,transcriber's ,notes3      ,underscores
 80 before and after a word or phrase   
indicate italics      in the original   
text4    ,equal signs 80 before and     
after a word or phrase indicate bold    
in the original text4    ,small capitals
 have been converted to ,,solid         
capitals4    ,illustrations have been   
moved so they do not break up           
paragraphs4    ,typographical and       
punctuation errors have been silently   
corrected4                              
,a ,,theory ,,of ,,pure ,,design        
,harmony1 ,balance1 ,rhythm             
,,with ,,illustrations ,,and ,,diagrams 
,,by ,,denman ,w4 ,,ross1 ,,ph4 ,d4     
,,lecturer ,,on ,,the ,,theory ,,of     
,,design ,,in ,,harvard                 
,,university1 ,,fellow ,,of ,,the       
,,american ,,academy                    
,,of ,,arts ,,and ,,sciences            
,,boston ,,and ,,new ,,york             
,,houghton1 ,,mifflin ,,and ,,company   
,,mdccccvii                             
,,copyright #aijg ,,by ,,denman ,w4     

,,ross                                  
,,all ,,rights ,,reserved               
,published ,april1 #aijg                
,,preface      ,my purpose in this book 
is to elucidate1 so far as ,i can1 the  
principles which underlie the practice  
of drawing and painting as a  ,fine     
,art4 ,art is generally regarded as the 
expression of feelings  and emotions    
which have no explanation except perhaps
 in such a word  as inspiration1 which  
is expletive rather than explanatory4   
,art is  regarded as the one activity of
 man which has no scientific basis1 and 
the appreciation of ,art is said to be a
 matter of taste in which no two        
persons can be expected to agree4 ,it is
 my purpose in this book to show  how1  
in the practice of ,art1 as in all other
 practices1 we use certain  terms and   
follow certain principles4 ,being       
defined and explained1 these  terms and 
principles may be known and understood  
by everybody4 ,they  are1 so to speak1  
the form of the language4    ,while an  

understanding of the terms and          
principles of ,art will not1  in itself1
 enable any one to produce important    
works1 such works  are not produced     
without it4 ,it must be understood1     
however1 that  the understanding of     
terms and principles is not1            
necessarily1 an  understanding in words4
 ,it may lie in technical processes and 
in visual  images and may never rise1 or
 shall ,i say fall1 to any formulation  
in  words1 either spoken or written4    
,the terms and principles of ,art have1 
as a rule1 been understood by the artist
 in the form of technical  processes and
 visual images1 not in words4 ,it is in 
words that they  will become generally  
understood4 ,it is in words that ,i     
propose to  explain them in this book4  
,i want to bring to definition what1    
until  now1 has not been clearly defined
 or exactly measured4 ,in a sense  this 
book is a contribution to ,science      
rather than to ,art4 ,it is a           
contribution to ,science made by a      

painter1 who has used his ,art in  order
 to understand his ,art1 not to produce 
,works of ,art4 ,in a passage  of ,plato
 7,philebus1  #ee7 ,socrates says3 8,if 
arithmetic1 mensuration1  and weighing  
be taken out of any art1 that which     
remains will not be  much48 8,not much1 
certainly10 was the reply4 ,the only    
thing which  remains in ,art1 beyond    
measurable quantities and qualities1 is 
the  personality1 the peculiar ability  
or genius of the artist himself4  ,that1
 ,i believe1 admits of no explanation4  
,the element of personality  is what we 
mean when we speak of the element of    
inspiration in a ,work  of ,art4        
,underlying this element of personality 
are the terms and  principles of the    
art4 ,in them the artist has found the  
possibility of  expression2 in them his 
inspiration is conveyed to his          
fellowmen4 ,i  propose to explain1 not  
the artist1 but the mode of expression  
which  the artist uses4 ,my purpose1 in 
scientific language1 is to define1      

classify1 and explain the phenomena of  
,design4 ,in trying to do that1 ,i  have
 often been at a loss for terms and have
 been obliged1 in certain  instances1 to
 use terms with new meanings1 meanings  
which differ1 more  or less1 from those 
of common usage and from those of       
writers in other  branches of learning4 
,in all such cases ,i have taken pains  
to define my  terms and to make my      
meanings perfectly clear4 ,i do not     
expect any one  to read this book who is
 not willing to allow to my terms the   
meanings  ,i have given them4 ,those who
 are unwilling to accept my definitions 
will certainly not follow me to my      
conclusions4    ,i am giving this book  
to the ,public with great reluctance4   
,though ,i  have had it in mind for many
 years and have put no end of thought   
and work into it1 it seems to me        
inadequate and unsatisfactory4 ,it  will
 hardly be published before ,i shall    
discover in it errors both  of omission 
and commission4 ,the book presents a new

 definition of  principles1 a new       
association of ideas4 ,it is            
inconceivable that this1  my first      
published statement1 should be either   
consistent or complete4  ,it will be a  
long time1 ,i am sure1 before it can be 
brought to a  satisfactory shape4 ,it is
 simply the best statement that ,i can  
make at  this time4 ,one reason1 perhaps
 my best reason1 for publishing this    
,theory1 before it is completely worked 
out1 is to bring other students  into   
the investigation4 ,i need their        
coperation1 their suggestions1  and     
their criticisms4 ,without assistance   
from others the book would not  be as   
good as it is4 ,i am indebted to a      
number of persons for helpful           
suggestions4 ,i am particularly indebted
 to three men1 who have been  associated
 with me in my teaching3 ,william       
,luther ,mowll1 ,henry ,hunt  ,clark1   
and ,edgar ,oscar ,parker4 ,each of them
 has had a share in the  work4 ,i am    
indebted to ,professor ,mowll for very  

