurement of the key-bed1 of the height of the action between the keys and striking-point of hammers1 the distance of hammer from strings when at rest and so on4 ,all these assist the action maker to adjust the alignment of the hammers and the height of the abstracts4 ,the size of the pianoforte sometimes requires the omission of the abstracts1 in which case the bottom of the wippen is felted and brought into contact with the capstan or rocker direct4 ,all these details are attended to by the action maker when the proper measurements are given4 ,the marking on a stick of the run of the strings is done just as was suggested for the grand scale4 ,in conclusion1 it may be mentioned that much similarity exists between certain parts of the action of both types of instrument4 ,it has become customary to make the length of the hammer shank and hammer butt1 when fitted together1 about five inches1 counting from the center pin of the butt to the middle of the hammer molding4 ,this measurement will be found correct for both grands and uprights4 ,the length of the hammer blow is always as nearly as possible #a-bd_/be inches for the bass end1 graduating to #a-i_/aj scant in the treble4 ,these dimensions should be maintained at all costs4 ,the key lengths that we gave before are applicable to all forms of uprights4 ,when provided with these data the action maker will be able to put out a mechanism that will fulfill the individual requirements of each kind of instrument4 ,,chapter ,,xiii4 ,,regulation ,,of ,,pianoforte ,,touch ,,mechanism4 ,we may presume that the reader is by this time quite familiar with the appearance and use of the various parts of the grand and upright pianoforte action1 both as assembled and detached4 ,we may therefore proceed to give general instructions for the adjustment of these within the instrument and the regulation of the various working parts into proper harmony with one another4 ,we say 8general instructions0 advisedly2 for it is quite out of the question to teach action finishing and regulating by means of written directions4 ,experience and the practical routine of the shop must be gone through by anyone who hopes to be able to do this kind of work well4 ,for there are few departments of mechanical endeavor that demand such skill1 care1 and patience as the regulation of pianoforte mechanism4 ,nevertheless the directions that we shall give in this chapter will be sufficient to make him who reads and digests them a very efficient critic4 ,it is much to the employer to be able to estimate correctly the value of each practical detail of the construction1 and the correctness of the manner in which it is executed4 ,this chapter is intended to provide as much of this knowledge as may be imparted by means of written words4 ,we shall begin with the grand action1 following the method that has been pursued throughout this work4 ,the first step in the regulating and adjustment of the grand action is taken by the 8action-finisher40 ,he receives the action and keys separately4 ,the former is without hammers or dampers and the latter without rockers or capstan screws4 ,the action has to be placed within the space destined for it in the instrument and the proper position for it noted4 ,if the action has been well made there should be no difficulty in seeing that it fits its place correctly4 ,the action is screwed on to the key-frame through its metallic brackets and the capstan screws are put into the keys at the proper points so that they engage with the cushions on the bottom of the wippens4 ,when this has been done the weight of the action upon any one of the keys should be noted and the action may then be removed4 ,a piece of lead should then be taken and fastened to the back of each key4 ,this lead must have the same weight as the action has upon each key4 ,the keys will then remain in their proper positions when the action is removed1 and the work of leveling them may then be begun4 ,remembering the depth of touch that was prescribed in the last chapter1 let the extreme bass and treble keys be adjusted to an equivalent height by wooden blocks through their front rail pins4 ,then run a straight edge over the keys and proceed to adjust their levels by means of the thin paper punchings that are provided for the purpose4 ,these come in various thicknesses and are laid over the balance rail pins and under the cloth punchings that must first have been placed in position both on the balance rail and the front rail4 ,when the leveling is accomplished let the action be screwed on again4 ,then let the hammers be glued on4 ,the striking point of the hammers must be carefully measured and the directions already given as to the striking of the highest hammer must be observed4 ,it will be remembered that one-tenth of the string was recommended for the highest hammers1 graduating down to the ideal one-ninth and one-eighth4 ,the scale draughtsman will prepare a marking stick showing the true hammer line4 ,the hammers are glued on absolutely at right angles to the plane of the strings4 ,after they are dry1 they must be adjusted to the proper position by the capstan screws or rockers4 ,they must lie just over and not quite touching the wippen cushions4 ,let them also be aligned to each other1 horizontally1 with great exactness4 ,be sure that the keys work easily and that the depth of touch is roughly adjusted as already provided for4 ,it next becomes necessary to fix the damper mechanism4 ,this is chiefly situated in the back of the action and the damper levers are to be so adjusted that they rest a little above the backs of the keys1 ready to be engaged with them when the fronts of the keys are depressed4 ,the dampers must fit on to the strings straight and must drop with sufficient force to effect an instantaneous damping4 ,the damper levers are leaded for this purpose4 ,the instrument is then taken in hand by the action regulator4 ,his work is most important4 ,he first sees that the level of the keys is perfect and that they are properly balanced when suspended without the action4 ,if any defects are found here they are remedied by changes in the leading4 ,the keys should be so leaded that they balance when tested on a scale and the weight of touch with the action fitted must not be more than two and one-quarter ounces4 ,the alignment of the hammers is then corrected and the length of the hammer stroke1 as laid down in ,chapter ,,xii1 is adjusted by means of the capstan screw or rocker4 ,the jack is so regulated by its button and screw that the trip up of the jack occurs when the hammer is #e_/cb of an inch from the string4 ,the checks must catch the hammers when they have fallen three-quarters of an inch away from the strings4 ,the tails of the hammer-moldings must be roughened and the checks be so slanted that the catch is sure and tight4 ,the escapement lever is then considered4 ,the spring that governs it requires adjustment4 ,it must be sufficiently strong to cause the hammer to dance and jump a little on the lever when the key is released4 ,the escapement lever must also be regulated by means of the hook that is found at its rear end4 ,there must be space enough between the hook and the lever to ensure that the catch of the hammer by the check is at all times free4 ,the screw that regulates the rise of the escapement lever must also be attended to4 ,it is necessary that the movement of the lever be arrested before the hammer has quite risen to the point of the trip up of the jack4 ,the after-touch under the front of the keys is regulated by means of paper punchings4 ,if enough punchings are placed under the keys to make very hard pressure necessary to force a release of the hammer1 then punchings of #a_/cb of an inch in thickness must be removed to make the after touch correct4 ,the keys must also be made to descend evenly as judged from the top4 ,unevenness is corrected also by the judicious use of punchings4 ,in regulating the dampers there are many small details to be watched4 ,the lifter-wires must work freely in the bushings and the heads must lie straight upon the strings4 ,this is especially important as regards the bass wedge-dampers4 ,there must be a small space between the damper levers and the felted backs of the keys and the rise of the damper heads when the levers are lifted must be even and facile4 ,the height of ascent of the damper heads must not exceed one-fifth of an inch1 and a little more when the whole of them are lifted by the pedal-rod4 ,the sostenuto rod must also be adjusted so that the damper lever tongues are caught when the rod is revolved4 ,care must be taken that the rod does not catch the tongues when the pedal is not in use4 ,the pedal mechanism is simple4 ,it is essential to see that the feet work in the lyre without scraping2 hence lubrication with graphite and tallow is necessary4 ,the rods that connect with the action levers must so engage as to be just in contact without bearing too much4 ,the soft 8piano0 pedal must engage with the shifting lever so as to allow a small space between it and the point of contact with the key-frame4 ,the strength of the reaction spring in the case must be arranged so that the key-board is pushed back with promptness upon the release of the pedal4 ,the 8forte0 pedal must be adjusted so that its connecting rod is in contact with the damper lever lifting rail1 but not enough to operate without the depression of the pedal4 ,the sostenuto pedal requires to be arranged to revolve the sostenuto rod instantly4 ,here the rod has to be revolved its entire distance before it operates and the adjustment may therefore be made quite close4 ,these directions will enable one at least to be sure that the regulation of a grand pianoforte action has been properly done2 although it is not to be expected that the innumerable small details of practical work are to be learned other than practically4 ,it must especially be borne in mind that the use of tools and facility in handling them and making definite adjustments with them is a matter of long and patient practice4 ,the above instructions are intended merely to set the routine method before the reader1 so that he may approach the subject with a correct knowledge of principles4 ,the regulation and adjustment of the upright action is precisely similar as to principles4 ,the differences occur through the somewhat dissimilar method whereby repetition is attained and the great variation in the general position of the parts with reference to the strings4 ,the action of the upright is fastened1 by means of the metallic brackets1 to iron bolts which are set up in the key-bed4 ,the height of these bolts depends upon the dimensions of the instrument and the striking point of the strings4 ,in setting the action in place great care must be exercised in seeing that the hammer line lies truly in regard to the run of the strings4 ,errors in the casting of the plate often lead to a distortion of the true string-line and the action finisher must take care to set the action with due regard to these matters4 ,when the action1 which is minus hammers and dampers1 is thus set in1 the keys may be placed under it for the purpose of marking the points where the capstan screws or rockers must be set4 ,the hammers and dampers are then glued in and adjusted for position with regard to the strings4 ,if the action and keys are truly proportioned1 it is always possible to make the length of the key just as recommended in the last chapter4 ,sometimes the size of the pianoforte makes impossible the employment of capstans or rockers with abstracts4 ,in this case it is customary either to use a dowel prop or to lay the wippen directly upon the key4 ,when the dowel prop is used it is driven firmly into the key1 and its upper end1 which is a wooden rod into which the lower spike is screwed1 impinges against the wippen4 ,in laying the place for the dowel to be driven1 it must be remembered that it is necessary for the head of the dowel to hit the bottom of the wippen squarely4 ,but the dowel describes a curve at its head when the key is moving1 and the wippen has to be provided with a felted foot1 curved so as to accommodate this circular motion of the dowel4 ,this motion must be observed carefully1 so that the dowel does not lay too far forward or back of the wippen foot when the key is at either of its extreme positions4 ,the regulation proper now begins4 ,abstracts1 or dowels1 are always regulated by a screw4 ,this is either in the form of a capstan or of a rocker1 or of the movable part of the dowel itself4 ,the adjustment must be made with reference to the position of the jack under the hammer butt4 ,it is necessary that the jack be just in contact with the notched heel of the butt4 ,after the hammers and dampers have been put in and their positions with reference to the keys adjusted1 it becomes necessary to regulate the escape of the hammer by means of the regulating buttons and the jacks4 ,the directions given for grands apply here4 ,the hammer springs must be put in place and the fall of the hammers noted4 ,if they stick1 the bushings are too tight or some cognate trouble exists which can be easily remedied with a drop of oil on the affected part4 ,the checks must be adjusted to the back-stops and made to stand square to them and they must also be arranged to catch the back-stops when the hammer has recovered about two-thirds of an inch from the string4 ,we know that the length of the hammer blow should be from #a-bd_/be of an inch in the bass to #a-i_/aj of an inch in the treble4 ,the tapes must be adjusted so that they begin to exercise their pull when the hammer is started away from the strings4 ,they must not be strained too tight1 but should be left just a little loose1 so that when the soft pedal pushes the hammers towards the strings the abstracts or dowels do not at once leave the keys4 ,the dampers are adjusted1 as to position1 like those of the grand--that is1 they must lie square on the strings and be in a straight line with one another4 ,their movements are directed by the spoons and these must be so bent that the damper begins to move when about one-third of the angular motion of the key has taken place4 ,when actuated by the pedal1 they must fall against the back of the hammer spring rail1 