---------------------------------------- -------- ,note3 ,bold surrounding text4 ,italics surrounding text4 ---------------------------------------- -------- ,,essentials ,,of ,,music ,,theory ,,elementary ,,by ,,carl ,e4 ,,gardner ,,author ,,of ,,music ,,composition ,illustration ,,new ,,york ,,carl ,,fischer #aiab ,,copyright1 #aiab1 ,,by ,,carl ,,fischer ,international ,copyright ,secured ,,preface4 ,the primary object in the following pages is to supply the teacher and student with a text book to accompany the work on instrumental or vocal technic4 ,because of the great amount of time required to obtain proficient technic1 text books are often neglected1 and1 if exhaustive1 are usually ignored4 ,brevity and conciseness characterize this volume and it is planned to meet the needs of the busy teacher and student4 ,many pupils may not see the importance of some of the following text1 such as the research for theoretical keys2 but the results thus obtained are nothing more than the natural outcome of simple mathematical reasoning1 and are inevitable if the -structure- of the scales is understood4 ,pupils should be impressed with the structure of scales rather than be taught their keys and signatures by rote4 ,rote methods have little to recommend them in modern pedagogical ideals1 and are used principally in teaching the young4 ,the lack of knowledge of the -whys- and -wherefores- of scales1 intervals1 and chords among instrumentalists and singers is appalling1 and is due partly to the neglect of text books and partly to incompetent teachers4 ,a further object of the text is to offer a course of preparation for the study of harmony1 composition1 and appreciation4 ,music ,appreciation1 as a cultural course of study1 is growing in popularity and large enthusiastic classes in this subject are to be found in all our colleges4 ,these students are frequently handicapped by poor preparation in the essential rudiments of music such as are treated in this volume4 ,the author's gratitude for valuable aid1 criticisms1 and suggestions is due his wife1 ,marion ,dillon ,gardner1 and his sisters1 ,mabel ,gardner ,bankart and ,lena ,gardner ,lewis4 ,,contents4 ,,page ,,preface iii ,i4 ,,rhythm3 ,,note ,,values3 ,,time ,,signatures3 ,,tempo #c ,,ii4 ,,theory ,,of ,,scales 7,major and ,minor7 #aj ,the ,major ,scale #aa ,the ,minor ,scale #ba ,,iii4 ,,intervals ,,and ,,chord ,,building #cb ,inversion of ,intervals #cf ,chord ,construction #ch ,inversion of ,triads #dj ,the ,seventh ,chord #da ,inversion of ,seventh ,chords #dc ,,iv4 ,,epitomized ,,acoustics #dg ,v4 ,,ear ,,training #ea ,the ,normal ,intervals of the ,major ,scale #eb ,the ,normal ,intervals of the ,minor ,scale #ee ,altered ,intervals #ef ,arpeggio ,chords #fj ,two ,voiced ,chords #fa ,the ,four ,voiced ,chord #fc ,,essentials ,,of ,,music ,,theory ,,chapter ,i4 ,,rhythm4 ,sound is the effect produced by propagated atmospheric waves which affect the sense of hearing4 ,irregular impulses1 propagated through the air1 produce noise4 ,regular impulses produce musical -tone-4 ,the duration of tone is indicated by symbols called -notes-4 ,following is a list of notes3-- ,double whole note or ,breve ,double whole note or -,breve-4 ,semibreve ,whole note or -,semibreve-4 ,minim ,half note or -,minim-4 ,quarter ,quarter note or -,crotchet-4 ,eighth ,eighth note or -,quaver-4 ,semiquaver ,sixteenth note or -,semiquaver-4 ,demisemiquaver ,thirty-second note or -,demisemiquaver-4 ,occasionally the sixty-fourth note 7,sixty-fourth note7 is used4 ,following is a table of the relative value of notes3-- ,illustration ,the -breve- or double whole note is not given in this table as it is but seldom used4 ,the value of it is twice the whole note1 four times the half1 etc4 ,the whole note is represented by an open oval2 the half1 by an open oval and stem2 the quarter1 by a closed head and stem2 the eighth note is the same as the quarter with a flag2 the sixteenth1 the same with two flags2 the thirty-second1 the same with three flags4 ,as is seen in the table1 the eighth1 sixteenth and thirty-second notes are often grouped when more than one occurs in succession4 ,suspension of tone is indicated by symbols called -rests-4 ,each note has its equivalent rest4 ,following is a list of rests3-- ,double whole rest ,double whole rest4 ,whole rest ,whole rest4 ,half rest ,half rest4 ,quarter rest ,quarter rest4 ,eighth rest ,eighth rest4 ,sixteenth rest ,sixteenth rest4 ,thirty-second rest ,thirty-second rest4 ,the rate of vibration is called -pitch-4 ,rapid vibrations produce high 7shrill7 tones4 ,slow vibrations produce low tones4 ,more complete information on sound1 tone and pitch is given later under the heading ,acoustics4 ,the notes are written on the staff which consists of five horizontal lines together with their spaces4 ,the duration of a tone is determined by the note used2 the pitch1 by the note's position on the staff4 ,a dot placed after a note or rest adds one half its value4 ,a tie is a curved line connecting two notes of the same pitch4 ,examples of dots and ties3-- ,semibreve with ,augmentation dot equals ,semibreve tied with ,minim or #a #a_/b4 dotted half note equals half note tied to quarter note or #a_/b #a_/d4 dotted quarter note equals quarter note tied to eight note or #a_/d #a_/h4 etc41 etc4 ,a double dot adds one half and one fourth its value1 thus3-- double dotted whole note equals tied notes2 tied whole1 half and quarter note or #a #a_/b #a_/d4 double dotted half note equals tied notes2 tied half1 quarter and eighth note or #a_/b #a_/d #a_/h4 double dotted quarter note equals music symbol2 tied quarter1 eighth and sixteenth notes or #a_/d #a_/h #a_/af4 etc41 etc4 ,bars are lines drawn vertically across the staff dividing music into -measures-4 ,the contents of the measure is determined by the fraction at the beginning4 ,the denominator of the fraction shows the kind of notes1 and the numerator1 the number of that kind contained in a measure4 ,each measure must contain the number and kind of notes or rests designated by the fraction1 or their equivalents4 -,artificial groups- are groups of notes played and summed in other than their fractional value4 ,the most common artificial groups are the -triplet- and -sextuplet-4 ,a triplet is a group of three notes played in the time and summed in the value of two of its own kind4 ,a sextuplet is a group of six notes played in the time and summed in the value of four of its own kind4 ,a group of five notes is played in the time and summed in the value of four of its own kind4 ,a group of seven notes is played in the time and summed in the value of six of its own kind4 ,occasionally a group of two notes occurs4 ,this group differs from other artificial groups inasmuch as it is played more slowly than the tempo notes4 ,a group of two notes is played in the time and summed in the value of three of its own kind4 ,artificial groups are designated by a curved line over or under the notes with a figure showing the kind of group1 thus3-- triplet ,illustration3 triplet sextuplet ,illustration3 sextuplet group of two notes ,illustration3 #b-note group ,in counting music1 it is customary to give as many counts to each measure as the numerator of the fraction indicates4 ,each of these counts is called a -pulse-4 ,pulses should occur regularly unless otherwise marked4 ,irregularities in the occurrence of pulses are marked in various ways4 ,the -ritardando-1 the -hold- 7,fermata71 and the -accelerando- are the principal marks of irregularities4 ,the -ritardando- 7abbreviated -ritard4- or -rit4-7 means to lessen the speed1 the -accelerando- 7abbreviated -accel4-7 to quicken the speed1 and the -hold- 7,fermata7 to hold the note1 over or under which it is placed1 as long as musical taste dictates4 ,this occurrence of pulses is called -rhythm-4 ,the most common rhythms are #d_/d or common time1 #c_/d1 #b_/d1 #f_/h1 #c_/h1 #d_/h1 #i_/h1 #ab_/h1 and #b_/b or #b_/b alla breve also called -alla breve-4 ,other rhythms not so common are #f_/d1 #h_/d1 #a_/d1 #b_/h1 #a_/b1 #f_/b1 #c_/b1 #d_/b1 #c_/af1 and less often #a_/a1 #e_/d1 #e_/h and #e_/af1 etc4 ,on the first pulse of all kinds of rhythm is a primary accent called -thesis-4 ,secondary accents1 called -arsis-1 occur in #d_/d on the third count and in #f_/h on the fourth count4 ,these natural accents give a swing to the music4 ,they can only be displaced or overshadowed by artificial accents which are designated in various ways4 ,the most common artificial accents are the -forzando- 7designated thus3 ,sforzato1 ,marcato1 or -fz-71 meaning a sudden strong accent to the note or chord over or under which it is placed2 the -rinforzando- 7which is not quite so marked as the -forzando-72 the -staccato- 7designated by a dot placed over or under the note or chord7 which makes the note thus indicated short and crisp1 and the -syncopation-1 which is a form of rhythm displacing the natural accent by the note's entrance on an unaccented part of the measure and its sustentation through the pulse4 ,the rapidity of the occurrence of pulses is called -tempo-1 which is indicated at the beginning of a movement by ,italian words usually1 the most common of which are as follows3-- -,grave-1 slow and solemn 7the slowest tempo74 -,largo-1 slow1 a trifle faster than ,grave4 -,larghetto-1 a trifle faster than ,largo4 -,adagio-1 a trifle faster than ,larghetto4 -,lento-1 slow4 -,andante-1 moderately slow4 -,andantino-1 translated literally means slower than ,andante1 but it is more often used incorrectly meaning faster than ,andante4 -,moderato-1 moderate2 the mediate between fast and slow4 -,allegretto-1 cheerful4 -,allegro-1 quick4 -,vivo-1 quick4 -,presto-1 very quick4 ,to many of the above words is added the ending -issimo- which gives the word to which it is added its superlative degree4 ,other terms are oftentimes combined with the above words to characterize the movement4 ,every pupil should have a dictionary of musical terms for constant reference4 ,the majority of piano students have an absolute disregard for note values and tempo marks which are so important that the pupils fail to gain any good results from their study unless they understand and pay strict attention to these marks4 ,the incompetency of so many teachers is somewhat responsible for this state of affairs1 but the majority of piano studies and methods is more largely responsible4 ,in second grade studies1 there are many which1 if written in a judicious manner1 would be excellent second grade work1 but when played as they are written and as their tempo mark demands require a virtuoso to execute them correctly4 ,these studies have led pupils to playing -allegro- movements in -largo- tempo4 ,at the end of a week's practice a -moderato tempo- may be the result4 ,continued enforced disregard can produce nothing but habitual disregard for tempo marks4 ,the teacher should constantly remind the student of these facts and1 in as far as possible1 omit such studies as cannot be played -a tempo-4 ,many exercises may be rewritten in a playable manner by the teacher1 who1 by so doing1 would not only impress the pupil with the importance of tempo marks1 but would develop his ability to read from manuscript1 an ability which1 unfortunately1 is almost universally lacking in pupils4 ,,exercises4 ,,oral ,,and ,,written4 #a4 ,what is sound8 #b4 ,tell the difference between noise and musical tone4 #c4 ,what is a note8 #d4 ,describe the most common notes4 #e4 ,write a table of the relative value of notes commencing with the whole note4 #f4 ,write a table of the relative value of notes commencing with the dotted half note4 #g4 ,describe the rests4 #h4 ,for each dotted note1 show its equivalent by two tied notes4 #i4 ,for each double dotted note1 show its equivalent by three tied notes4 #aj4 ,describe measure and bar and upon what the measure's contents depends4 #aa4 ,describe the manner of counting the different rhythms4 #ab4 ,name the marks that designate irregularities in rhythms and describe the character of each mark4 #ac4 ,describe the natural accent4 #ad4 ,name the most common artificial accents and describe the character of each4 #ae4 ,what is meant by tempo8 #af4 ,name and define twelve different tempo marks4 #ag4 ,explain and notate artificial groups4 ,,chapter ,,ii4 ,,theory ,,of ,,scales4 ,,major ,,and ,,minor4 ,as stated before 7,chapter ,i1 page #d71 the rate of vibration is called pitch4 ,tones vibrating an equal number of times produce an -unison- which is a perfect concordance and is pleasant to the ear4 ,equally as pleasant to the ear is the ratio of two vibrations against one4 ,a tone vibrating twice as fast as a given tone is called the given tone's -octave-4 ,between these two tones many tones may be found4 ,for example1 suppose a note vibrating two hundred times in a second1 its octave would vibrate four hundred times in the second4 ,between these two tones there would be 7avoiding fractions which would produce more different pitches7 one hundred and ninety-nine tones of different pitch4 ,the ear is incapable of locating all these tones and modern custom has divided all octaves into twelve parts1 each part being called a half step or1 literally incorrect1 a -semi-tone-4 ,these semi-tones sounded successively upwards or downwards from any tone to its octave produce the -chromatic scale-4,a ,footnote ,a3 ,all references to scales1 intervals and enharmonic changes treat of the tempered scale4 ,a -diatonic scale- is a progression from any tone to its octave in which certain chromatic steps are omitted4 ,in modern music there are three forms of diatonic scales1 called3-- #a4 ,major4 #b4 ,harmonic minor4 #c4 ,melodic minor4 ,all three forms have eight tones1 the eighth being the octave of the first and is given the same name4 ,the tones of the diatonic scale are named in four different ways3-- #a4 by numerals 7,arabic and ,roman71 #b4 by the first seven letters of the alphabet1 #c4 by the ,italian syllables 7-do-1 -re-1 -mi-1 -fa-1 -sol-1 -la-1 -si-17 and #d4 by the theory names 7-tonic-1 -supertonic-1 -mediant-1 -subdominant-1 -dominant-1 -submediant- and -subtonic-74 -,the key-tone is the tone from which a diatonic scale is built4- ,the numerical system is a movable system which means that #a is always the key-tone4 ,the theory name system is a movable system1 the tonic being always the key-tone or #a4 ,the alphabet system is a fixed system which means that a letter is always the same tone or its octave4 ,the ,italian system is treated as both a fixed system and a movable system4 ,this book treats of the movable -do-1 -do- always being the key-tone1 #a and tonic4 ,,the ,,major ,,scale4 ,a major scale is a progression from any tone to its octave in which chromatic steps are omitted between #a and #b1--b and #c1--d and #e1--e and #f1--f and #g2 from #c to #d and from #g to #h half steps are made4 ,following is a diagram of a two octave keyboard3-- ,illustration3 ,c ,d ,f ,g ,a ,c ,d ,f ,g ,a or or or or or or or or or or ,d ,e ,g ,a ,b ,d ,e ,g ,a ,b ,c ,d ,e ,f ,g ,a ,b ,c ,d ,e ,f ,g ,a ,b ,c ,the keyboard shows white and black keys4 ,the black keys are in groups of two and three4 ,as can be seen in the diagram1 the white key next to the left of the group of two black keys is -c-4 ,the white keys in order to the right of -c- are respectively -d-1 -e-1 -f-1 -g-1 -a- and -b-4 ,following -b- is a repetition of -c- at the distance of an octave4 ,notice that between -e- and -f- there is no black key as is also the case between -b- and -c-4 ,in these two cases1 where no black key separates the white keys1 the white keys are one semi-tone apart4 ,two white keys separated by a black key are one whole step apart4 ,a black key is at the distance of a semi-tone from an adjoining white key4 ,the black keys derive their letter names from the white keys4 ,a black key is named from either of the white keys between which it is situated4 ,the black key between -c- and -d- is named -c sharp- 77 or -d flat- 774 ,starting at -c- and sounding the white keys in order to the right as far as the octave produces the ascending major scale of -,c-2 sounding in order to the left produces the descending major scale of -,c-4 ,notice that no black keys are necessary in the case of the -,c- major scale1 the whole and half steps being in their proper places2 namely1 whole steps between #a and #b1 #b and #c1 #d and #e1 #e and #f1 #f and #g1 and half steps between #c and #d and between #g and #h4 ,the student must constantly keep in mind the order of whole and half steps in all scales explained4 ,in each scale explained the letters will be numbered and a curved line will connect those figures representing tones one half step apart4 ,all major keys except -,c- major require one or more black keys4 ,the number of sharps or flats required for a key is placed at the beginning of the staff and this is called the signature4 ,a sharp 77 placed before a note raises the tone one half step and a flat 77 lowers a tone one half step4 ,the sharp keys will be considered first and a sharp major scale will be built from each of the twelve tones4 99 99 99 99 99 ,rule #a4 ,the ,fifth of a ,scale is the ,tonic 7or #a7 of the ,scale having the next ,number of ,sharps4 -,c- has no sharps1 the fifth of -,c- is -g- and therefore by following the rule1 we find that -,g- has one sharp4 ,the scale of -,g- is as follows3-- ,g a b c d e f ,g #a #b #cd #e #f #gh ,notice that the seventh of the scale is a black key4 ,the fifth of -,g- is -d- and has two sharps3-- ,d e f g a b c ,d #a #b #cd #e #f #gh ,notice that -f- remains sharped and the added sharp is the seventh of the scale4 ,this is always the case1 the added sharp is the seventh of the new scale4 ,the fifth of -,d- is -a- and has three sharps3-- ,a b c d e f g ,a #a #b #cd #e #f #gh ,the fifth of -,a- is -e- and has four sharps3-- ,e f g a b c d ,e #a #b #cd #e #f #gh ,the fifth of -,e- is -b- and has five sharps3-- ,b c d e f g a ,b #a #b #cd #e #f #gh ,the fifth of -,b- is -f- and has six sharps3-- ,f g a b c d e ,f #a #b #cd #e #f #gh ,notice that -e- is not a black key but the white key which has been previously considered as -f-4 ,it must be called -e- to retain the alphabetical order4 ,the fifth of -,f- is -c- and has seven sharps3-- ,c d e f g a b ,c #a #b #cd #e #f #gh ,in this scale all the notes are sharped4 ,the -b- as well as the -e- is a white key4 ,the fifth of -,c- is -g- and has eight sharps4 ,this key necessitates one double sharp and -f- is double sharped4 ,the double sharps are added in the same order that the single sharps are4 ,the double sharp 