which is felted for the purpose1 and their motion must be instantaneous when the pedal is depressed4 ,the pedal mechanism is concealed behind the bottom frame of the case and will be found to be precisely similar to that of the grand1 except as regards the mounting and pivoting of the levers4 ,these must be kept lubricated with graphite and tallow to prevent squeaking4 ,the connection of the soft pedal with the hammer rail must be close so that instantaneous action results when the pedal is operated4 ,the motion of the pedal may push the hammers one-half of their stroke length towards the strings1 not more4 ,the leveling of the keys and the regulation of touch have already been described2 nothing further need be said except that these operations are more easily performed in the upright owing to the open way in which everything is set in4 ,it is unnecessary to go further into detail in regard to the regulation of actions4 ,enough has been said to lay bare the general principles1 and1 as was stated before1 the rest comes from experience only4 ,a text-book can never replace an apprenticeship1 but we cannot deny its value in laying down correct principles for the man who wants to know how things should be done4 ,as a fitting conclusion to the present discussion1 we may now note the order of the various processes which combine to make up the manufacture of a pianoforte1 from the cutting of the lumber to the final tuning in the wareroom4 ,the various kinds of lumber that are to be used are exposed1 after cutting and rough dressing1 in a lumber-yard4 ,here they remain from three to ten years according to the kind of wood and the degree of care that is taken by the manufacturer4 ,the best makers take the greatest care in seasoning their lumber4 ,the first operations to be considered are those of the saw-mill4 ,here the rough work for the case-making is done1 and the moldings for actions and cases are turned out4 ,the rough cases are then sent to the case department and made up into shape4 ,the bent rims are there glued together for the grands1 and the sides and frames of the uprights are shaped4 ,the back framing1 wrest-planks and other parts of the case and back construction are also put together in the case department4 ,in the meantime1 the machine work has gone in the rough from the saw-mill to the 8action department10 where it is cut1 shaped and made up into the delicate action parts4 ,these have to be leathered1 felted1 provided with brackets1 springs and the other accessories and assembled4 ,the hammers are covered1 dampers1 prepared1 and the whole of the action work is thus made ready against the time when the case shall be in condition to receive it4 ,this action and hammer work is generally done by specialists1 who supply many different makers with actions according to their particular scales and patterns4 ,meanwhile the cases have been sent to the varnish room and are here prepared with filler and stain to receive the varnish finish4 ,the best instruments have their cases left about four months in the varnish room1 receiving eight or ten coats at intervals of ten days or more4 ,while this is going on1 the sound-board department is occupied in preparing the sheets of spruce for manufacture into sound-boards4 ,here great care and skill are necessary to obtain the proper gradation of thickness at all parts of the board's surface4 ,when the boards are finished1 they are put into drying rooms1 to remain until wanted for ribbing1 bridging and insertion within the instruments4 ,the first operation in the assembling of the parts is performed by the 8bellyman40 ,he takes the sound-board1 ribs it and affixes the bridges according to pattern1 bores the tuning pin holes in the wrest-plank1 and fastens on the iron plate1 which was cast to pattern in the iron foundry1 to the back1 upon which the completed sound-board has by this time been glued4 ,then the 8stringer0 receives the bellied back1 puts on the strings and pressure bar 7if the latter is used instead of agraffes74 ,the first rough approximation to pitch is then made by the 8chipper10 who pulls the strings up roughly two or three times in succession at intervals of about twenty-four hours4 ,the case is then turned over to the 8side-gluer10 if the instrument be an upright4 ,the case of the grand is incorporated with the back and is put together before the bellying4 ,the side-gluer affixes the sides and key-bed of the upright and also the bottom-board1 which contains the trap-work for the pedal mechanism4 ,if the instrument be a grand this department confines itself to the fitting and adjustment of the lyre4 ,after the sides are thus affixed the case is returned to the 8flowing-room10 where the final coat of 8flowing0 varnish is carefully applied4 ,this requires ten days to dry hard4 ,the case is now ready for the 8action finisher40 ,his work of setting in the action and keys and putting the instrument into rough playing condition has been described in detail4 ,the pianoforte is then given its first rough tuning by the 8rough-tuner10 who surrenders it in turn to the 8fly-finisher40 ,in this department the top and bottom frames1 fall-board1 panels1 key-blocks1 name-board1 key-slip1 hinges1 music desk and other parts of the cabinet work are adjusted and fitted4 ,after fitting they are removed from the case and sent to the 8polishing department0 to be made ready for the final setting up4 ,the next operation is performed by the 8action regulator40 ,his work1 which includes the finishing touches to the adjustments made by the action-finisher and side-gluer1 has already been gone over in detail4 ,the instrument is by this time ready for another and somewhat more careful tuning4 ,here appears the 8second tuner40 ,the instrument then is permitted to remain in its existing condition until two more tunings have been given at intervals of a week4 ,the 8fine-regulator0 next takes the instrument and proceeds to review the work of the action-regulator and correct any deficiencies in touch or repetition that may have been effected by the pounding of the rough tuners4 ,the 8tone-regulator0 is next called upon1 and his delicate work is needed to give to the pianoforte evenness of tone throughout and an agreeable quality4 ,then the polishers rub down the sides1 the smaller parts being already polished as noted before1 and give to the instrument its glossy and mirror-like finish4 ,the 8setter-up0 then puts the various cabinet work parts together and the 8fine-tuner0 gives the final tuning4 ,lastly1 the superintendent looks over the whole work1 and woe betide the unlucky wight who has slurred or skimped his part4 ,the details listed above are1 of course1 subject to variations in the order in which they are performed4 ,the variations are according to the practice of individual shops4 ,of course1 it may at any time be required to give more tunings1 especially if the pianoforte is left on the floor of the factory very long4 ,but there should never be less than four or five4 ,when the instrument is sent to the wareroom or shipped to the dealer extra tunings are given according to the caprice or knowledge of both4 ,,chapter ,,xiv4 ,,tuning ,,and ,,tone ,,regulation ,,of ,,the ,,pianoforte4 ,the art of tuning the pianoforte is one of considerable complexity and obscurity4 ,during all the time that has elapsed since the key-board instrument first came into being1 controversies innumerable have raged over the multifarious questions that the practice of the art implies4 ,this distressing state of affairs is primarily due to the fact that a system of 8tempering0 the sounds produced by key-board instruments is necessary1 in order that playing in more than one key may be possible4 ,the whole matter of musical intonation was treated with some completeness in the early part of this work1 and the reader may be expected to comprehend the principles of the ,equal ,temperament upon which the tuning of the pianoforte and of all other fixed tone instruments is now universally based4 ,it is not within our province1 in the course of a treatise upon the principles of pianoforte construction1 to venture too deeply into the quagmires that surround the aspirant for the honors of the tuner4 ,the discussion of musical intonation and the ,equal ,temperament was made for the principal purpose of acquainting the student with the reason for the peculiar construction of scales1 as to their string lengths1 and to make clear the raison d'etre of the frequent divergences from theoretical proportions of strings and tones that we have been obliged to note4 ,the scale designer is better equipped for his task1 however1 if he possess a working knowledge of the principles upon which the science and art of tuning are based4 ,this is the justification for the space and time devoted to the exhibition of certain of these principles in the earlier portion of this book4 ,as a further contribution to this useful body of knowledge1 we shall point out here the general scheme whereby the tuner proceeds to the execution of his important1 indeed essential1 portion of the whole work4 ,the practical work of tuning is performed by the aid of certain acoustical phenomena which enable the tuner to distinguish between sounds that are very nearly in unison4 ,as the ,equal ,temperament requires the slight roughening of all the intervals with the exception of the unison and octave1 it is clear that there is great value in a method of estimating1 not only the unisonal or non-unisonal condition of two sounds1 but also the exact amount of difference that may occur between them4 ,the phenomena mentioned are called 8beats10 and it is well that their physical basis should be described here4 ,from what has been said before1 it is clear that musical sounds1 generated as they are by the periodic agitation of the air according to fixed laws1 are but the audible manifestations of a peculiar form of air-motion4 ,the particular form of air-motion can best be described as a wave4 ,whenever a sonorous body is excited into vibration it causes the surrounding atmosphere to make motions that correspond to its own4 ,a vibrating body such as we have described 7together with the segments thereof7 partakes of a motion that may be compared to that of a pendulum4 ,there is a rhythmic swinging back and forth of the body and its segments1 with the result that the immediately adjacent layers of air are excited into alternate states of compression and expansion2 or1 more correctly1 of condensation and rarefaction4 ,this rhythmic motion is imparted by the layers of air adjacent to the sonorous body to the next adjacent layers1 and so on4 ,the result of this is that a wave is formed1 the length of which varies inversely as the number of vibrations performed by the sonorous body4 ,this wave is called a sonorous wave4 ,now we know that sounds are at the same pitch when they are generated by sonorous bodies having the same speed of vibration1 and it is easy to perceive that1 if two such bodies are sounding together1 the condensations and rarefactions of the layers of air will synchronize with each other1 so that both will be exciting condensations at the same instant and likewise will generate rarefactions simultaneously4 ,and even if the two bodies have not exactly the same speed1 the result will be equally simple as long as their speeds bear simple ratios to each other4 ,thus two bodies which are emitting sounds at the interval of an octave or of a fifth or fourth will generate condensations and rarefactions in such a manner that they will not interfere one with another4 ,but the case is different where two sounds are separated by differences in pitch that cannot be expressed by simple ratios4 ,for example1 if one sound be one vibration per second higher than another1 it is clear that by the time that the first sounding body has completed its given number of vibrations in one second1 the other will be one vibration behind4 ,when1 therefore1 the vibrations of the first body are continued into the next second the condensation of one wave will be completely synchronous with neither the condensation nor the rarefaction of the other4 ,the obvious result is that at a certain point the condensations of each wave concur while at another point the condensation of one crosses the rarefaction of the other4 ,in the first case we have a considerable augmentation of sound and in the other case a complete silence4 ,as the waves thus approach and recede there is a gradual diminution of sound followed by a complete cessation for a small fraction of a second1 and then a gradual increase until the point of greatest augmentation occurs4 ,this latter happens when the two condensations concur1 and the gradual rise and fall of the sound correspond to the gradual approach of this concurrence in the first case and to the similar advance of the point of crossing in the second4 ,this phenomenon of alternate augmentation and diminution of sound separated by an almost inappreciable interval of silence occurs whenever two sounds of nearly the same pitch are heard simultaneously4 ,these peculiar changes in the intensity of a sound are denominated 8beats40 ,this description of the physical nature of 8beats0 will be sufficient to make clear to us how a recognition of them is of value to the tuner4 ,from what we have just said1 it will be observed that the number of beats that may be set up between any two sounds depends upon the difference in the frequency of the two sonorous bodies4 ,so that the number of beats form a true guide to the exact amount of difference between sounds that are nearly in consonance4 ,thus1 if it becomes a matter of tuning a certain interval a little flat or sharp1 in order to comply with the requirements of ,equal ,temperament1 the operation may be readily performed by observing the number of beats that are heard between the two sounds when one of them is sharpened or flattened4 ,so that all schemes of tuning must necessarily be founded upon a recognition of this important phenomenon4 ,at this point it will be well to reiterate the fact that the ,equal ,temperament owes its popularity and long prevalence to the wonderful facility of modulation which it possesses4 ,while it certainly involves discords and disharmonics that the mesotonic system1 for instance1 