7designated thus3 x7 raises a tone one whole step4 ,g a b c d e fx ,g #a #b #cd #e #f #gh ,the fifth of -,g- is -d- and has nine sharps 7two double sharps1 -f- and -c-73-- ,d e fx g a b cx ,d #a #b #cd #e #f #gh ,the fifth of -,d- is -a- and has ten sharps 7three double sharps1 -f-1 -c- and -g-73-- ,a b cx d e fx gx ,a #a #b #cd #e #f #gh ,the fifth of -,a- is -e- and has eleven sharps 7four double sharps1 -f-1 -c-1 -g- and -d-73-- ,e fx gx a b cx dx ,e #a #b #cd #e #f #gh ,the fifth of -,e- is -b- and has twelve sharps 7five double sharps1 -f-1 -c-1 -g-1 -d- and -a-73-- ,b cx dx e fx gx ax ,b #a #b #cd #e #f #gh -,b- has taken us back to our starting key called by a different name4 ,all twelve keys have now been named with their sharp signatures4 ,to continue counting five would take us over the same keys called by different names4 ,the student is advised to do a little of this for mental discipline4 ,if this is done beyond fourteen sharps1 it will be necessary to add triple sharps4 ,of course1 triple sharps are never used in musical notation and such a research would be entirely arithmetical4 ,the order of the letters in the sharp signature which follows should be committed to memory3-- ,f ,c ,g ,d ,a ,e ,b4 ,all keys having one double sharp or more would be difficult to read1 and so instead of using the sharp signatures on such keys1 the flat signatures are used4 ,all twelve keys with their flat signatures will now be given4 99 99 99 99 99 ,rule #b4 ,the ,fourth of a ,scale is the ,tonic of the ,scale having the ,next ,number of ,flats4 -,c- has no flats2 the fourth of -,c- is -f-2 therefore1 by following the rule1 we find that -,f- has one flat3-- ,f g a b c d e ,f #a #b #cd #e #f #gh ,notice the fourth of the scale is a black key4 ,the fourth of -,f- is -b- and has two flats3-- ,b c d e f g a ,b #a #b #cd #e #f #gh ,notice that the -b- remains flat and that the added flat is the fourth of the scale4 ,this is always the case--the added flat is the fourth of the new scale4 ,the fourth of -,b- is -e- and has three flats3-- ,e f g a b c d ,e #a #b #cd #e #f #gh ,the fourth of -,e- is -a- and has four flats3-- ,a b c d e f g ,a #a #b #cd #e #f #gh ,the fourth of -,a- is -d- and has five flats3-- ,d e f g a b c ,d #a #b #cd #e #f #gh ,the fourth of -,d- is -g- and has six flats3-- ,g a b c d e f ,g #a #b #cd #e #f #gh ,the fourth of ,g is -c- and has seven flats3-- ,c d e f g a b ,c #a #b #cd #e #f #gh ,the fourth of -,c- is -f- and has eight flats4 ,this key necessitates one double flat and -b- has the double flat4 ,the double flats are added in the same order that the single flats are4 ,the double flat 7designated3 7 lowers a tone one whole step4 ,f g a b c d e ,f #a #b #cd #e #f #gh ,the fourth of -,f- is -b- and has nine flats 7two double flats1 -b-and -e-73-- ,b c d e f g a ,b #a #b #cd #e #f #gh ,the fourth of -,b- is -e- and has ten flats 7three double flats1 -b-1 -e- and -a-73-- ,e f g a b c d ,e #a #b #cd #e #f #gh ,the fourth of -,e- is -a- and has eleven flats 7four double flats1 -b-1 -e-1 -a- and -d-73-- ,a b c d e f g ,a #a #b #cd #e #f #gh ,the fourth of -,a- is -d- and has twelve flats 7five double flats1 -b-1 -e-1 -a-1 -d-1 and -g-73-- ,d e f g a b1 c ,d #a #b #cd #e #f #gh ,d has taken us back to our starting key called by a different name as was the case when we had twelve sharps4 ,to continue counting four would take us over the same keys called by different names4 ,as was advised in the sharp keys1 this research should be continued by the student4 ,if more than fourteen flats are considered1 it will be necessary to add triple flats4 ,the order of the letters in the flat signature which follows should be committed to memory3-- ,b ,e ,a ,d ,g ,c ,f4 ,by comparing the order of the letters in the flat signature with that of the sharp signature1 it will be seen that the order of the letters in the flat signature is that of the sharp signature reversed4 ,notice that each key has more than one name2 for example1 the white key next to the left of the group of two black keys has been called -,c-1 -,d- and -,b-4 99 99 99 99 99 ,rule #c4 ,an ,enharmonic ,change is the ,change of a ,name of a ,tone without ,altering its ,pitch4 ,two or more scales played from the same pitched tone but called by different names are called -enharmonic scales-4 ,in practice1,b fifteen major scales are used1 three of which are enharmonic scales4 ,following is a list of the major scales used in practice together with their signatures3-- ,c no sharps or flats ,g #a sharp 7f7 ,d #b sharps 7f and c7 ,a #c sharps 7f1 c and g7 ,e #d sharps 7f1 c1 g and d7 ,f #a flat 7b7 ,b #b flats 7b and e7 ,e #c flats 7b1 e and a7 ,a #d flats 7b1 e1 a and d7 ,d #e flats 7b1 e1 a1 d and g74 enharmonical to ,c4 ,g #f flats 7b1 e1 a1 d1 g and c7 enharmonical to ,f ,c #g flats 7b1 e1 a1 d1 g1 c and f7 enharmonical to ,b ,b #e sharps 7f1 c1 g1 d and a7 ,f #f sharps 7f1 c1 g1 d1 a and e7 ,c #g sharps 7f1 c1 g1 d1 a1 e and b7 ,footnote ,b3 ,theoretical keys appear in many compositions during transitions1 but they are not obvious 7except by analysis7 because of the fact that their signatures do not appear4 ,the enharmonic keys used in practice are3-- ,b 7five sharps7 enharmonical to ,c 7seven flats7 ,f 7six sharps7 enharmonical to ,g 7six flats7 ,c 7seven sharps7 enharmonical to ,d 7five flats7 99 99 99 99 99 ,rule #d4 ,the ,sum of the ,enharmonic ,flat and ,sharp ,signatures is ,twelve4 ,notice that this is true in the above three keys4 ,by this rule the theoretical keys 7that is1 those having more than seven sharps or flats7 are easily found4 ,for example3--to find the key having eleven flats2 the key having eleven flats is enharmonical to the key having one sharp 7#aa #a #ab74 -,g- has one sharp and changing its name to the enharmonic flat key1 we obtain -,a- which1 therefore1 has eleven flats4 ,this process should be applied to all keys having eight to eleven sharps and eight to eleven flats inclusive4 ,as stated in the first chapter1 the pitch of a tone is determined by the note's position on the staff4 ,the staff of five lines with its spaces allows of the designation of but one octave and one step1 whereas1 in modern music1 there is need of the notation of at least six octaves4 ,this necessitates the use of symbols called -clefs-1 and lines added to the staff called ledger lines4 ,ledger lines are short lines parallel to the staff lines added above or below the staff lines4 ,there are three clefs3-- #a4 the treble or ,g clef1 #b4 the tenor1 movable or ,c clef1 #c4 the bass or ,f clef4 ,middle -,c- is the tone which all voices can sing4 ,it is in the lower register of the high female voice and in the upper register of the low male voice4 ,the -,g clef- 7treble clef7 is for high voices or instruments4 ,its symbol shows the position of the -,g- next above middle -,c- thus3 ,illustration3 music4 ,middle -,c- is found on the first ledger line below the -,g clef-1 thus3 ,illustration3 music4 ,the -tenor- or -,c clef- is for the use of medium voices or instruments4 ,its symbol shows the position of middle -,c-4 ,this clef is movable and may place middle -,c- on any line or space of the staff4 ,its most common position is on the third line of the staff1 thus3 ,illustration3 music4 ,it is not uncommon1 however1 to find it on the second or fourth line4 ,for vocal music it is often written in the third space4 ,the -bass- or -,f clef- is for the use of low voices or instruments4 ,its symbol shows the position of the -,f- next below middle -,c-1 thus3 ,illustration3 music4 ,middle -,c- is found on the first ledger line above the -,f clef-1 thus3 ,illustration3 music4 ,the notation in the treble clef of all the major scales used in practice follows3 ,scale of ,c ,illustration3 ,music3 ,c d e f g a b ,c ,scale of ,g ,illustration3 ,music3 ,g a b c d e f ,g ,scale of ,d ,illustration3 ,music3 ,d e f g a b c ,d ,scale of ,a ,illustration3 ,music3 ,a b c d e f g ,a ,scale of ,e ,illustration3 ,music3 ,e f g a b c d ,e ,scale of ,b ,illustration3 ,music3 ,b c d e f g a ,b ,scale of ,f ,illustration3 ,music3 ,f g a b c d e ,f ,scale of ,c ,illustration3 ,music3 ,c d e f g a b ,c ,scale of ,f ,illustration3 ,music3 ,f g a b d e ,f ,scale of ,b ,illustration3 ,music3 ,b c d e f g a ,b ,scale of ,e ,illustration3 ,music3 ,e f g a b c d ,e ,scale of ,a ,illustration3 ,music3 ,a b c d e f g ,a ,scale of ,d ,illustration3 ,music3 ,d e f g a b c ,d ,scale of ,g ,illustration3 ,music3 ,g a b c d e f ,g ,scale of ,c ,illustration3 ,music3 ,c d e f g a b ,c ,,the ,,minor ,,scale4 ,there are two forms of minor scales1 -harmonic- and -melodic-1 both differing in construction from the major form4 ,the minor key having no sharps or flats in the signature is -a-4 ,starting at -a- and sounding the seven white keys in order to the right produces a form of scale with whole steps between #a and #b1 #c and #d1 #d and #e1 #f and #g1 #g and #h1 and half steps between #b and #c and between #e and #f4 ,this scale is unsatisfactory to the ear as its subtonic is not a -leading tone-4 ,the effect of a leading tone should be urgent1 restless1 and demand its tonic in order to obtain a restful effect4 ,this urgent effect can only be obtained by the subtonic being one half step below the tonic4 ,this may be obtained by simply raising the seventh one semi-tone in the above scale formation and thus is produced the so-called -harmonic minor- scale4 ,the symbols for raising a note are the -sharp- 771 the -double sharp- 7x71 and the -cancel- 77 7also called -natural-7 when placed before a note that has been previously affected by a flat4 ,the symbols for lowering a note are the -flat- 771 the -double flat- 771 and the -cancel- when placed before a note that has been previously affected by a sharp4 ,by these statements it can be seen that the cancel 77 is both a lowering and a raising symbol4 ,the -cancel- lowers a tone when it cancels a sharp and raises a tone when it cancels a flat4 -,the harmonic minor scale- is formed by whole steps between #a and #b1--c and #d1--d and #e1--;half steps between #b and #c1--e and #f1--g and #h1 and an interval of one and one-half steps 7called an augmented step7 between #f and #g4 ,in demonstrating the minor keys1 a curved line will be used to connect those figures representing tones one half step apart and a bracket to connect those figures representing tones an augmented step apart4 ,the key of -a minor- 7harmonic form7 is as follows3-- a b c d e f g a #a #b #cd #efgh ,the student will notice that this scale has one sharp 7-g-74 ,nevertheless1 the -a minor- is the minor key which has neither sharps nor flats in its signature4 ,the raised seventh of all minor keys is -never- present in the signature1 but appears as -accidental-4 ,when a sharp1 double sharp1 flat1 double flat or cancel1 which is not present in the signature1 is placed before a note1 it is called an accidental4 ,if the raised seventh were present in the signature1 uniform signatures in the minor would be impossible4 ,it may also be remarked here that the seventh is not always raised during the course of a composition and is necessarily raised only when the composer desires the listener's ear to come at rest on the tonic1 in which case the tonic must be preceded by the raised seventh1 if the subtonic precedes the tonic in the melody or harmony4 ,the same rules 7pages #ac and #ae7 used in the major for finding the key having the next number of sharps and the key having the next number of flats are applicable in the minor4 ,the order of the letters in both the sharp and flat signatures is the same in the minor as in the major4 -,a- minor has no sharps1 the fifth of -a- is -e- and has one sharp 7-f-73-- e f g a b c d e #a #bc #d #efg #h ,the fifth of -e- is -b- and has two sharps 7-f- and -c-73-- b c d e f g a b #a #bc #d #ef #gh ,the fifth of -b- is -f- and has three sharps 7-f-1 -c- and -g-73-- f g a b c d e f #a #b #c #d #ef #g #h ,the fifth of -f- is -c- and has four sharps 7-f-1 -c-1 -g- and -d-73-- c d e f g a b c #a #b #c #d #e #fg #h ,the fifth of -c- is -g- and has five sharps 7-f-1 -c-1 -g-1 -d- and -a-73-- g a b c d e fx g #a #b #c #d #ef #g #h ,the student will notice that in this key1 -f- is double sharped4 -,f- is sharped in the signature1 but because the subtonic requires raising1 -f- demands a double sharp4 ,the fifth of -g- is -d- and has six sharps 7-f-1 -c-1 -g-1 -d-1 -a- and -e-73-- d e f g a b cx d #a #b #c #d #e #fg #h ,the fifth of -d- is -a- and has seven sharps 7-f-1 -c-1 -g-1 -d-1 -a-1 -e- and -b-73-- a b c d e f gx a #a #b #c #d #e #f #gh ,the minor keys having more than seven sharps should be found by the student and submitted to the teacher for correction4 ,for the sake of brevity1 they are not given here1 but the student should be thoroughly capable1 by this time1 of finding them all4 -,a- minor has no flats1 the fourth of -a- is -d- and has one flat 7-b-73-- d e f g a b c d #a #bc #d #ef #gh ,the fourth of -d- is -g- and has two flats 7-b- and -e-73-- g a b c d e f g #a #b #c #d #ef #gh ,the fourth of -g- is -c- and has three flats 7-b-1 -e- and -a-73-- c d e f g a b c #a #bc #d #ef #gh ,the student will notice a contradiction in the above scale2 it is stated that -c- has three flats and in the example1 -b- is cancelled4 ,this cancel1 however1 appears as -accidental- 7the raised seventh7 and must be a flat in the signature4 ,the fourth of -c- is -f- and has four flats 7-b-1 -e-1 -a- and -d-73-- f g a b c d e f #a #bc #d #ef #g #h ,the fourth of -f- is -b- and has five flats 7-b-1 -e-1 -a-1 -d- and -g-73-- b c d e f g a b #a #b #c #d #ef #gh ,the fourth of -b- is -e- and has six flats 7-b-1 -e-1 -a-1 -d-1 -g- and -c-73-- e f g a b c d e #a #bc #d #e #f #g #h ,the fourth of -e- is -a- and has seven flats 7-b-1 -e-1 -a-1 -d-1 -g-1 -c- and -f-73-- a b c d e f g a #a #b #c #d #e #f #g #h ,the student should find the minor keys having more than seven flats4 ,the harmonic minor scale is awkward in formation on account of the augmented second step between steps six and seven4 ,all augmented intervals sound harsh and are difficult to sing tunefully4 ,for this reason1 another form of minor scale is sometimes used which eliminates the augmented second step4 ,this form is called -melodic minor- and is used1 as its name implies1 only for melodic purposes4 ,it defies harmonization for the obvious reason that its ascending form differs from its descending form4 -,the melodic minor scale- has the sixth as well as the seventh raised by -accidental- in ascending1 but in descending1 both the sixth and seventh are restored4 ,the ascending form has whole steps between #a and #b1--c and #d1--d and #e1--e and #f1--f and #g1 and half steps between #b and #c and between #g and #h4 ,the descending form has its half steps between #f and #e and between #c and #b4 ,notice that the descending form is as its signature dictates4 raised raised ,ascending3--#a #bc #d #e #f #gh ,descending3--#h #g #fe #d #c #b #a ,the ascending form of the melodic minor is nearly the same as the major scale1 and for this reason it is best not to retain the raised sixth and seventh in descending4 ,the subtonic in a descending scale does not lead 7progress7 to the tonic and therefore need not necessarily be situated one half step below the tonic4 ,any minor key is called the relative of the major key having the same signature2 therefore1 the relative minor of -,c- major is -a-,c as they both have neither sharps nor flats4 ,footnote ,c3 ,capital letters are used to designate major keys and small letters to designate minor keys4 99 99 99 99 99 ,rule #e4 ,the ,relative ,minor is found on the ,sixth of the ,major ,scale4 99 99 99 99 99 ,rule #f4 ,the ,relative ,major is found on the ,third of the ,minor ,scale4 ,some writers have called the -relative- minor -parallel- minor1 using -relative- and -parallel- synonymously4 ,this is a usage to be regretted as it causes considerable confusion4 ,by most writers1 the parallel minor is treated as the scale commencing on the same key-note as the major and will thus be treated in this book1 therefore3-- the relative minor of ,c is -a-2 the parallel minor of ,c is -c-4 ,the parallel minor scale has three more flats or three less sharps in its signature than the major scale4 ,in other words1 by lowering steps #c1 #f and #g of the major scale one semi-tone1 the signature of the parallel minor is obtained4 ,the notation in the treble clef of all the minor scales 7harmonic and melodic7 follows3-- ,scale of a ,illustration3 music ,harmonic ,scale of a ,illustration3 music ,melodic ,scale of e ,illustration3 music ,harmonic ,scale of e ,illustration3 music ,melodic ,scale of b ,illustration3 music ,harmonic ,scale of b ,illustration3 music ,melodic ,scale of f ,illustration3 music ,harmonic ,scale of f ,illustration3 music ,melodic ,scale of c ,illustration3 music ,harmonic ,scale of c ,illustration3 music ,melodic ,scale of g ,illustration3 music ,harmonic ,scale of g ,illustration3 music ,melodic ,scale of d ,illustration3 music ,harmonic ,scale of d ,illustration3 music ,melodic ,scale of a ,illustration3 music ,harmonic ,scale of a ,illustration3 music ,melodic ,scale of d ,illustration3 music ,harmonic ,scale of d ,illustration3 music ,melodic ,scale of g ,illustration3 music ,harmonic ,scale of g ,illustration3 music ,melodic ,scale of c ,illustration3 music ,harmonic ,scale of c ,illustration3 music ,melodic ,scale of f ,illustration3 music ,harmonic ,scale of f ,illustration3 music ,melodic ,scale of b ,illustration3 music ,harmonic ,scale of b ,illustration3 music ,melodic ,scale of e ,illustration3 music ,harmonic ,scale of e ,illustration3 music ,melodic ,scale of a ,illustration3 music ,harmonic ,scale of a ,illustration3 music ,melodic ,,exercises ,,oral ,,and ,,written #a4 ,into how many parts does modern custom divide an octave8 #b4 ,what is each part called8 #c4 ,what is the difference between a chromatic scale and a diatonic scale8 #d4 ,how many forms of diatonic scales are there and what are their names8 #e4 ,name and define the four ways in which the tones of the diatonic scales are named4 #f4 ,what is the key-tone8 #g4 ,describe the movable and fixed systems4 #h4 ,describe the major scale4 #i4 ,describe the effect of a sharp2 of a double sharp2 of a flat2 of a double flat2 of a cancel4 #aj4 ,state the rule for finding the key having the next number of sharps and the rule for finding the key having the next number of flats4 #aa4 ,write on the staff1 using the treble clef1 all the major keys to eleven sharps and eleven flats4 ,write several scales 7the teacher deciding the number7 using