avoided1 yet the fact that it does not limit the expression of musical ideas to a few scales1 but permits the composer to roam at will through the whole field of tonalities1 has given to it a deeply founded popularity that has not yet been seriously challenged4 ,we must bear in mind that the ,equal ,temperament is the first fact1 the 8prius10 the 8proton hemin10 as it were1 of musical performance4 ,obviously1 therefore1 the importance of a proper and close adherence to this system in the tuning of fixed-tone instruments cannot be insisted upon too strongly4 ,the reader has already had occasion to examine a comparative table which showed the pitches of a true and of a corresponding tempered scale4 ,he will have noted that the tempered scale errs very greatly in respect to certain intervals4 ,the task of equalizing the thirteen sounds which a fixed-tone instrument allows to the octave1 involves in each interval a greater or less divergence from purity1 according to the ratio of such interval4 ,thus we find that the error of a tempered third is greater than that of a fifth1 and so on4 ,now1 if the four minor thirds within the compass of an octave be considered1 it will be found that the octave to the tonic which is produced from the last of these is a good deal sharper than the octave taken direct from the tonic4 ,again the octave produced from the building up of the three major thirds within the same compass is very much flatter than the octave taken direct from the tonic4 ,again1 it will be remembered that there are twelve fifths within the compass of seven octaves4 ,the last sound in this progression of fifths is considerably sharper than the sound that is produced by taking a series of seven octaves from the tonic4 ,without going into figures1 we may give the differences thus noted concisely as follows3 ,in the cases above considered the octaves obtained by building up intervals differ from the straight octave in the following proportions3 ,the octave produced from minor thirds is sharper in the ratio #abif3abej4 ,the octave produced from major thirds is flatter in the ratio #abe3abh4 ,the octave produced from fifths is sharper in the ratio #ecadda3ebdbhh4 ,obviously1 therefore1 it will be necessary to tune all the minor thirds1 within an octave1 flat by one-fourth each of the ratio given for them4 ,it will also be necessary to tune each of the major thirds sharp by one-third of the ratio proper to those intervals4 ,likewise each of the perfect fifths must be made flat by one-twelfth of the ratio given above for fifths4 ,we are thus able to understand just how great divergencies from purity are involved in the ,equal ,temperament of major thirds1 minor thirds and fifths4 ,as far as the other intervals are concerned1 it is obvious that if the thirds and fifths are equally tempered and the octaves tuned quite purely1 the other intervals will be subjected simultaneously and automatically to a similar process of temper4 ,now from what we learned of the phenomena of beats1 we must conclude that the tempering process when applied to these intervals will generate beats between the sounds that compose each interval4 ,we know that beats must occur when the sounds that form any consonant interval are not quite in tune with one another4 ,we also know that the frequency of the beats depends upon the difference in frequency of the generating sounds4 ,we can1 therefore1 easily see that those intervals that are subjected to the greatest amount of tempering will produce the greatest number of beats4 ,and further1 as the actual frequencies of the sounds increase according to their pitch1 it is equally obvious that the tempering will result in greater differences as to actual frequency between the true and the corresponding tempered intervals4 ,therefore the number of beats that any tempered interval generates varies directly as the pitch of the sounds that form the interval4 ,the higher the pitch1 the greater the number of beats4 ,conversely1 the lower the pitch1 the smaller the number of beats4 ,now we have already noted that the phenomena of beats afford an absolutely precise test for the consonance or otherwise of an interval4 ,if we can estimate the number of beats that should occur between the sounds of any given equally tempered interval1 we can always tune such an interval in the ,equal ,temperament by noting the number of beats and adjusting this to the theoretical number in the calculations4 ,it is not possible accurately to follow the number of beats that are supposed to be between any given intervals in ,equal ,temperament even when the pitch of the tonic of the interval that is being tuned is precisely similar to the corresponding sound in the calculations4 ,it is not possible1 therefore1 in practice1 to tune with such accuracy as theory would demand1 but an approximation may be obtained4 ,if we could secure an absolute standardization of pitch for the pianoforte it would be possible to construct tables that would show the exact number of beats that ought to occur between all the equally tempered sounds within the whole compass4 ,in default of such a method1 it is necessary to resort to a variety of tests and to prove the correctness of the tempering of each interval by comparison of the different intervals of various kinds that to which each sound1 as it is completed1 gives rise4 ,if1 for example1 we find that any given sound1 when tuned1 gives the same number of beats with the tenth below as it does with the third below1 which is one octave above the tenth1 then we have some assurance that the sound in question is properly tempered4 ,if this assurance is confirmed by a complete absence of beats between the given sound and its octave1 above or below1 then we have an almost absolute assurance as to the correctness of the work4 ,it is then upon the phenomena of beats that the tuner depends for a guide to the correctness of the work in which he is engaged4 ,by noting the frequency of the beats at some places1 or their absence at others1 he is able to judge most accurately whether any interval is tuned too sharp or too flat1 or whether any octave is tuned purely or the reverse4 ,all good tuning depends entirely upon such estimation of the beats1 and the greatest difficulty that the tuner encounters lies in the fact that he must try to equalize the frequencies of the beats between all the intervals of the same kind within the compass of each octave4 ,if this work is well and truly done it properly deserves the name of art1 and1 indeed1 fine tuning is a fine art1 one to be acquired by the painful and slow processes of manual practice and mental application4 ,he who overcomes all obstacles to success and masters thoroughly the principles and practice of tuning is an artist in the truest sense4 ,in applying these principles to the tuning of the pianoforte1 the problem that confronts us is to devise a rapid and simple means of tempering each sound within the seven odd octaves of the instrument1 and to do this in such a manner that the deviation from purity shall be the same for all similar intervals within the compass of each octave4 ,now it follows1 from what has gone before1 that the tempering of each separate interval1 by itself1 and without reference to any other1 would be a very tedious and inaccurate process4 ,it would1 in fact1 be quite impracticable to employ such means for intervals that require relatively large deviations from purity1 especially in the higher pitched registers4 ,there is1 however1 a method that largely obviates these difficulties4 ,the middle octave of the instrument1 which runs from ,f below middle ,c to ,f above it1 is chosen1 and the intervals within this octave are so tuned that the thirteen semitones which it contains become equally tempered sounds4 ,the sounds within the next octave above or below are thereupon tuned from the former1 each to its octave above or below1 and this process is continued until all the sounds upon the key-board have been tuned4 ,it is easy to see that such a method possesses many and great advantages4 ,all the difficult tempering of intervals that require large deviations from purity is confined to that portion of the piano where beats are most easily estimated2 while the rest of the instrument is tuned by means of octave intervals1 in which the test of purity is absence of beats1 rather than the estimation of any number of them4 ,the tempering of the intervals in the middle octave is called 8laying the bearings0 and is the most difficult1 as it is the most important1 of the various processes incident to the practice of pianoforte tuning4 ,the 8accumulation of insensible into almost intolerable errors10 as ,mr4 ,ellis aptly terms it1 continually besets the path of the tuner1 especially if his preliminary knowledge be imperfect4 ,the true estimation of beats1 as generated by various intervals1 is an art that is but slowly and painfully acquired1 by long practice and training of the ear4 ,examination of the pianoforte key-board shows us thirteen sounds within the compass of an octave4 ,in proceeding to the conversion of these into equally tempered sounds1 we have more than one method presented to us4 ,we shall1 of course1 choose the octave which1 as stated above1 runs from ,f below middle ,c to ,f above it1 and shall use1 for our purposes1 such adjacent sounds as we may consider necessary4 ,it is usual to take from a tuning-fork the pitch of the sound from which the tuning is begun4 ,these instruments are tuned either to ,c1 or ,a next above middle ,c4 ,it is usual1 in this country1 to tune from ,c1 and we shall1 therefore1 adopt that method4 ,now there are various ways of setting about the 8laying of the bearings40 ,some tuners work by thirds1 others by fourths and fifths2 others again use a series or circle of fifths joined by octaves4 ,whatever intervals are tuned1 the idea is to include all the thirteen sounds within the octave and to use1 as far as possible1 only one or two kinds of intervals4 ,of all these methods1 the shortest1 easiest and most accurate is that which employs fourths and fifths only4 ,it is used in such a manner that1 by tuning a circle of fifths and fourths1 the last sound tuned provides the octave to the first1 thus completing the circle and the octave of tempered sounds4 ,illustration3 tuning music notation ,in this method we proceed as follows3 #a4 ,pitch ,c is tuned by the tuning fork4 #b4 ,f below pitch ,c is tuned1 being a tempered fifth4 #c4 ,g below pitch ,c is tuned1 being a tempered fourth4 #d4 ,d above ,g is tuned1 being a tempered fifth4 #e4 ,a below ,d is tuned1 being a tempered fourth4 #f4 ,e above ,a is tuned1 being a tempered fifth4 #g4 ,b below ,e is tuned1 being a tempered fourth4 #h4 ,f sharp below ,b is tuned1 being a tempered fourth4 #i4 ,c sharp above ,f sharp is tuned1 being a tempered fifth4 #aj4 ,g sharp below ,c sharp is tuned1 being a tempered fourth4 #aa4 ,d sharp above ,g sharp is tuned1 being a tempered fifth4 #ab4 ,a sharp below ,d sharp is tuned1 being a tempered fourth4 #ac4 ,f above ,a sharp is tuned1 being a tempered fourth4 ,this last ,f is the octave to the first ,f tuned1 and should coincide exactly with the latter4 ,the reader will1 of course1 realize that the tempering of these various intervals must be tested by means of the generated beats4 ,helmholtz1 in 8,die ,lehre der ,tonempfindungen10 calculates that the tempered fifths should average 4#f of a beat per second at standard pitch within the octave that we are treating4 ,this is equivalent to three beats in five seconds4 ,but it is impracticable to measure the generated beats upon the pianoforte in this manner4 ,the tone of the instrument is too evanescent and fleeting4 ,we may1 however1 attain to a very fair approximation4 ,if1 for example1 each fifth be tuned so that two distinct beats are heard before the sound dies away1 it will be found that the beat-rate is a near approximation to the calculated average4 ,the two beats that we speak of occur in about three seconds1 while the ,helmholtz rate is three and one-third seconds for two beats4 ,again ,helmholtz gives an average beat-rate for tempered fourths in the same octave2 namely1 one per second4 ,if we tune the fourths so that we hear three distinct beats we shall likewise obtain a very fair approximation to the calculated beat-rate4 ,we showed above that the last sound produced by the building up of a progression of twelve fifths is sharper than the sound produced by the piling up of seven octaves from the same tonic4 ,the two sounds thus produced ought to coincide1 for the compass of twelve fifths and of seven octaves is the same4 ,we concluded1 therefore1 that the ,equal ,temperament required the flattening of all the fifths4 ,the meaning of the discussion is1 therefore1 that the fifths within the octave where the 8bearings0 are being laid must each be tuned flat by two beats4 ,or1 rather1 that the higher sound of every fifth must be flatter by two beats than if it were in consonance with the lower sound4 ,again1 if we tune the ,f below middle ,c two beats sharp of the latter 7which is equivalent to tuning the fixed pitch sound ,c two beats flat of ,f7 we shall obtain a properly tempered fifth4 ,now1 if the octave above this ,f be taken it will be found to form a sharp fourth with middle ,c4 ,for example1 if the pitch of middle ,c be #bfd1 then the pitch of ,f below it1 in pure intonation1 is two-thirds or #agf4 ,assuming that the ,f be then tempered so as to be sharp by two vibrations1 it will have a frequency of #agh4 ,the octave to this is #cef ,but this latter is a fourth above ,c #bfd and should1 therefore1 be #ceb ,consequently we see that the fourths in ,equal ,temperament are to be tuned sharp ascending1 or conversely1 flat descending4 ,as already explained1 the beat-rate in the 8bearings0 should be nearly one per second or three beats1 while the sound of the interval remains audible4 ,when the deviations from purity are as slight as in the cases that we have been considering1 it is by no means easy to determine1 at all times1 whether the note that is being tuned is sharp or flat of its tonic4 ,for the beats occur similarly in either case and few ears can determine the relative sharping or flatting without some extraneous aid4 ,fortunately1 however1 