the bass and tenor clefs4 7,show by curved line those notes situated one semi-tone apart47 #ab4 ,what is the order of the letters in the sharp signature8 ,in the flat signature8 #ac4 ,what is meant by -enharmonic8- #ad4 ,what are the -enharmonic- scales used in practice8 #ae4 ,give -enharmonic- letter names for each of the twelve keys4 #af4 ,what is the sum of sharp and flat signatures of enharmonic keys8 #ag4 ,by the use of this enharmonic sum1 find all the theoretical keys4 #ah4 ,what is the construction of the harmonic minor scale8 ,of the melodic minor8 #ai4 ,write on the staff all the minor scales 7both harmonic and melodic7 to eleven sharps and eleven flats1 letting the teacher determine which clef or clefs to use4 #bj4 ,what is the reason for raising the seventh in harmonic minor8 #ba4 ,what is the reason for raising the sixth in melodic minor8 #bb4 ,why does the descending form of melodic minor differ from the ascending form8 #bc4 ,why does not the raised sixth or seventh appear in the signature8 #bd4 ,what is an accidental8 #be4 ,what is the -relative- minor and how is it found8 #bf4 ,what is the -parallel- minor and how does its signature differ from its parallel major8 ,n4 ,b4 ,before proceeding to the next chapter all these exercises should be properly answered and corrected by the teacher4 ,,chapter ,,iii4 ,,intervals ,,and ,,introduction ,,to ,,chord ,,building4 ,an interval is the distance between two tones2 intervals are named by the ordinals4 ,the number of letters comprised in the notation of two tones determines the ordinal name of the interval4 ,example3 ,illustration3 music -c- to -d- is an interval of a second because two letters are comprised4 ,it makes no difference whether or not either or both of the above tones is affected by an accidental1 the interval still comprises two letters and is a second4 ,reckoning from the tonic of the major scale to each degree of the scale produces the following intervals3-- #hth or prime4 #bnd #crd #dth #eth #fth #gth octave #ith ,illustration3 music prime4 #bnd #crd #dth #eth #fth #gth #hth or #ith octave ,the interval of the ninth is often called a second1 the octave not being considered4 ,these intervals are the normal intervals of the major scale4 ,these normal intervals are qualified in two ways4 ,the prime1 fourth1 fifth and octave are called perfect4 ,the second1 third1 sixth and seventh are called -major2- thus3-- ,illustration3 music perf4 maj4 maj4 perf4 perf4 maj4 maj4 perf4 maj4 prime #bnd #crd #dth #eth #fth #gth octave #ith ,all intervals should be reckoned from the lower note1 which is considered a major key-note4 ,if the upper note is in the major scale of the lower note1 the interval is normal2 that is1 either perfect or major4 ,if the upper note is not in the major scale of the lower note1 the interval is a derivative interval4 ,the derivative intervals are called -minor-1 -diminished- and -augmented-4 ,a minor interval is derived from a major interval and is one semi-tone smaller4 ,by lowering the upper tone of any major interval one half step or by raising the lower tone of any major interval one half step 7not altering the letter name in either case7 a minor interval is formed1 thus3-- ,illustration3 minor #bnd music ,illustration3 minor #crd music ,illustration3 minor #fth music ,illustration3 minor #gth music etc4 ,a diminished interval is one half step smaller than a minor or a perfect interval4 ,by lowering the upper tone of any minor or any perfect interval one half step1 or by raising the lower tone of any minor or any perfect interval one half step 7not altering the letter name in either case7 a diminished interval is formed1 thus3-- ,illustration3 dim4 dim4 dim4 dim4 dim4 dim4 dim4 #bnd #crd #dth #eth #fth #gth #hth music etc4 ,the tones of the diminished second are the same pitch1 but must be called a second because two letters are comprised4 ,the diminished prime is possible melodically1 but harmonically1 only in theory4 ,it is ,illustration3 music4 ,an augmented interval is one half step larger than a major or a perfect interval4 ,by raising the upper tone of any major or perfect interval one half step1 or by lowering the lower tone of any major or perfect interval one half step 7not altering the letter name in either case7 an augmented interval is formed1 thus3-- ,illustration3 aug4 aug4 aug4 aug4 aug4 aug4 aug4 aug4 prime #bnd #crd #dth #eth #fth #gth #hth music etc4 ,notice that the tones of the augmented seventh are the same pitch1 but must be called a seventh as seven letters are comprised4 ,the following intervals are the same in sound1 but not in name3-- perfect prime sounds the same as diminished #bnd augmented prime minor #bnd diminished prime minor #bnd major #bnd diminished #crd minor #crd augmented #bnd major #crd diminished #dth perfect #dth augmented #crd augmented #dth diminished #eth perfect #eth diminished #fth minor #fth augmented #eth major #fth diminished #gth minor #gth augmented #fth major #gth diminished #hth perfect octave augmented #gth ,from the preceding list the following rule is apparent3-- 99 99 99 99 99 ,rule #g4 ,by ,changing ,enharmonically ,either or ,both of the ,tones of an ,interval1 a ,different ,interval is ,obtained ,which ,sounds the ,same as the ,original ,interval4 ,the distance in semi-tones of all the intervals to an octave is as follows3-- prime unison comprises #a letter augmented prime #a semi-tone #a diminished #bnd unison #b letters minor #bnd #a semi-tone #b major #bnd #b semi-tones #b augmented #bnd #c #b diminished #crd #b #c minor #crd #c #c major #crd #d #c augmented #crd #e #c diminished #dth #d #d perfect #dth #e #d augmented #dth #f #d diminished #eth #f #e perfect #eth #g #e augmented #eth #h #e diminished #fth #g #f minor #fth #h #f major #fth #i #f augmented #fth #aj #f diminished #gth #i #g minor #gth #aj #g major #gth #aa #g augmented #gth #ab #g diminished #hth #aa #h perfect #hth #ab #h ,a quicker and better method of determining an interval than by committing to memory the above table is to consider the lower note the tonic of the major scale4 ,if the upper note is in the major scale of the lower note1 the interval is normal 7major or perfect74 ,after a little practice the number of letters in an interval can be determined at a glance4 ,if the upper note is not in the major scale of the lower note the interval is derivative and is determined by the information heretofore given4 ,,inversion ,,of ,,intervals4 ,intervals are said to be inverted when the lower note of the original interval is placed an octave higher1 thereby becoming the upper note of the interval thus formed4 ,example3 the inversion of ,illustration3 music is ,illustration3 music4 ,the same letters are in both intervals1 but the first interval is a third and the inverted interval is a sixth4 99 99 99 99 99 ,rule #h4 ,the ,sum of an ,interval and ,its ,inversion is ,nine4 ,the above rule1 therefore1 gives the following inversions3-- a prime inverts to an octave 7#a #h #i7 a second a seventh 7#b #g #i7 a third a sixth 7#c #f #i7 a fourth a fifth 7#d #e #i7 a fifth a fourth 7#e #d #i7 a sixth a third 7#f #c #i7 a seventh a second 7#g #b #i7 an octave a prime 7#h #a #i7 ,to find to what intervals ninths1 tenths1 elevenths1 twelfths1 etc41 invert1 consider them respectively as seconds1 thirds1 fourths1 fifths1 etc41 and consider the lower note placed two octaves higher instead of one octave4 ,qualifications invert in the following manner3-- -major- intervals invert to -minor- intervals -minor- -major- -perfect- -perfect- -diminished- -augmented- -augmented- -diminished- ,by the use of the above table and rule #h1 all inversions may be determined4 ,examples3-- major minor #bnd #gth ,illustration3 music inverts to ,illustration3 music major minor #fth #crd ,illustration3 music ,illustration3 music perf4 perf4 prime #hth ,illustration3 music ,illustration3 music perf4 perf4 #dth #eth ,illustration3 music ,illustration3 music aug4 dim4 #dth #eth ,illustration3 music ,illustration3 music dim4 aug4 #gth #bnd ,illustration3 music ,illustration3 music etc4 etc4 ,the -prime- is also called an -unison-1 but in speaking of intervals1 it should always be called a -prime-4 ,correctly speaking1 a -perfect prime- is not an interval1 but in the theory of music it is so called4 ,there is good reason for making this error1 but none for calling a -diminished prime- a -diminished unison-4 ,notice that the -diminished second- as well as the -perfect prime- is an -unison-4 ,intervals are considered both harmonically and melodically1 or in other words1 both when sounded together or separately4 ,in either case1 the lower note is the one from which to determine the interval4 ,,chord ,,construction4 ,a chord is a combination of two or more tones sounded simultaneously4 ,all chords are constructed in -thirds-4 ,the -fundamental tone- of a chord is the tone on which the chord is constructed4 ,a chord of three tones is a -triad- which consists of a -fundamental- together with its third and its fifth4 ,triads are divided into two classes1 -independent- and -dependent-4 ,the independent triads have no dissonant intervals and may end a composition4 ,the dependent chords have one or more dissonant intervals and are restless chords and demand another chord to follow4 ,the progression