we have a variety of tests open to us1 which for completeness and accuracy leave nothing to be desired4 ,to take a concrete example1 during the 8laying of the bearings0 we first tune the ,f below middle ,c1 then the ,g below middle ,c1 and then the ,d above ,g4 ,when we reach this last note1 we find that a sixth has been obtained2 namely1 ,f--,d4 ,now if the notes already tuned have been tempered1 so as to be too flat1 the resultant sixth will beat too slowly1 and1 conversely1 if the tuned notes be too sharp the sixth will beat too fast4 ,this test may be amplified when we proceed to the next interval1 ,d--,a4 ,when this latter note has been tuned1 we have the triad ,f--,a--,c4 ,f--,a is a major third1 and by referring to previous calculation we see that as such it must1 when properly tempered1 be considerably sharp4 ,by noting the beats of the major third and likewise the beats of the sixth we may correct the tuning of all the sounds with which we have hitherto dealt4 ,the same process is1 of course1 carried on throughout the whole process of 8laying the bearings40 ,the major thirds and sixths are tested continually as the tuning proceeds1 and thus is provided a sure guide to the correctness of the fourths and fifths4 ,the correct beat-rates for the major thirds may be stated as about eight per second1 while that for the major sixths is approximately eleven in the same period4 ,of course1 as already stated1 these rates per second cannot be measured with accuracy1 but with practice one soon discovers by ear the proper roughness in each case1 and is thus enabled to estimate the beat rates without much trouble4 ,every opportunity of examining the work of good tuners should be taken by the observer1 who should note carefully the beat-rates which they assign to each kind of interval4 ,in this way he will provide himself with practical examples of tempering of intervals which will be of great value to him4 ,having thus determined the proper beat-rates for each of the intervals that are used in the 8laying of the bearings10 we may proceed to the further consideration of that convenient method for tuning the middle octave that has already been demonstrated4 ,in order to facilitate comprehension of the argument1 the following table is given1 showing graphically the sounds that are tuned in laying the bearings and the tests and trial chords-- ,the white notes are those to be tuned4 ,the black notes are those already tuned4 ,the kind of deviation from purity of interval and the beat-rates are as follows3 ,upper notes of fifths must be tuned flat so as to give two distinct beats4 ,lower notes of fourths must be tuned flat so as to give three distinct beats4 ,upper notes of major thirds must be sharp so as to give approximately eight beats per second4 ,upper notes of major sixths must be sharp so as to give approximately eleven beats per second4 ,if the laying of the bearings has been accurately performed1 the chords that are produced by the combination of the various sounds will be found to have very nearly the same roughness and to generate approximately the same number of beats4 ,the best work is that which most closely approaches this standard4 ,after the bearings have thus been laid1 it is necessary to continue the tuning of the instrument above and below the octave already treated4 ,now1 since the octave to any given sound has exactly double the frequency of the former1 and since octaves are to be tuned purely1 it follows that we need only tune the remainder of the instrument by octaves up and down from the 8bearings40 ,the consonance of an octave is determined by the absence of beats1 and1 consequently1 we have only to follow this rule to reproduce1 in all parts of the piano1 deviations from purity relatively the same as those which we have been at such pains to secure4 ,of course1 the actual number of beats in any given interval varies as the frequencies1 and1 consequently1 the frequency of the beats increases regularly in the higher registers1 while it similarly decreases in the lower portions4 ,thus the deviations from purity become much greater in the higher portions of the compass and incorrect laying of the bearings is1 therefore1 productive of more and more disagreeable results as the scale ascends4 ,on the contrary1 in the lower register these inaccuracies are less productive of irritation1 as the frequencies of the beats become continually less4 ,such1 then1 is the process of tuning the pianoforte in ,equal ,temperament4 ,we have made no attempt to go into those practical details that are concerned with the ear-training1 the manipulation of the hammer1 or other cognate matters4 ,these are entirely 8ex provincia0 of this work4 ,nevertheless the person who digests the foregoing statement of the laws and methods of the art will be well equipped to pass upon the correctness of tuning1 and this is sufficient for our purpose4 ,the work of tone-regulation opens up varying but not entirely dissimilar fields of research4 ,the material of which the pianoforte hammer is constructed has an important influence upon the coloring of the sound that it draws from the string4 ,in order that the influence of the pianoforte hammer in tone-coloring may be understood clearly1 we shall investigate the matter with some completeness4 ,we have already investigated the compound nature of the sounds excited by the pianoforte strings4 ,we know that the nature of these sounds varies as the method of excitement and as the nature of the resonance apparatus that surrounds the strings4 ,now the pianoforte strings are excited by being struck1 and we have already noted that the point of striking must be carefully chosen4 ,further1 we know that the amount of metal framing1 the manner of adjusting the bridges1 the nature of the sound-board and innumerable other details must be taken into consideration4 ,but by the time that the pianoforte comes into the hands of the tone-regulator1 it is out of his power to affect the construction in any fundamental points4 ,he is able to change only two things4 ,these are the striking point and the condition of the hammer-heads4 ,even the former cannot be changed to any great extent4 ,in the highest treble1 however1 it often becomes necessary to bend the hammer-shanks slightly in order that a more correct striking point may be obtained4 ,but this must be done with great discretion and caution4 ,the object of tone-regulation is to ensure an agreeable tone and perfect evenness of quality throughout4 ,obviously1 this is so intimately bound up with the whole construction that it may be said that the tone-regulation begins with the drawing of the scale and is never finished until the pianoforte itself is completed4 ,this would be a perfectly proper statement1 but we have here to consider the final touches1 as it were1 that the tone-regulator may give to the tonal equipment4 ,when the instrument comes into his hands the hammers are still covered with the hard outer skin of the felt head4 ,this must be removed with a sand-paper file4 ,it then is necessary to sound each tone slowly and carefully1 first loudly1 and then less so4 ,it will be found that some of the hammers produce a harsh and disagreeable timbre1 while others may be too soft and mushy4 ,under all circumstances it is far better to endow the instrument1 as far as is possible1 with a quality that shall be comparatively mellow and round4 ,brilliancy cannot be forced artificially without spoiling the whole quality and imparting a thinness and roughness that is most disagreeable4 ,if the hammers are too hard at the crown1 they have the acoustical effect upon the strings of exciting the upper dissonant partials to undue prominence4 ,this occurs from the fact that when the head is hard it rebounds instantly from the string1 and thus does not damp any of the dissonant partials4 ,on the other hand1 if the head be soft1 the felt clings for a fraction of a second longer to the strings and effects the damping to a greater or less degree1 according to the relative softness or hardness of the head4 ,it is thus possible1 by discreet manipulation of the felt1 to influence the character of the sounds to no small degree4 ,the method is to pick up the felt1 when it is to be softened1 with a set of felt needles mounted in a handle for the purpose4 ,it is essential to note whether the sound is the same when the hammer strikes with great force as it is when it strikes gently4 ,if1 for example1 a gentle pressure on the key gives an agreeable quality1 but harder strokes on the key destroy this1 then we see that the crown of the hammer head is soft enough1 but the felt cushion underneath is too hard4 ,fine needles are1 therefore1 employed to dig into the lower cushion of felt1 while disturbing the consistency of the upper crown as little as possible4 ,on the other hand1 when the quality of sound is hard under all conditions1 the upper surface of the hammer-head must be treated by picking it with heavier needles4 ,hardening of the felt may also be undertaken by covering the hammer-head with a damp cloth and then applying a hot iron4 ,the whole work is primarily one of practice and experience4 ,no directions can do more than give an outline of the processes and the physical reasons for them4 ,it is well1 however1 to lay down the laws that underly these processes1 in order that practice may be supplemented and improved with theory4 ,,chapter ,,xv4 ,,the ,,draughting ,,of ,,the ,,pianoforte ,,scale4 ,although1 for obvious reasons1 we speak of it thus late1 yet it is true that the first and most important step in the designing of a pianoforte is the draughting of the scale4 ,this process includes a complete planning of the iron plate and of the bridges1 in fact of the whole arrangements for stretching the strings and maintaining their tension4 ,this plan must indicate very clearly the exact length both of the vibratory portion and of the waste ends of each string2 it must show the place on each string where the stroke of the hammer is to be directed1 while the exact positions of each tuning-pin and hitch-pin must be laid down with equal certitude4 ,further1 the place of the belly-bridges1 their dimensions and manner of pinning1 have to be shown on the drawing4 ,lastly1 the fastening of the iron plate by screws and bolts must be indicated2 together with the precise position of each individual screw1 bolt and pin4 ,when this plan is in all respects complete1 it has to be transferred to a wooden pattern4 ,the inevitable shrinkage of paper always makes the retention of the proper measurements a matter of difficulty4 ,this may be overcome by making the first drawing upon a sheet of wood1 varnished to give a clear surface4 ,if the drawing be made with ,india ink instead of with pencil1 we shall have a complete and permanent record obtained in a superior manner4 ,when the wooden templet is to be made from such a drawing1 it will not be found that there has been the shrinking or swelling caused by the use of paper1 and the first drawing1 if made after the method described1 may be laid aside for any length of time4 ,let us suppose that it is desired to draught the scale of an upright pianoforte4 ,having selected the size of pianoforte that is to be designed and the wooden 8table0 which is to serve for the drawing surface1 we proceed as follows3 ,first lay down the line whereon all the hammers are to strike the strings4 ,from this line as base we plot out the string lengths and the direction in which each runs2 also the distance of each group from the immediately adjacent groups4 ,having laid down the striking point line1 we next proceed to indicate upon it1 by suitable lines1 the middle string of each three-string group4 ,for the two-string groups a line is taken in the middle of the two strings4 ,we call these lines 8running lines40 ,then the string dimensions must be taken into consideration and calculated according to the rules laid down already4 ,the highest treble strings run at right angles to the striking point line1 and the running lines indicating the positions of the groups are to be placed accordingly4 ,the distance between the running lines should be a shade more than one-half of an inch at the highest portions of the scale4 ,it is found necessary to draw the running lines with increasing obliquity as their length increases1 until at the end of the treble sections they are running at an angle of about #aaj degrees counting from the treble end or #gj degrees counting from the bass end of the striking point line4 ,the lengths of the strings as determined by previous calculations mark the line of the belly-bridge4 ,the bars that are to be cast in the plate must be allowed for in plotting the string plan4 ,it is usual to place one of these at about ,f and another at ,c1 where the over-stringing customarily begins4 ,the variations of individual scales and the requirements of particular sizes of instruments sometimes cause changes in this regard4 ,this is one of the points that the designer must decide for himself4 ,the space between the running lines increases gradually as the length of them1 on account of their oblique direction and the necessity for providing sufficient space for the dampers and hammers4 ,the actual length of the strings as calculated must be laid down with reference to the striking point line4 ,as has been pointed out1 it is found better in practice to have the hammers strike the very high strings a little above the theoretical place4 ,a good average would contemplate one-tenth of the length for the six highest strings1 graduating down to one-ninth for the rest of the highest octave and the next below it4 ,before the lowest string of this last-named octave 7,c7 is reached1 the striking point is gradually lowered and two or three strings below ,c it becomes one-eighth4 ,if we follow out this scheme we obtain the place where the scale rib intervenes at the pressure bar by taking one-tenth1 one-ninth or one-eighth1 as the case may be1 of the length of each string4 ,the remaining fraction of the length represents the correct distance between the striking point line and the nearest pin on the belly-bridge4 ,thus the belly-bridge and pressure bar lines are automatically formed as we go along4 ,illustration3 ,,method ,,of ,,plotting ,,string ,,plan ,,by ,,means ,,of ,,striking ,,point ,,line ,,and ,,running ,,lines4 ,the sketch is intended merely as a general guide to the method outlined above1 and only a few of the running lines are shown4 ,the dark lines show the direction and position of the bars4 ,when the scale rib and pressure bar line has been obtained1 it is necessary to make provision for the tuning pins1 and particular care must be taken that the strings shall not rub against each other owing to incorrect placing of the pins4 ,when the drawing has thus been completed1 we may take up the design of the iron plate4 ,it will be remembered that we calculated a compensation factor for the shrinkage4 ,this factor is #ea_/ej1 and all dimensions where shrinkage may have effect must be multiplied by this amount4 ,such dimensions are those of the height and width of the plate4 ,hence the lengths of the bars1 the distances between them1 and the positions of the bolts and screws as well as the string lengths must all be modified according to the shrinkage factor4 ,the wooden templet may be taken directly from the wooden table drawing by filling in the outlines and details of the iron plate on the latter and then copying these on to the templet subject to the shrinkage modifications required4 ,it is well to regard one top side and also that at the treble as immovable1 and to consider the shrinkage as coming from the bottom to the top and from the bass to the treble4 ,when the dimensions of the proposed plate are thus laid out on the surface of the templet1 the bars1 screw-sockets and bolt holes must be copied in wood and laid on the templet in the exact places that they will occupy in the finished plate4 ,thus we gradually evolve a complete wooden model of the iron plate1 so that the iron founders may readily obtain a correct casting4 ,when the first casting comes back from the foundry1 it should be carefully punched for the tuning-pin1 bolt and screw holes4 ,the first casting must be considered in reference to the fact that it represents only one shrinkage4 ,after the second casting is made from the first1 the correctness of the calculations may be judged4 ,but not until the first pianoforte is turned out according to the new scale can the designer find out how well his efforts have been rewarded4 ,of course1 the foregoing directions are but outlines of the method4 ,the true inwardness of scale draughting cannot be explained here1 or1 indeed1 otherwise than by practical experience4 ,a certain facility in mechanical draughtsmanship is essential1 and also close attention to the methods that have been laid down in regard to striking points1 number of covered strings1 number and place of bars1 compensation for shrinkage1 and the various other points that have been mentioned4 ,for the convenience of the plate-finisher1 wooden patterns are provided1 showing the position of hitch-pins1 tuning-pin holes1 screw-holes and bolt holes1 corrected for shrinkage4 ,the belly-man must have patterns for the position of the bridges and for the bridge-pin boring4 ,a wooden pattern is also required for the pressure bar4 ,when these details are completed1 the draughtsman must possess himself in patience until his completed instrument is turned out4 ,if the rules so carefully demonstrated throughout this treatise are fully digested1 the designer will be far on the way towards correct scale draughting4 ,his native cunning1 however1 must be relied upon to carry him through when written directions fail4 ,,chapter ,,xvi4 ,,conclusion4 ,if the present treatise has convinced the reader that the making of pianofortes is a very serious matter1 and one not to be attacked in a spirit of levity1 then one of its immediate objects has been attained4 ,indeed there has been an abiding fear in the breast of the author that he might presently be charged with piling on the agony too strongly and searching with excessive zeal for scientific causes and rules when the shortest solutions may be found by empirical methods4 ,this is not really the case1 however1 for the whole problem of the construction of pianofortes is naturally acoustical4 ,while it is doubtless true that many pianofortes have been and are continually made1 not merely with indifference to1 but in defiance of1 every law that has been expounded in these pages1 it nevertheless remains that none of these have been good pianofortes4 ,of the making of thump-boxes there is no end4 ,unfortunately for the public1 musical ignorance is well-nigh universal1 and the impostor finds it easy to palm off shoddy in place of the real article4 ,of course1 it is quite true that bad pianofortes are soon found out1 but when the inevitable discovery comes1 the mischief has been done and the purchaser is1 as usual1 the victim4 ,a student of the construction of good instruments cannot fail to be astonished that anyone should wish to turn out anything but the best4 ,for1 as one continues to investigate the multifarious problems that are continually suggested1 the desire to overcome them and to produce perfect instruments becomes almost irresistible4 ,perhaps this is why the clever designer1 if left to himself1 often develops into a crank4 ,and1 indeed1 there is not an industry on the face of the globe that has produced more cranks4 ,the files of the patent office are full of the ideas of unrewarded genius that has spent its time1 its money and its enthusiasm in the unenviable task of producing innovations in pianofortes4 ,no feature of construction has been left unimproved2 yet how many of these inventions ever see the light8 ,few1 indeed2 and the fact is a sad commentary on the unpractical nature of genius in general4 ,these reflections lead one to the feeling that a fitting conclusion to a treatise on pianoforte construction may be made by giving particulars of some of the most famous and revolutionary inventions that at one time and another have been launched upon the unfeeling world of piano-making4 ,not all of these by any means can be denominated freaks2 indeed there are the germs of most valuable developments in many of them4 ,we shall consider a few of the really valuable ideas at least4 ,among these primacy must be given to the screw-stringing device of ,mason ,hamlin4 ,this invention was intended to substitute a positive mechanical fastening for the tuning-pin1 in place of the wooden wrest-plank4 ,it consisted of a screw1 threaded vertically in a socket1 which was cut in a projecting shoulder on the iron-plate4 ,as it extended below its socket1 it was provided with an universal joint which ended in a hook4 ,on this hook the string was wound1 and was then free to pass on to the agraffe4 ,a small ,t-hammer sufficed to turn the screw and the string was tightened or slackened as the screw turned in the threaded socket4 ,the action was slow but sure1 and the strings had the curious property of sharping under a test blow instead of the opposite1 as is usual4 ,the method of tuning was the same except that the screw turned in the opposite direction to the ordinary style and required much more turning to bring the string to the desired point4 ,on the other hand1 however1 setting the pin was unnecessary1 and the evils engendered by bad wrest-planks and sticking or twisting pins were unknown4 ,moreover1 the turning of the screw involved very slight effort4 ,with all these advantages1 however1 the reverse motion and the slowness of action were fatal2 and after several years of effort ,mason ,hamlin gave up the attempt to popularize their invention1 and let it drop4 ,it is1 indeed1 unfortunate that this device did not become more popular1 as in that case its many inherent advantages would doubtless have been emphasized and the bad points in it eliminated4 ,prejudice and the tuners1 however1 were against it1 and it died4 ,the well-known house of ,brinsmead in ,london has also experimented with a similar device1 but it is not known with what success4 ,one of the advantages held out by the makers of such string devices was the supposed facilitation of the work of tuning--that is to say1 it was alleged that every musician could become his own tuner as soon as he had learned the theoretical principles of the ,equal ,temperament4 ,the hope was delusive1 however4 ,perhaps the professional tuners attended to this point4 ,another similar but more successful device is being manufactured by the ,wegman ,piano ,co4 ,this is in the form of a fastening for the pin in the iron plate4 ,the appearance of the plate and pin is not different from the usual design1 but the tapered end is done away with and the pin1 instead of being driven into the wooden wrest-plank1 is fastened in the plate by means of the friction set up between the peculiarly bored hole and the back of the pin4 ,a special twist is needed to fasten the pin when a string is drawn up to pitch1 but otherwise the method of operation is not unusual4 ,the device appears to be of value4 ,the sound-board has ever afforded a fertile field for inventive genius4 ,it has been altered in every conceivable manner1 but the old style continues to flourish with all its pristine activity4 ,this is not to say that it is ideal and insusceptible of improvement4 ,on the contrary1 one cannot deny that many praiseworthy ideas have been patented for the purpose of improving it4 ,the ribbing has been the subject of much attention from inventors4 ,it is true that this method of giving strength and tension to the board is by no means perfect4 ,yet we find that the various devices proposed for the abolition of ribbing have almost uniformly failed4 ,a large number of these failures owe their conditions to the lack of acoustical knowledge of the inventors4 ,it has often been supposed that the enormous relative resonance power of the violin belly was connected in some way with the duplicate nature of the resonance table and the consequent hollow shape of the resonating body4 ,this has been conclusively disproved1 however1 for it has been shown that the violin's special shape is given to it merely for the purpose of bearing the strain of its strings4 ,moreover1 the tone and resonance of a violin have been reproduced by means of a vibrating diaphragm and a horn4 ,this device1 known after its inventor as the ,stroh violin1 satisfactorily disproves many cherished theories in regard to violin resonance4 ,in spite of these facts we find that several patents have been taken out for pianoforte sound-boards1 of which the guiding principles have been ingenious applications of the violin idea4 ,the 8equilibre0 pianoforte of ,frederic ,mathushek was an example of this type4 ,it seems passing strange that experimenters have not all become aware long ago of the essential differences between the resonance apparatus required for struck and for bowed strings4 ,there have been other and saner variations of sound-board construction4 ,it has been suggested that the use of a double board composed of two cross-grained thicknesses glued to each other would obviate the necessity of ribbing and increase the power of resonance4 ,there seems to be little doubt that there is the germ of a valuable idea in this1 and if the notion is properly worked out1 it will very likely produce valuable additions to our knowledge of the phenomena of resonance4 ,unusual ideas have been less frequent in the domain of action-making4 ,there have been several praiseworthy attempts to get rid of the troublesome1 but hitherto necessary1 tape in the upright action4 ,the patent of ,leo ,battalia is one of these4 ,he abolishes the tape and bridle wire1 and substitutes a two-branched spring fork projecting from the jack4 ,one branch works in a slot cut in the hammer butt and the other bears against the back check4 ,the back stop is done away with and excellent repetition is assured1 superior to that which is obtained by ordinary methods4 ,in the domain of pure scale design1 we note the ever present and perennial notion of sympathetic strings4 ,this idea has taken various forms4 ,the most conventional development is1 of course1 the 8duplex scale0 of ,steinway and others4 ,this utilizes the waste ends of the strings and scales off lengths of them that correspond to aliquot parts of the vibrating length of each string1 thus obtaining the advantage of sympathetic partial tones4 ,most of the ideas in this direction have gone further than this1 however4 ,some makers have gone so far as to have a fourth string tuned to the octave of every three-string group4 ,but this is surely unnecessary when we consider that the octave is1 on the pianoforte1 the strongest partial tone of any musical sound1 and least of all needs adventitious aid4 ,there are many other similar devices used and unused that we should waste our time in considering4 ,in any case the true test of the utility of an invention is use1 and each one of these unusual notions that have been put on the market would have been universal long ago had they been uniformly practical and valuable4 ,we cannot close this hasty survey without mention of the remarkable innovation in action mechanism devised by ,mr4 ,morris ,steinert4 ,here the forcible hammer-blow is superseded by a gradual push on the hammer at the strings1 executed through the interposition of an articulated double lever between the hammer and the jack4 ,the result is to produce a different form of hammer attack and a noticeable modification in the coloring of the tone produced from the string4 ,while the claims of the inventor are somewhat exaggerated1 there is no doubt that ,mr4 ,steinert has hit upon a valuable variation in the method of actuating the hammer1 and his invention opens up new prospects of pleasure to the pianist4 ,if all these and the innumerable others have no other value1 they at least teach that inventive genius and the hunger for improvement do not entirely sleep2 that the pianoforte is continually being improved1 and that many are spending their time in finding new ways of improvement4 ,it shows that the value of the pianoforte to the community is sufficiently great to cause the expenditure of much valuable thought upon its mechanical and musical betterment4 ,the fact that these things happen should console anyone who has ever thought that the limit of mechanical excellence had been reached4 ,the designing of a pianoforte is art with a big ,a4 ,it demands of its practitioners the temperament of an artist and the skill of an excellent mechanic4 ,there is no greater pleasure and no nobler work than the construction of an instrument equipped to give forth lovely tone and to interpret the inspired works of the masters of music4 ,may the advancing years bring the pianoforte as much more of mechanical and musical excellence as the last two centuries have so richly imparted4 ,and now our task is done4 ,it has been a labor of love to place the results of long study and much practical experience before those to whom this exposition of the principles of pianoforte construction might be expected to appeal4 ,it has been far from easy to put into really intelligible and concise ,english an explanation of certain of these laws2 and if the reader finds here aught of vagueness or obscurity1 may he blame the subject rather than the author4 ,the latter has1 as best he might1 laid down the principles that underly the right building of the noblest musical instrument that man has yet devised4 ,and in the contemplation of these principles he may properly be content to leave his patient readers4 ,,theory ,,and ,,practice ,,of ,,pianoforte ,,building4 ,,appendix ,a4 ,,the ,,development ,,of ,,the ,,player-,,piano4 ,events are moving quickly in these latter days1 and the conservative pianoforte trade is feeling the effect of the extraordinarily active spirit of constructive commercialism that is so pronounced a feature of the contemporary industrial movement4 ,when the first chapters of the present work were in course of preparation1 some two years ago1 the pianoforte equipped with an interior playing mechanism was just beginning to be heard of2 to-day its manufacture and marketing are recognized features in the policy of nearly all pianoforte houses4 ,it would therefore be unwise to conclude the present treatise without certain observations on the player-piano question1 although a truly philosophic temper would probably prefer that some further time elapse before any feature of the player-piano problem be considered in a work of the same scope and character as this4 ,abandoning the strict scientific view of our duty in this matter1 however1 we may better adopt a more popular point d'appui and round off this work with a few observations on the more important and essential underlying problems connected with this new and remarkable movement in the pianoforte world4 ,had the exterior type of pianoforte playing device--the so-called cabinet-player1 in fact--remained alone and supreme in the territory that it first opened to exploration and development1 this work would contain no notice of any mechanism of the kind4 ,but since the movement has spread until it comprehends the pianoforte itself1 since1 in the nature of things1 such a development must profoundly affect the solution of the problems that confront the pianoforte maker in the construction of his instrument1 it seems to be not only natural1 but imperative1 that we should devote some space to certain notes on the player-piano problem and its relation to the application of such acoustical and mechanical principles as are germane to the theory of pianoforte construction4 ,we are under no obligation to delve into the history of these ingenious devices4 ,the plan of this work requires nothing of the sort4 ,we may say1 however1 that the first impetus towards the production of a piano playing mechanism came about through the success of the self-playing organ which began to appear about fifteen years ago4 ,meanwhile various inventors had experimented with electrical devices and had succeeded in producing a mechanism that could be placed within the case of the instrument without entailing any great distortion of form4 ,such devices1 however1 were1 with some exceptions1 exceedingly mechanical in effect1 and did little to show the possibility of adequately rendering pianoforte music through artificial means4 ,it was1 however1 through the successful development of mechanism for the automatic operation of organs that the true principles for piano-player construction began to come to light4 ,two leading manufacturers had both produced reed organs of a very superior kind1 equipped with mechanical playing devices4 ,the principle was pneumatic1 and was applied through the medium of compressed air4 ,the organs themselves were also operated on this principle1 this being a return to the old force bellows system1 adopted in the ,european harmonium1 and always used in connection with the pipe organ4 ,when developed to their highest point1 these pneumatic self-playing organs produced superior musical effects1 so that they became1 and still are1 well known and popular4 ,the latest styles1 indeed1 rival the orchestra in their versatility and coloring1 especially when operated by a skillful musician4 ,the pneumatic principle thus applied1 and the success of the attempts to adapt it to the organ1 led experimenters to emulate1 and if possible improve upon1 the early attempts at the practical manufacture of pianoforte-playing mechanism4 ,without going too much into details1 it may be recorded that the two concerns previously referred to were nearly ready in #ahif to come out with such an instrument1 and patents were granted in #ahig for a complete piano-player of the cabinet style1 attachable to any piano1 and easily detachable therefrom4 ,other patents soon followed1 and other manufacturers fell into line1 with the result that the great piano-player movement had soon begun in earnest4 ,the productions of the different firms1 of course1 varied in details1 but only two widely separated schools have developed1 and inasmuch as both of these employ the pneumatic principle1 which has triumphed over all others1 and is now adapted unanimously by manufacturers who desire to render possible an approximation to artistic rendition of pianoforte music1 it will be unnecessary to treat of any instruments constructed on other lines4 ,in the meantime it will be well to note that the above short sketch of the preliminary skirmishing1 as it were1 is intended to be nothing more than an outline1 as the policy adopted throughout this entire work has been to avoid the historical view-point1 as much as possible1 and to confine ourselves strictly to the business in hand2 namely1 constructional principles and their application4 ,the pneumatic principle has been adopted in all the piano-players that we have occasion to survey1 and its application has been in all cases essentially similar4 ,indeed1 the two schools of construction differ1 not in the application of the pneumatic principle1 but in certain details of construction1 which are important but not vital4 ,one general description will be quite sufficient to acquaint the reader with the make-up of these instruments1 and it will be easy to undertake any further explanations of important variations4 ,the underlying idea1 upon which the whole player is built1 may be described as arising from the knowledge that a bag or bellows of suitable material will collapse whenever the air is exhausted from it1 and become inflated again when the air is permitted to rush into it1 which happens as soon as the vacuum is destroyed4 ,now it is obvious that here1 in these two processes1 we have the possibility of producing a reciprocating motion1 and the value of this is evident when it is remembered that the process of pianoforte playing1 when reduced to its lowest terms1 is essentially the combination of the alternate manual motions required to depress and release a key4 ,consequently1 the matter of designing a pianoforte-playing machine is reduced to the problem of placing a bellows over a key1 or in mechanical connection with it1 in such a way that the inflation and deflation of the bellows will operate levers to depress and release the key4 ,thus far1 it may be understood1 we are dealing with elementary mechanical principles4 ,but the questions arising from consideration of the control of these bellows are far more delicate1 and require for their solution a high degree of mechanical talent4 ,let us see how the problem has been worked out4 ,a musical composition which is to be performed on the pianoforte by means of one of these 8players10 as they are called colloquially1 is first reduced to a series of perforations on a long sheet1 the perforations being of uniform width1 but varying in length according to the duration of the musical tone for which each stands4 ,the sheet is then wound upon a spool and is connected with motor mechanism which is adapted to draw it across a 8tracker-board0 pierced with holes1 each of which corresponds to some hole in the sheet4 ,the latter1 when so drawn across the plane of the 8tracker-board10 is wound up on another spool1 and the motor mechanism of the player is so arranged that the sheet can be re-wound on to its own spool when the whole composition has been played1 so that it may be withdrawn from the 8player10 and another substituted in its place4 ,the actual process of operation is as follows3 ,the 8player0 is provided with foot pedals1 which operate exhaust bellows1 and thus maintain a reservoir bellows in a state of exhaust1 on the same principle as in the reed organ4 ,as long as the exhaust bellows are operated1 and the reservoir is kept in a state of vacuum1 it is possible to maintain an 8exhaust chamber0 within the 8player0 also in a state of vacuum4 ,this exhaust chamber communicates with a 8diaphragm chamber10 in connection with the 8tracker-board0 hole1 and with an 8inflation and deflation channel0 in connection with the striking pneumatic or bellows which depresses the pianoforte key4 ,the connection with the 8diaphragm chamber0 is by means of a very small hole pierced in a leather diaphragm which is stretched between the 8exhaust chamber0 and the 8diaphragm chamber10 so that the latter will be in a state of partial vacuum4 ,resting on the leather diaphragm is a button1 attached to an upright spindle which stretches through an orifice into the inflation and deflation chamber1 and there operates a poppett valve which1 in one position of the spindle1 will close the chamber against the exhaust chest1 while opening itself and therefore also the pneumatic to the outer air1 and in another position will reverse the process1 opening the chamber to the power of the vacuum in the exhaust and simultaneously closing itself and therefore the pneumatic to the vacuum1 which will cause the latter to collapse1 and thus bring down the key4 ,now1 when a hole in the perforated sheet comes opposite a hole in the 8tracker-board10 an atmospheric communication is opened with the 8diaphragm chamber10 and air will immediately rush down into the 8diaphragm chamber0 and at once destroy the partial vacuum which existed there4 ,as a consequence of this1 the leather diaphragm will immediately rise to its fullest extent1 influenced by the vacuum in the chamber above it1 and will therefore push up the poppett valve4 ,this action will open communication between the exhaust and inflation and deflation chambers and will expose the latter to the vacuum1 while shutting off the outer air which has kept the pneumatic inflated4 ,thus the pneumatic will collapse1 and the piano key will be held down until the closing of the 8tracker-board0 hole once more restores the partial vacuum in the 8diaphragm chamber10 thus permitting the poppett valve to sink1 and reopening the connection between the pneumatic and the outer air1 which re-inflates it and releases the key4 ,as will have been anticipated1 there are endless small variations of detail in the construction of different 8players10 but they all work on the same principle1 and the above description will be sufficient to give an idea of what goes on inside the 8player0 when the perforated sheet is put into position and drawn over the 8tracker-board40 ,variations on the mechanical carrying out of these principles are dependent upon the ideas of the different makers4 ,it can easily be understood that there is plenty of room for endless changes in details1 and that every maker of 8players0 has his own special notions on the subject4 ,we have spoken above of the motor mechanism designed to move the perforated sheet across the 8tracker-board10 and to rewind it when required4 ,it is clear that such a motor device must be very sensitive to changes in speed control1 very light and very easily operated4 ,in the search for the ideal device manufacturers have gradually separated themselves into two schools of practice1 each being champions of one particular type of motor4 ,these two schools of opinion and practice have adopted respectively the pneumatic and the clock-work motors4 ,both have virtues2 neither are free from vices4 ,it is no part of our plan to enter into didactic discussion of the relative merits and demerits of the two styles1 but we shall confine ourselves to an exposition of the method whereby each is adapted to its required work1 and shall point out the more obvious of the good and bad features of both4 ,the pneumatic motor has the initial advantage of simplicity and lightness4 ,it consists of a number of bellows1 usually three or five1 which are arranged in series on a board and connected by passages with the exhaust chest4 ,they are adapted to be collapsed and inflated alternately by means of the exhaust from the bellows of the 8player10 and are governed by valves so arranged as to cause one bellows to be open to the atmospheric air1 and therefore inflated1 while the next to it is simultaneously closed to the atmospheric air and exposed to the vacuum from the wind-chest1 and therefore collapsed4 ,this alternate process produces a motion which can1 of course1 easily be transferred by means of connecting rods to a crank-shaft1 which by reciprocation produces a rotary motion1 and also permits the take-up spool of the 8player0 to be connected with it by suitable gearing4 ,the controlling valves are generally connected with the crank-shaft somewhat after the manner of the valves of a steam cylinder1 and are operated by the motion of the shaft through suitable connecting rods4 ,the reverse motion of the spool1 for rewinding1 is accomplished by gearing between the motor and spool1 and the reversing lever1 while operating this gear1 