of a dependent chord to an independent chord1 thereby obtaining a restful effect1 is called -resolution-4 ,there are two kinds of independent triads1 -major- and -minor-4 -,a major triad- consists of the fundamental1 the -major- third1 and the -perfect- fifth4 ,example3-- ,illustration3 music4 -,a minor triad- consists of the fundamental1 the -minor- third1 and the -perfect- fifth4 ,example3-- ,illustration3 music4 ,if the fifth of a triad is augmented or diminished1 the triad is a dependent4 ,dependent triads are found constructed on the subtonic of major keys2 on the subtonic1 supertonic1 and mediant of the minor keys4 ,the triad on the mediant of the minor key is an augmented triad and the first three mentioned triads are diminished4 ,music written for four voices necessitates the doubling of one of the factors of the triad4 ,any factor of the triad may be doubled4 ,the factor most frequently doubled is the fundamental in the octave1 double octave1 or unison4 ,the four voices are -soprano- 7high female voice71 -alto- 7low female voice71 -tenor- 7high male voice71 and -bass- 7low male voice74 ,chords are figured under the bass by ,roman numerals4 ,large numerals designate -major- triads2 small numerals designate -minor- triads2 large numerals with the mark 77 affixed designate augmented triads2 small numerals with a cipher affixed designate diminished triads4 ,the notation of the triads on each degree of the major and minor scales follows3-- ,illustration3 ,major ,mode4 ,n4,b4 music ,i ,,ii ,,iii ,,iv ,v ,,vi ,,vii ,illustration3 ,minor ,mode4 music ,i ,,ii ,,iii ,,iv ,v ,,vi ,,vii ,n4 ,b4 ,although doubled in the above examples1 the fundamental of the subtonic triad is seldom doubled in four voice writing and if doubled1 a bad progression results in many cases4 ,the three upper voices in a fundamental chord may be arranged in a different manner3-- ,with the fundamental in the soprano3-- ,illustration3 music ,c ,i4 ,with the third in the soprano3-- ,illustration3 music ,c ,i4 ,if the three upper voices do not exceed the compass of an octave1 the chord is said to be in close position4 ,if the three upper voices exceed the compass of an octave1 the chord is said to be in open position4 ,,inversion ,,of ,,triads4 ,a chord is inverted when a factor other than the fundamental is in the bass4 ,the first inversion of the triad is where we have the third in the bass4 ,it is called the chord of the sixth1 because the fundamental is the sixth of the bass4 ,this chord is figured by a small ,arabic figure 77 over the bass note1 the ,roman numeral under the bass showing the fundamental4 ,examples3-- ,illustration3 doubled fundamental music3 ,c ,i ,illustration3 doubled third music3 ,c ,i ,the second inversion of the triad has the fifth in the bass and is called the chord of the sixth and fourth1 or six-four chord1 because the fundamental is the fourth of the bass4 ,this chord is figured by the small ,arabic figures 7#f_/d7 over the bass1 the ,roman numeral under the bass showing the fundamental4 ,examples3-- ,illustration3 doubled fifth music3 #f_/d1 ,c ,i ,illustration3 doubled fundamental music3 #f_/d1 ,c ,i ,,the ,,seventh ,,chord4 ,the seventh chord is obtained by adding the seventh of the fundamental to any triad4 ,a seventh chord may be formed on each degree of the major and minor scales4 ,it is figured with the ,roman numerals below the bass and a small ,arabic 7#g7 over the bass4 ,the notation of the seventh chords on each degree of the major and minor scales follows3-- ,illustration3 ,c ,major4 music #g #g #g #g #g #g #g ,i ,,ii ,,iii ,,iv ,v ,,vi ,,vii ,illustration3 a ,minor4 music #g #g #g #g #g #g #g ,i ,,ii ,,iii ,,iv ,v ,,vi ,,vii ,the tonic and subdominant of the major mode and the submediant of the minor mode are formed with the major triad and the major seventh4 ,the dominant seventh in both modes is formed with the major triad and the minor seventh4 ,the seventh chords on ,,ii1 ,,iii and ,,vi in the major mode and on ,,iv of the minor mode are formed with the minor triad and the minor seventh4 ,the seventh chords on ,,vii in the major mode and on ,,ii in the minor mode are formed with the diminished triad and the minor seventh4 ,the subtonic seventh chord in the minor mode is called the -diminished seventh- and is formed with the diminished triad and the diminished seventh4 ,the seventh chord on the mediant in the minor mode is formed with the augmented triad and the major seventh4 ,the seventh chord on the tonic of the minor mode is formed with the minor triad and the major seventh4 ,in four voice writing1 all the seventh chords with the exception of those on the subtonic of both modes are often written without the fifth and with the doubled fundamental4 ,all seventh chords are dependent chords and their natural resolution is to the chord the fundamental of which is situated a fourth above or a fifth below the fundamental of the seventh chord4 ,this progression is called cadencing resolution4 ,the subtonic seventh chord of both modes may also naturally resolve to the tonic4 ,the most important seventh chord is the dominant1 which resolves to the tonic4 ,this progression is called the -authentic close-4 ,another method of ending a composition is by the -plagal close- which is a progression from subdominant harmony 7triad7 to tonic4 ,the plagal close is preceded by the authentic close and is also called the -after cadence- and the -,amen cadence-4 ,,inversion ,,of ,,seventh ,,chords4 ,the first inversion of the seventh chord is called the chord of the fifth and sixth 7six-five chord74 ,the chord is figured by the ,roman numeral below the bass note and the ,arabic figures 7#f_/e7 over the bass4 ,example3-- ,illustration3 music #f_/e ,c ,v ,the second inversion is called the chord of the third1 fourth and sixth 7four-three chord74 ,it is figured by the ,roman numeral below the bass and the ,arabic figures 7#f_/d_/c7 or simply 7#d_/c7 over the bass4 ,example3-- ,illustration3 ,music #d_/c ,c ,v ,the third inversion is called the chord of the second and fourth4 ,it is figured by the ,roman numeral below the bass and the ,arabic figures 7#f_/d_/b71 7#d_/b71 or simply 7#b7 over the bass4 ,example3-- ,illustration3 ,music #b ,c ,v ,the study of chord progression1 altered chords1 melody writing1 passing tones1 etc41 belongs properly to the study of harmony and counterpoint which is not the subject of this volume4 ,,exercises4 ,,oral ,,and ,,written4 #a4 ,what is an interval8 #b4 ,how are intervals named8 #c4 ,what are the normal intervals8 #d4 ,qualify the derived intervals2 from what is each derived8 #e4 ,notate all the normal intervals and all the derivative intervals4 #f4 ,name all the following intervals3-- 7,accidentals affect only those notes before which they are placed47 ,illustration3 music #g4 ,name several intervals 7the teacher to determine the number7 having different names1 but sounding the same4 #h4 ,what is the sum of inversions8 #i4 ,state the manner in which qualifications invert4 #aj4 ,invert all the intervals given in exercise #f4 #aa4 ,notate and figure all the triads in several different major and minor keys4 ,which are dependent and which are independent8 #ab4 ,describe a dependent triad4 #ac4 ,describe open and close position4 #ad4 ,notate and figure several sixth chords2 several six-four chords4 #ae4 ,notate and figure all the seventh chords in several different major and minor keys4 #af4 ,what is the most important seventh chord8 #ag4 ,what is the authentic close8 #ah4 ,what is the plagal close8 #ai4 ,notate and figure a six-five dominant chord in several major and minor keys4 #bj4 ,notate and figure a four-three dominant chord in several major and minor keys4 #ba4 ,notate and figure a four-two dominant chord in several major and minor keys4 #bb4 ,choose some standard chorals 7,bach's are advised7 and analyze the chords therein4 ,,chapter ,,iv4 ,,epitomized ,,acoustics4 ,the science of sound1 including its cause and effect and the manner1 velocity1 and intensity of its conveyance through different media1 is called -acoustics-4 ,the medium through which sound is most commonly propagated is air4 ,through this medium1 at a temperature of #cb ,fahrenheit1 sound travels at a rate of #ajij feet per second4 ,the quality and intensity of sound do not alter the rate of speed4 ,if this were not true1 ensemble music would be impossible4 ,intensity of sound is greater in condensed air2 velocity of sound is greater in a warm temperature4 ,many experiments have been made to determine the velocity of sound1 the most reliable of which vary not over seven feet per second4 ,the average of six of the best experiments1 made in the early part of the nineteenth century1 is #ajhi4g feet per second at #cb ,fahrenheit4 ,ten hundred and ninety feet per second is the rate now generally adopted4 ,wind and temperature are the only circumstances affecting the velocity of sound in the air to any extent4 ,sound travels about four times faster through water than through air1 and about ten times faster through solids such as metals and wood than through air4 ,a sudden displacement of the molecules of a medium produces sound which travels in waves at an equal velocity in all directions4 ,an idea of the manner in which sound waves travel may be obtained by throwing a stone