also closes the valve between the exhaust reservoir bellows and exhaust chamber so as to permit the full power of the exhaust to be exercised on the motor when the rewinding is required4 ,the speed control of the pneumatic motor is governed by another finger lever adapted to operate a valve which can entirely close the passage between the exhaust chest and motor board1 the gradual opening or closing of which increases or diminishes the power of the exhaust upon the motor bellows and hence the rapidity with which they collapse and reinflate4 ,this speed control combines simplicity and effectiveness4 ,in considering the less agreeable qualities of the pneumatic motor we have to note that a great deal of the alleged deficiency of the type arises from the fact that its operation depends upon the same agency as is employed for the striking pneumatics2 namely1 the exhaustion of air from the exhaust bellows reservoir4 ,this means1 of course1 that the striking pneumatics and the motor are artificially brought into relations which would never naturally subsist between them4 ,in consequence1 there is a continual tendency on the part of one of the elements to monopolize the power reserve1 to the detriment of the other4 ,thus1 a fortissimo passage will tend to use up so much power that the motor will be slowed down2 while1 contrariwise1 the latter1 when driven at its highest speed1 will take too much power from the pneumatics and prevent the expression of their highest dynamic forces4 ,here we touch upon the most serious defect of the pneumatic motor1 and while we find the practical workings of these devices quite excellent1 there is no doubt that they would be far more responsive and far lighter in operation if these fundamental defects did not exist4 ,the clock-work motor1 on the other hand1 is entirely separated from the striking mechanism1 except as far as it is sometimes connected with the pedals for the purpose of winding the spring4 ,even this1 however1 is not a real interference with the striking pneumatics4 ,the chief advantages of the clock-work motor are that it is built of steel and brass1 instead of wood and leather2 that it is independent of the rest of the player1 and therefore always self-contained and free from extraneous influences2 that rewinding is effected by the reserve power of the spring1 and that the use of the pedals as in the pneumatic motor1 is therefore not necessary4 ,its disadvantages1 as alleged by its critics1 may be considered as follows3 ,that it requires oiling and cleaning frequently1 and that if neglected will rapidly become impaired2 that it is sometimes slow in acceleration and retarding2 that it is heavy and complicated1 and that the winding1 when done by pedals1 is wasteful1 and when effected by a handle1 is tiresome4 ,the above tables of vices inherent in both types are by no means as terrible as they look1 however1 and experience seems to show that many of them do not appear in practical work4 ,on the whole1 the clock-work motor seems to have much in its favor1 although the question still remains open1 and time alone can show which is practically better4 ,it is neither necessary nor profitable to go into any considerable detail as to the pianoforte pedal operating devices1 the soft stops1 or other details of the sort4 ,we may better employ the space at our command in a short discussion of the movement which has resulted in incorporating the mechanism described above into the case of the pianoforte itself4 ,this movement is1 of course1 a natural outcome of the successful introduction of the exterior 8player40 ,the public soon began to find fault with the latter on account of the space it occupied1 and also because of the annoyance incidental to its removal from the instrument for manual playing4 ,it was not long before the makers of 8players0 were experimenting1 with a view to using the waste space in the upright pianoforte for the purpose of including the 8player0 therein4 ,the advantages of such a plan are obvious1 provided that the actual mechanical difficulties can be overcome4 ,these difficulties proved very stubborn at first1 and it is not to be supposed that all are entirely overcome1 even now4 ,it has been very hard1 indeed1 to arrange the mechanism in such a manner as to make all parts accessible for adjustment and repair4 ,the results of any neglect of this important requisite are very serious4 ,makers should bend their first energies to the removal of all difficulties incidental to the obtaining of access to the playing mechanism or to the rest of the pianoforte1 before they consider anything else4 ,for example1 it should be possible to remove the action or keys of the pianoforte without having to detach pipes and tubes4 ,nor should it be difficult to disconnect the pumping apparatus1 or some individual valve or pneumatic which may need attention4 ,again1 the manner in which the pneumatics strike the keys or action is very important4 ,the earlier player-pianos generally had the pneumatics placed below the key-bed1 so that they operated from the rear end of the latter1 striking them upwards4 ,this had the double disadvantage of inflicting a hard1 rigid kind of blow1 and of making the pneumatics very inaccessible4 ,a better plan has lately been devised1 which puts the pneumatics over the keys1 so that they operate at the front ends1 just back of the ivories4 ,some such method as this is excellent always1 since it permits a considerable concentration of the mechanism and a consequent curtailment of the inconveniently long tubes leading from the 8tracker-board0 to the valve chambers4 ,all these matters1 however1 are in process of practical development1 and the future holds the key to the ultimate solution of any such problems4 ,in considering the influence of the 8player0 mechanism upon the pianoforte itself1 we may note that the general adoption of these devices1 if it occurs1 will inevitably produce certain modifications in the action mechanism1 as well as in the general design4 ,there is no doubt that the ordinary action mechanism of the pianoforte will not prove strong enough to endure the furious onslaught of the 8player10 and it is questionable whether pianofortes constructed on the old plan will not more rapidly deteriorate when exposed to this wear and tear4 ,the precise direction in which this modification is likely to come may not now be accurately determined1 but it is probable that a general strengthening of centres and flanges will be the first result4 ,as for the distortion of the pianoforte case1 this1 as far as it now exists1 may very easily be corrected4 ,but it will not be easy to arrange the playing mechanism so as to avoid interference with the acoustical or mechanical forces of the pianoforte4 ,for one thing1 there is a great deal of machinery to put into a very small space1 and for another there are certain parts of the pianoforte that must under no circumstances be touched4 ,thus the sound-board1 the strings and the iron plate must be left severely alone4 ,but the elimination of the ,boston or double-rolling fall-board1 and its replacement by something that will take less room1 will provide a sufficient space to house the pneumatics and exhaust chamber above the keys4 ,this is where they ought to be1 and the only possible place where they can be reached without trouble or damage4 ,the pumping apparatus must be kept away from the sound-board1 and placed where it will do no harm2 under the key-bed1 necessarily1 but not so as to interfere with the piano pedals or the resonance apparatus4 ,some portion of the bottom frame can usually be eliminated with advantage1 and this will assist in providing the necessary space4 ,the position of the motor should be such that the minimum of waste occurs between the crank-shaft and the take-up spool4 ,thus1 if possible1 the motor ought to be above the key-bed4 ,if it be of the clock-work type1 it can hardly be placed anywhere else4 ,lastly1 the whole of the exterior apparatus1 such as levers1 pedals1 spool1 etc41 should be arranged to fold away or be covered up out of sight when the instrument is in use for manual playing4 ,while it has only been possible in this appendix to give the barest outline of the player-piano problem1 the reader is besought to recollect that the industry is still new1 and that the 8present state of the art0 hardly admits of any didactic assertions on principles of construction4 ,we do not even know1 today1 whether the pneumatic principle will continue to prevail1 or whether some new refinement of electric mechanism will not eventually surpass every device now known1 both in responsiveness and convenience4 ,,appendix ,b4 ,,the ,,small ,,grand4 ,it is a curious fact1 but none the less characteristic of that most curious of industries--the pianoforte craft--that in it the development hypothesis1 so familiar to all other branches of human endeavor here1 appears not to be fully applicable4 ,while the aim of the present treatise has been to systematize and codify1 as it were1 the laws that underly all right constructional methods1 we have been forced to recognize that there is no appearance of any accurate and uniform generalization which may be applicable to the future guidance of pianoforte builders in their efforts to attain to the greatest perfection in later types4 ,although we have succeeded in laying down the broad and universal principles that govern intelligent practice of the art1 yet we cannot fail to note that a progressive evolution is not yet possible4 ,that is to say1 there is no progressive synthesis in the art which shall carry us continually further from the original types1 so that the ancient models shall become in time quite unrecognizable in the light of modern improvement4 ,rather would it seem that the course of improvement is leading us back to reversions towards the original types1 and of this tendency the rise of the small grand pianoforte is one of the most striking illustrations4 ,it is not to be supposed that this reversionary movement is to be taken as implying a dissatisfaction with the methods that have grown up in the course of the last hundred years1 and the systematization of which has been our task in the present work2 it is rather that the tendency today is in the direction of utilizing the most modern methods in the resuscitation and further development of the type of pianoforte that was earliest in the field4 ,in other words1 as the reader well knows1 the last few years have seen a general tendency towards a revival of the grand1 in forms suitable for modern ways of life1 and with the advantages carried by the wealth of experience and practice on which the modern pianomaker can make unlimited drafts4 ,this resuscitation has not taken the form of any attempt to bring the large-sized concert instrument into more popular use1 but it has rather been a matter of evolving a new type out of the old1 and of developing this latter along comparatively original lines4 ,with the commercial success of such an experiment we are not here immediately concerned1 but we have great and lively interest in the question of its constructional value and in the possibilities that are implied in its future development4 ,without entering into wearisome detail1 it may be stated that the last five years have seen a most systematic attempt on the part of leading manufacturers to construct and popularize a very small style of grand pianoforte1 and to endow this new instrument1 as far as possible1 with the musical advantages possessed by the larger and older horizontal forms4 ,the dimensions of the 8small grand10 as it has come to be known1 range from a length of five feet to one of six1 with width in proportion1 and the smallest sizes are continually attracting greater attention on the part of experts4 ,the idea is to reduce the dimensions to the very lowest point compatible with something approaching to grand pianoforte tone1 and to make the general outline as beautiful to the eye as possible4 ,the latter of these desires is easier of consummation than the former1 and it has therefore appeared that some of the makers of these instruments have been somewhat apt to overlook truly musical results in deference to a public sentiment in favor of something that is graceful1 if nothing else4 ,in fact1 when considering the small grand we are obliged to note that it has been developed1 and is now being produced rather to appeal to that portion of the pianoforte-buying public that demands something for its homes more beautiful than the upright and less bulky than the large parlor or concert grand than in answer to any general cry for the better musical development of the instrument itself4 ,if we bear this fact in mind1 and its truth is obvious to the student of pianoforte history1 we can the more easily understand and appreciate the essential features of this latest development4 ,the small grand has been produced1 we repeat1 to please the public1 and the public at large is not exclusively composed of musicians4 ,but even while acknowledging the probability of this statement1 we need not conceal from ourselves that the small grand can thus fulfill a very useful function4 ,reduced to its lowest terms1 it remains a grand pianoforte1 with the action and touch so essentially associated with the horizontal form1 and so immeasurably superior to anything that is found in even the best uprights4 ,and here the small grand has an enormous advantage1 nor does it appear that its truly musical and tonal development need be permanently stationary1 if only the limitations of the instrument be appreciated1 and work on it be directed with especial reference to its own size1 and without dependence upon the traditions that have supported the building of larger forms4 ,in a word1 the builders of small grands have the opportunity1 if they care to avail themselves of it1 to produce a form of miniature horizontal pianoforte that shall possess all the advantages of the large concert instruments1 with the exception of the great tonal volume peculiar to the latter1 and none of the disadvantages of bulkiness and ungracefulness4 ,they can never hope to obtain the same tonal results from a #e-;foot as from a #i-;foot instrument2 but they have the opportunity to popularize a touch and technique that is impossible of achievement for players of the upright1 and a quality of tone that is equally unattainable on vertical instruments4 ,under all circumstances1 it must be borne in mind that the results of small grand building1 even when most carefully and skilfully executed1 are essentially different from anything that has yet been produced in the tonal development of the pianoforte1 and that no attempt to imitate the tonal properties of the large grand can be successful4 ,the action and the touch are fit subjects for this kind of imitation1 but such tonal quality as is susceptible of development is entirely original and indigenous to the miniature grand4 ,the only legitimate field of inquiry along these lines1 then1 is that which has reference to the development and constructional principles of the small grand considered as a distinct type1 and needing particular and definitely differentiated principles and methods4 ,assuming the correctness of these premises 7and their truth would appear to be obvious71 we have to ask ourselves what is the exact nature of the problem which is set for solution1 and wherein it differs from any that we have had to consider as yet4 ,bearing in mind that we are dealing with what is known as the 8small grand10 although it is marketed under various other names selected by different manufacturers1 we can state the constructional problem in fairly definite and exact terms4 ,it is required to build a pianoforte in horizontal form1 of which the extreme length shall preferably not exceed five feet and six inches1 and which shall be compensated for shortening by means of extra widening2 which shall have the lines of a larger grand1 refined to the highest degree1 and within which the greatest possible tonal value shall be contained4 ,viewed thus1 it appears that the principal factors to be considered are string-length and sound-board area4 ,it is obvious that the diminution of the former and restriction of the latter are inevitable2 and the net result must be seen in a radical alteration1 if not deterioration1 of the tonal property of the instrument4 ,it remains to be seen how we shall set about to transform this disadvantageous condition into one that shall work for us1 and in accordance with our desires4 ,in other words1 as we cannot get a sound-board containing1 say 8n0 square feet of superficial area into a case that only contains #c_/d 8n0 square feet of space1 we must resign ourselves to the inevitable1 and search for ways and means whereby the difficulty of putting into a quart bottle more than it will hold may be evaded1 if not explained away4 ,and first1 then1 let it be remembered that the only line where-from we can safely base any calculation is that which leads in the direction of a continual refinement of the means of applying sound-board construction to the instrument4 ,we must utilize every inch of the superficies2 we must discover and apply methods for opening up the vibratory area to the impressions received from the strings in a manner superior to that which has been deemed sufficient when space has been at a discount4 ,we must arrange bridges and bearing-bars so that the string-lengths may be stretched to the utmost1 and1 lastly1 we must use such minute care in the treatment of the hammer-striking line that the inevitable 8breaks0 in the tone shall be minimized4 ,the intelligent reader will not fail to observe that we have put forth here a tolerably difficult set of requirements4 ,but he will likewise be equally quick to note that ultimate success in small grand designing depends entirely upon the manner in which these conditions are met4 ,if they are slighted or slurred1 if the designer attempts to ignore them1 he will find that failure will surely follow4 ,on the other hand1 it would be too much to say that even the most faithful and conscientious effort applied to the elucidation of the problem will under all circumstances have the desired effect4 ,the conditions are unusual2 in some cases they do not admit of any direct and positive settlement4 ,but in so far as these conditions can be met1 in so far as they are susceptible of solution1 the designing of the small grand can properly be made successful4 ,it must be recollected that the 8striking-point0 of the hammers is a vitally important element in the success of pianoforte building4 ,it is the one factor that cannot be trifled with1 and in treating which there must be rigid adherence to rule4 ,now it is well known that the correct striking distance has been ascertained 7as shown in the body of this work7 to be at a point between one-seventh and one-ninth of the speaking length of the string1 the exact place for each string being calculated with reference to the actual speaking length4 ,as worked out in the best practice1 the shortest and highest pitched strings have their striking points at about one-tenth of the speaking lengths1 while the longer and lower pitched elements further down the scale are made to conform more closely to rule4 ,now it is obvious that the application of this law to the very much shortened strings of a small grand will result in distinctly unsatisfactory quantity and quality of tone4 ,but it will not do for us arbitrarily to change the actual striking point1 for that would change the position of the hammer line1 and experience has amply demonstrated that no such idea will work4 ,inasmuch1 therefore1 as we are estopped from interfering with the striking point1 as far as concerns the actual hammer line1 it becomes necessary to discover some means for obtaining a somewhat greater length of string in proportion to the dimensions of case4 ,careful measurement will show that the higher strings do not fall under the classification of 8dangerous40 ,it is only when we approach the point where the overstringing begins that the disadvantage of decreased case length becomes apparent4 ,the treble string-lengths at or near this place will be too great1 if carried out according to the well-known and practiced laws of scale designing2 while1 if they are unduly shortened1 the tensions and thicknesses will require to be submitted to such radical alteration as to make most unpleasant changes in the tonal quality and volume4 ,but while an absolute solution is out of the question1 there is no doubt that we are able to find a fairly satisfactory substitute4 ,there are two courses open to us4 ,we are not permitted to make any great change in the tension1 but1 within certain limits1 we may weight the string1 and we may even stretch out its length1 if we be very careful and watch out for every inch4 ,the first method must always be used with caution4 ,it is susceptible1 and very easily1 too1 of improper application1 and when abused becomes an enemy rather than a friend4 ,in fact1 the weighting of treble strings with iron or copper wire should be undertaken with the greatest caution1 and only indulged in when the designer is absolutely unable in any other manner to obtain a proper vibrating length4 ,the last two or three strings above the overstrung portion of the pianoforte may usually be wrapped without troublesome complications1 but under no circumstances should the highest of these have a frequency greater than #abh4 ,on the other side1 where the bass strings begin1 this condition does not apply1 for it is possible by means of suspension belly bridges1 to increase the actual speaking lengths several inches4 ,these suspension or extension bridges1 as they are called1 may also be used1 though with caution1 for the lowest treble strings4 ,we have never advocated the splitting up of bridges1 but there are cases1 such as these1 where unusual methods are quite unavoidable4 ,in the several ways thus sketched out1 the designer of small grands may do something to overcome the manifest difficulties of his task4 ,he may likewise take heart of grace when he approaches the matter of sound-board area1 for in treating the string-lengths there appears a partial solution of the latter problem4 ,in speaking of the use of suspension bridges we omitted to note that the position of these may be modified so as to give greater length to the speaking portions of the strings1 by increasing the obliquity of the angle of the overstringing4 ,of course1 this would be obvious1 but it is perhaps not quite so clear that such adaptation will result in an opening out of spaces on the sound-board that are usually left severely alone4 ,moreover1 if the necessary splitting up of the bridges be avoided by means of connecting strips of the same material1 it is clear that the opening up of the sound-board may thus be carried up to the highest possible value4 ,along such lines as these1 it would seem1 must the course of small grand designing be laid1 at least as far as concerns the vital elements of string-length and sound-board area4 ,there remains the question of the metal plate1 and this deserves separate treatment4 ,we have taken pains already to insist upon the necessity for compromise in the building of small grands4 ,regarding the iron plate1 we have to observe that great care must be taken to avoid undue massiveness1 for this will entirely spoil the tone quality1 as the other dimensions are not capable of supporting a large mass of metal without tonal deterioration4 ,on the other hand1 it is equally certain that we can afford to sacrifice nothing in the way of strength1 as we purpose to have the highest tensions and the greatest lengths possible within the space limitations of our instrument4 ,the ordinary form of plate1 copied from the large grand1 may very advantageously be modified by the adoption of a truss or arch construction1 which will enable a large amount of metal to be cut away from the treble sides without sacrificing any strength4 ,along such lines1 as we have already said1 the design of small grands must of necessity proceed4 ,we feel that it would not be improper to repeat our formerly expressed opinion as to the nature and functions of the small grand4 ,it has come into existence in answer to a public demand for something differentiated from the upright1 possessing great beauty of outline1 and yet adapted to the confined surroundings of contemporary domestic life4 ,it is not and cannot be a rival of larger horizontal forms2 it is physically estopped from the realization of such ambitions4 ,but it has a place in the economy of the musical world1 and such a place as nothing else would satisfactorily fill4 ,wielding the mighty influence of the name 8grand pianoforte0 and with the initial advantages over the upright that its form1 touch and action imply1 it would indeed be remarkable if the production of the small grand did not become more and more a part of the regular routine of all pianoforte manufacturing establishments4 ,the design of its case will always1 surely1 be above criticism4 ,it is out of our province to enlarge upon the details of case architecture1 but it may be pointed out that such details as graceful trusses1 well-designed lyre1 and carefully molded curves do much to make or mar the future of a small grand1 entirely apart from the excellence of its scale4 ,the general effect should be that of lightness and grace2 a touch of frivolity even will not be out of place4 ,the little instrument is likely to find its way into homes where money is not always an object1 and where the ability to enjoy the best that life contains is usually present4 ,the designer will make no mistake if he keeps this in mind4 ,,unusual ,,methods ,,of ,,construction4 ,as the reader is well aware1 the greater part of the present work has been devoted to an exposition of the broad principles underlying all right methods of pianoforte construction4 ,we have devoted little space therefore to the elaboration of features without this classification1 or to the consideration even of such ideas and methods as do not fall within the lines laid down in the theoretical portion of this treatise4 ,busily occupied1 as we have been1 with the development of acoustical and mechanical principles and their application along the most obvious and natural lines1 we have been forced to neglect one of the most interesting studies that can be taken up by the investigator2 to wit3 the ideas1 inventions and devices that have sprung from the brains of the numerous mechanical and acoustical geniuses who have illuminated the course of pianoforte history and development4 ,many of these ideas have proved impracticable under the stress of use2 others1 again1 have been shown to be commercially unprofitable2 a still larger number have flourished during a longer or shorter period or have been neglected by all others than their original inventors4 ,the true place for a study of these neglected children of enthusiastic1 if not always practical1 brains is in a history of the pianoforte rather than in a technical treatise on construction4 ,,the ,,end4 ,the following corrections have been made to printer's errors in this text3 ,page ,correction ,location in ,text #bj ,handel to ,hndel time of ,hndel2 #bj pianforte to pianoforte which the grand pianoforte #bg begin to begun now about to be begun4 #cb closing parenthisis inserted staff in the bass clef7 #cb ,b-sharp to ,b-,natural note #ae in harmonic series table #da ,b double ,f-flat to ,b double flat minor sixths table #db clasisfied to classified ,these sounds are thus classified3 #di of to or imply a length or height of #ec asumption to assumption made on the assumption #fh veenered to veneered turning out of such veneered cases1 #gg missing comma inserted 7more elaborate than the other two71 #hf homogenous to homogeneous plate as homogeneous with the sides #hg is to it ,in fact it occupies #ii ,,repetiton to ,,repetition ,,double ,,repetition ,,action #aji fough to fought already been fought out #aac any one to anyone through by anyone who hopes #abc synchromize to synchronize will synchronize with each other1 #abd mesontonic to mesotonic that the mesotonic system1 #abe period added in the ratio #abif3abej4 #aca turned to tuned conversely1 if the tuned notes #adh closing quote added vacuum in the 8diaphragm chamber10 #aed ,wtihout to ,without ,without entering into wearisome detail1 #aed possesed to possessed musical advantages possessed #aee circustances to circumstances ,under all circumstances1