in water2 small waves are propagated from the point of impact which1 if the water be still1 spread equally in all directions1 but if it be running water1 the waves extend a greater distance down stream than up stream4 ,the effect of wind on sound waves may be compared to the effect of running water on the waves propagated by the impact of the stone4 ,musical tone is produced by regular vibrations2 noise by irregular vibrations4 ,the tones of the tempered chromatic scale have the following number of vibrations per second3-- ,middle c #beh4f c or d #bgd4j d #bij4c d or e #cjg4f e #cbe4i f #cde4b f or g #cfe4h g #chg4e g or a #daj4e a #dce4j a or b #dfj4h b #dhh4b ,the preceding figures represent the vibrations of the ,international ,pitch which was adopted by the ,piano ,manufacturers' meeting in #ahia4 ,a is the standard pitch having #dce double vibrations per second at a temperature of #fh ,fahrenheit4 ,many pitches have prevailed in different countries at different times4 ,at the time of ,handel and ,mozart1 the pitch was lower 7#dbb4e and #dba4f74 ,england has had the pitch run as high #ded4g and the ,united ,states as high as #dfj4h4 ,sounds vibrating below a certain number lose the character of musical tones as do those vibrating above a certain number4 ,great discrepancies of opinion exist among theorists on this subject4 ,savart claims the lowest audible sound has eight vibrations per second2 ,helmholtz claims that there is no definite pitch of sounds having less than forty vibrations per second2 ,herr ,appum claims to hear fifteen vibrations by the use of specially loaded tongues in reed pipes4 ,he claims the character of tone commences at twenty vibrations1 but the musical character of bass tones does not exist until frequencies exceed twenty-four vibrations per second4 ,on the subject of the audibility of acute sounds1 opinions are advanced ranging from #f1djj to #cf1jjj vibrations per second4 ,the limits of the human voices are tabulated below3-- ,bass ,e #ha4e ,d #bij4c ,baritone ,f #hf4c ,f #cfe4h ,tenor ,a #ajh4g ,a #dce4j ,contralto ,e #afc4j ,f #fij4e ,mezzo ,soprano ,f #agb4f ,a #hgj4j ,soprano ,a #bag4e ,c #ajcd4f ,occasionally there are exceptional voices having a wider range than the above scale indicates4 ,ratio of ,intervals3-- ,octave #a-- #b ,perfect fifth #b-- #c ,perfect fourth #c-- #d ,major third #d-- #e ,minor third #e-- #f ,major sixth #c-- #e ,minor sixth #e-- #h ,major second #h-- #i ,minor second #ae--af ,major seventh #h--ae ,minor seventh #i--af ,each tone generates over tones called -harmonics-4 ,these -harmonics- are the octave1 the twelfth 7perfect fifth71 the seventeenth 7major third71 the twenty-first 7minor seventh7 and the twenty-third 7minor ninth74 ,other -harmonics- than the above exist but are not used at the present time in chord construction4 ,the old theorists treated chords of the eleventh and thirteenth1 but modern theorists treat these intervals as suspensions1 anticipations1 etc4,d ,the origin of chord construction may be seen from these -harmonics-4 ,these over tones1 generated from a fundamental1 are the pure 7untempered7 intervals4 ,the tempered intervals1 with the exception of the octave1 are slightly out of tune but not enough so to shock the ear4 ,footnote ,d3 ,composers of the present day often use these intervals as chord factors4 ,the pure 7untempered7 scale of ,c has the following number of vibrations per second3-- ,middle c #bfa4j d #bic4f e #cbf4b f #cdh4j g #cia4e a #dce4j b #dhi4c ,an entire volume would be necessary to explain completely the science of acoustics4 ,all ambitious students should consult books on acoustics4 ,the author recommends the books on sound by the following writers3-- ,appum ,g4 ,b4 ,airy ,pietro ,blaserno ,helmholtz ,pole ,benjamin ,peirce ,rodolphe ,radau ,savart ,tyndall ,j4 ,august ,zahn ,,chapter ,v4 ,,ear ,,training4 ,a person with an untrained ear can appreciate music comparatively little1 even though he is well educated in the theory of music4 ,absolute pitch is the ability to recognize and intonate any tone indicated4 ,very few persons possess naturally absolute pitch1 but it may be acquired by a systematic study of ear training4 ,relative pitch is the ability to recognize a tone by comparison with a known tone4 ,advancement in relative pitch eventually leads to the attainment of absolute pitch4 ,in practicing ear training1 only a few minutes at a sitting are advised4 ,too much time at once devoted to this practice tires the ear and does more harm than good4 ,on the other hand1 these sittings should be many each day4 ,students who do not have a teacher daily1 should have a member of the household play the exercises in ear training and correct the mistakes4 ,if no member of the household is musical1 the student should co-operate with another student4 ,each exercise should be thoroughly learned before proceeding to the following exercise4 ,it may be recognizable and properly intonated at once or it may take several sittings4 ,the pitch ,a at #dce is the standard for orchestral tuning and is recommended to the student for a fundamental4 ,the student should carry upon his person a tuning fork of this pitch and sound it as often as an opportunity permits1 and thereby fix this fundamental thoroughly in his mind4 ,eventually1 the student will recognize this pitch whenever he hears it4 ,other tones will be recognizable by comparison with this fundamental4 ,any other pitch for a fundamental may be chosen with equally good results4 ,the argument is in favor of ,a because of its use in orchestral tuning4 ,many systems of ear training1 which produce the desired results1 exist4 ,the following system has been found the most satisfactory by the author4,e ,deviations from and additions to this system do no harm and are advisable in certain individual cases4 ,footnote ,e3 ,many young children find difficulty in intonating small intervals and it is necessary in such cases to commence with large intervals and work toward the smaller intervals4 ,the ,italian syllables should be used in singing the exercises4 ,movable -do- is advised4 ,any instrument may be used by the teacher or co-operator to play the exercises4 ,for low voices1 the exercises should be played two octaves lower than indicated1 and for medium voices1 one octave lower4 ,the teacher1 after having played an exercise1 should explain the interval or intervals therein4 ,the student should sing the exercise first with the instrument and then without4 ,each exercise should be faultlessly intonated before proceeding to the following exercise4 ,,group ,i4 ,,the ,,normal ,,intervals ,,of ,,the ,,major ,,scale4 #a4 ,major scale3-- ,illustration3 music #b4 ,all intervals of the major scale3-- ,illustration3 music #c4 ,tonic triad3-- ,illustration3 music #d4 ,perfect fifth3-- music ,the teacher should use various rhythms besides those given4 #e4 ,perfect fourth3-- ,illustration3 a7 music ,illustration3 b7 music #f4 ,perfect octave3-- ,illustration3 a7 music ,illustration3 b7 music #g4 ,perfect intervals combined3-- music ,the teacher should combine these intervals in various ways and in several different rhythms and the student should notate the exercise4 ,the teacher may also choose some melody free from accidentals and play it slowly while the student notates4 ,such practice accomplishes a two-fold result1 ability to notate rhythm as well as intervals4 #h4 ,major third3-- ,illustration3 music #i4 ,minor sixth3-- ,illustration3 music #aj4 ,major sixth3-- ,illustration3 music #aa4 ,minor third3-- ,illustration3 music ,the first measure of exercise #b contains the major second which is an easily recognized interval4 ,the last measure but two of exercise #b contains the major seventh4 ,this interval is ordinarily a difficult interval to intonate but coming as it does in exercise #b it is easy to intonate because of the ascending scale on the second half of the measures4 ,for the present1 it is not advisable to practice the major seventh except in some such sequence as exercise #b4 ,all other normal intervals may be practiced separately and in combinations4 ,after the student has become thoroughly proficient in recognizing and properly intonating all the intervals in group ,i1 he may proceed to the intervals of the minor scale found in group ,,ii4 ,,group ,,ii4 ,,the ,,normal ,,intervals ,,of ,,the ,,minor ,,scale4 #a4 ,melodic minor scale3-- ,illustration3 music #b4 ,harmonic minor scale3-- ,illustration3 music ,if the student finds difficulty in singing the harmonic form with the awkward augmented step1 the singing of this scale may be postponed4 #c4 ,play alternatively the major scale and both forms of minor1 and require the student to distinguish between them4 ,do not proceed until the student is capable of recognizing and distinguishing between all diatonic scales4 #d4 ,all intervals of the harmonic minor scale3-- ,illustration3 music #e4 ,all intervals of the ascending melodic minor scale3-- ,illustration3 music #f4 ,the minor triad3-- ,illustration3 music #g4 ,the minor third3-- ,illustration3 music #h4 ,the major sixth3-- ,illustration3 music #i4 ,the minor sixth3-- ,illustration3 music #aj4 ,the major third3-- ,illustration3 music #aa4 ,play slowly several minor melodies free from modulations and require the student to notate4 ,the teacher should now play melodies in which are transitions from major to -parallel- minor and -vice versa-4 ,great familiarity with the normal intervals is necessary before studying altered intervals4 ,it is hoped that the major seventh may now be properly intonated4 ,the student may experience considerable difficulty with the following group1 in which case it is advisable to postpone this group until the ear is more thoroughly trained4 ,the object of its following the normal intervals is to fix firmly the fundamental and all intervals by comparison with this fundamental4 ,,group ,,iii4 ,,altered ,,intervals4 #a4 ,the chromatic scale3-- ,illustration3 music ,in syllabicating the chromatic scale or any of the altered intervals1 the syllable -ah- may be used on each tone4 ,to those wishing to adhere to the ,italian syllables1 the tonic sol-fa syllables1 invented by ,miss ,sarah ,ann ,glover1 may be used which are as follows3 ascending chromatic scale---doh-1 -de-1 -ray-1 -re-1 -me-1 -fah-1 -fe-1 -soh-1 -se-1 -lah-1 -le-1 -te-1 -doh2- descending chromatic scale---doh-1 -te-1 -ta-1 -lah-1 -la-1 -soh-1 -sa-1 -fah-1 -me-1 -ma-1 -ray-1 -ra-1 -doh-4 ,miss ,glover changed the spelling of the ,italian syllables to coincide with the ,english pronunciation4 ,she also changed the subtonic from -si- to -te-4 #b4 -,the augmented fourth- is found as a scale interval between the fourth and seventh steps of the major scale 7-fah- to -te-74 ,it is more difficult to conceive and intonate properly the augmented fourth when it is constructed upon the tonic4 ,in order to make this interval less difficult1 the following exercise contains the intermediate scale steps previous to the skip of an augmented fourth3-- ,illustration3 music ,it may be necessary with some students to interpolate some or all the intermediate steps previous to skips to all altered intervals4 ,it may not be amiss to state here that in correct melody writing augmented and diminished intervals are usually avoided4 ,singers almost invariably intonate them out of tune4 ,when these intervals exist as constituent parts of an arpeggio chord progression1 they are comparatively easy4 ,as altered intervals these skips are given to instruments 7instruments being capable of properly intonating all skips7 when a dramatic effect is desired4 #c4 -,the diminished fifth- is analogous to the augmented fourth4 ,being the inversion of the augmented fourth1 it is found as a scale interval between the seventh and fourth steps 7-te- to -fah-74 ,the following exercise contains the diminished fifth built upon the tonic3-- ,illustration3 music #d4 -,the augmented fifth- is analogous to the minor sixth4 ,it is found as a scale interval between the third and seventh steps of the harmonic minor scale and ascending melodic minor scale4 ,the following exercise contains the augmented fifth built upon the major tonic3-- ,illustration3 music #e4 -,the diminished fourth- is the inversion of the augmented fifth and is analogous to the major third3-- ,illustration3 music #f4 -,the augmented second- is analogous to the minor third4 ,it is found as a scale interval between the sixth and seventh steps of the harmonic minor4 ,the following exercise contains the augmented second built upon the major tonic3-- ,illustration3 music #g4 -,the diminished seventh- is the inversion of the augmented second and is analogous to the major sixth3-- ,illustration3 music #h4 -,the augmented third- is analogous to the perfect fourth4 ,this interval is found in the altered minor triad between the third and the raised fifth of the triad4 ,derivation of the augmented third3-- ,illustration3 music ,e ,,ii ,exercise3-- ,illustration3 music #i4 -,the augmented sixth- is analogous to the minor seventh4 ,this interval is found in the augmented sixth chord4 ,origin of the augmented sixth chord3-- ,illustration3 music ,e ,,ii -,the diminished sixth-1 which is the inversion of the augmented third and analogous to the perfect fifth1 is not used melodically4 -,the diminished third-1 which is the inversion of the augmented sixth and analogous to the major second1 is but seldom used melodically4 ,if the singing of the harmonic minor scale has been postponed1 it should now be practiced4 ,exercises containing the major seventh may now be given4 ,,group ,,iv4 ,,arpeggio ,,chords4 ,if the fundamental is not yet fixed in the student's mind exercises pertaining to groups ,i and ,,ii should be given before proceeding4 ,the intervals already given should be expanded1 the major second to a major ninth1 the major third to a major tenth1 etc41 etc4 ,in practicing the following exercises1 the student should name the intervals between consecutive notes and between each note of the chord and the fundamental4 #a4 ,the major triad3-- ,illustration3 music #b4 ,the minor triad3-- ,illustration3 music #c4 ,the diminished triad3-- ,illustration3 music #d4 ,the augmented triad3-- ,illustration3 music ,a ,,iii' #e4 ,the dominant seventh chord3-- ,illustration3 music ,the teacher should explain the dominant seventh chord and its resolution4 ,also give exercises on the skip of a minor seventh4 #f4 ,the supertonic seventh chord3-- ,illustration3 music #g4 ,the subtonic seventh chord3-- ,illustration3 music #h4 ,the diminished seventh chord3-- ,illustration3 music ,a great many exercises on these chords should be given together with the natural resolution of the dependent chords4 ,exercises on the inversions of these chords may be given when the student has obtained proficiency on the fundamental position4 ,the inversions may be found in ,chapter ,,iii4 ,,group ,v4 ,,two ,,voiced ,,chords4 ,the student should name the interval that one voice forms with the other4 ,the upper melody should then be sung as the exercise is played4 ,repeat the exercise1 the student singing the lower melody this time4 ,if the student experiences difficulty in naming the intervals1 the chords should be played in arpeggio style4 #a4 ,thirds3-- ,illustration3 music #b4 ,sixths3-- ,illustration3 music #c4 ,mixed intervals and rhythm 7contrapuntal73-- ,illustration3 ,cherubini music ,,group ,,vi4 ,,the ,,four ,,voiced ,,chord4 ,it becomes necessary to use organ or piano for this group4 ,the student should name the kind of chord and sing the upper voice4 #a4 ,the primary triads3-- ,illustration3 music #b4 ,the primary and secondary triads3-- ,illustration3 music #c4 ,introducing the dominant seventh chord3-- ,illustration3 7a7 music ,illustration3 7b7 music #d4 ,introducing the dominant and secondary seventh chords3-- ,illustration3 7a7 music ,illustration3 7b7 music ,the chorals that were chosen for analysis in ,chapter ,,iii should now be played for ear training4 ,the teacher's judgment is very necessary in deciding the limitations of each individual student4 ,at the proper time modulations may be made4 ,before the student may be called proficient1 he must be capable of instantly recognizing and properly intonating any and all chords sounded4 ,can ,you ,compose ,music8 ,in this1 the latest of methods for the study of ,harmony1 the author1 ,carl ,e4 ,gardner1 presents a system of training which1 both in purpose and plan1 provides1 what up to the present has frequently been hinted at1 but never practically accomplished--a direct method for the teaching of music composition4 ,in the writing of the work the student's practical development has been uppermost in the author's mind and to this end he has provided not a mere treatise on musical grammar1 along conventional1 hackneyed lines1 but a new method which will -allow and encourage the student to compose as he advances and develops-4 ,,music ,,composition ,a ,,new ,,method ,,of ,,harmony ,,by ,,carl ,e4 ,,gardner ,author of ,essentials of ,music ,theory4 ,price1 #a4ej 99 99 99 99 99 ,,opinion ,,of ,,the ,,press ,his work--numbering #afa small pages--is of necessity simply an abbreviated affair4 ,it is soundly done1 the work of a man who knows his subject through and through1 and it is capitally written4 ,,musical ,,america4 ,the author calls his method the direct method1 in that he makes the pupil begin to compose from the beginning instead of after a long and tedious course of technical rules4 ,time will tell whether this new method will make better composers than the old way or not1 but the new method will certainly make the way of the pupil less thorny4 ,the average student will probably enjoy learning composition according to the method by ,carl ,e4 ,gardner4 ,there is no reason whatever why this method should not be as useful as the long established methods of ,jadassohn1 ,prout1 ,richter and others who believe in keeping the pupil's nose to the grindstone for several years before furnishing him with wings4 ,,musical ,,courier4 ',music ,composition1' a 'new method of harmony1' by ,carl ,e4 ,gardner1 published by ,carl ,fischer1 ,new ,york1 is a meritorious text book which seeks to combine1 in efficient manner1 the teaching of simple forms with the customary guidance in chord connection4 ,the abandoning of the isolated manner in which harmony is generally taught and the stimulus of life it undoubtedly receives by joining to it symmetry1 rhythm and melody1 is undeniably a progress4 ,,canadian ,,journal ,,of ,,music4 ,,published ,,by ,,carl ,,fischer ,,boston ,,new ,,york ,,chicago