important contributions  to the doctrine
 of ,rhythm1 as it is presented in this 
book1 and he has  kindly helped me in   
the revision of the work for the press4 
,my friend  ,dean ,briggs has kindly    
read my proof sheets1 and ,i am indebted
 to him  for many suggestions4          
,,denman ,w4 ,,ross4     ,,harvard      
,,university1        ,february #af1     
#aijg4          ,,contents              
,,introduction                          
#a     ,,positions ,,in ,,harmony1      
,,balance1 ,,and ,,rhythm          #i   
,,lines ,,in ,,harmony1 ,,balance1 ,,and
 ,,rhythm             #cg     ,,outlines
 ,,in ,,harmony1 ,,balance1 ,,and       
,,rhythm          #if     ,,tones ,,and 
,,tone-,,relations                      
#aca     ,,sequences ,,of ,,values ,,and
 ,,colors                   #adc        
,,tone-,,harmony                        
#aeh     ,,tone-,,balance               
#agb     ,,tone-,,rhythm                
#ahb     ,,composition1 ,,general       
,,rules                       #ahf      

,,the ,,study ,,of ,,order ,,in ,,nature
 ,,and ,,in ,,works ,,of ,,art #aij     
,,conclusion                            
#aib     ,,paragraph ,,index            
#aie          ,,introduction      ,,the 
,,meaning ,,of ,,design    #a4 ,by      
,design ,i mean ,order in human feeling 
and thought and in the  many and varied 
activities by which that feeling or that
 thought is  expressed4 ,by ,order ,i   
mean1 particularly1 three               
things1--,harmony1  ,balance1 and       
,rhythm4 ,these are the principal modes 
in which ,order is  revealed in ,nature 
and1 through ,design1 in ,works of ,art4
      ,,the ,,order ,,of ,,harmony      
#b4 ,whenever two or more impressions or
 ideas have something in common  that is
 appreciable1 they are in harmony1 in   
the measure of what they  have in       
common4 ,the harmony increases as the   
common element increases2  or the common
 elements4 ,it diminishes in the measure
 of every  difference or contrast4 ,by  
the ,order of ,harmony ,i mean some     

recurrence  or repetition1 some         
correspondence or likeness4 ,the        
likeness may be in  sounds or in sights1
 in muscular or other sense-impressions4
 ,it may lie  in sensations1 in         
perceptions1 in ideas1 in systems of    
thought4      ,,the ,,order ,,of        
,,balance    #c4 ,by the ,order of      
,balance ,i mean some equal opposition  
and consequent  equilibrium1 as it      
occurs at some moment of ,time or at    
some point  of ,space2 an equilibrium   
which induces1 for the moment and in its
  place1 a suspension of all change or  
movement1 and causes a pause  or a rest4
 ,the equilibrium may be one of physical
 forces 7forces of  weight or           
resistance7 or forces of will4 ,it may  
be an equilibrium  of sense-impressions 
or attractions1 of interests1 of        
alternative  propositions or ideas4 ,it 
may be the equilibrium of a perfect     
antithesis4 ,certain moments of ,time1  
certain points of ,space1 are           
distinguished from others by instances  

of equilibrium or balance4 ,the  balance
 being lost1 in any case1 we have at    
once some movement4 ,if this  movement  
is regular1 and marked in its           
regularity1 we get1 instead of          
,balance1 ,rhythm4      ,,the ,,order   
,,of ,,rhythm    #d4 ,by the ,order of  
,rhythm ,i mean changes of sensation2   
changes in  muscular impressions as we  
feel them1 in sounds as we hear them1 in
  sights as we see them2 changes in     
objects1 people1 or things as we know   
them and think of them1 changes which   
induce the feeling or idea of  movement1
 either in the duration of ,time or in  
the extension of ,space2  provided that 
the changes take place at regular and   
marked intervals of  time or in regular 
and marked measures of space4 ,by       
regular intervals  and measures ,i mean 
equal or lawfully varying intervals and 
measures4 ,i  do not mean1 by ,rhythm1  
changes simply1 inducing the sense or   
idea of  movement3 ,i mean1 by ,rhythm1 
a regularity of changes in a regularity 

of  measures1 with the effect of        
movement upon our minds4    ,rhythms in 
,time differ from ,rhythms in ,space1   
inasmuch as the movement  in ,time is in
 one direction1 inevitably4 ,it lies in 
the duration and  passing of time1 from 
which nothing escapes4 ,the movement in 
space1  on the contrary1 may be in any  
one of many possible directions4 ,a     
movement in different directions1       
particularly in contrary directions1    
amounts to a negation of movement4 ,in  
any space-rhythm1 therefore1  the       
direction in which the rhythm leads us1 
the direction in which we  follow it1   
must be unmistakable4    #e4 ,of these  
three principles of ,order1 the first   
and foremost1 the most  far-reaching and
 comprehensive1 is the principle of     
,harmony4 ,we have  ,harmony in all     
balances1 and we have it also in all    
rhythms4 ,it is1  therefore1 undesirable
 to think of the three principles as    
cordinate4  ,it will be better to think 
of the principle of ,harmony first1 and 

then  of two other principles1 those of 
,balance and of ,rhythm1 as lying       
within the range of ,harmony but not    
coextensive with it4 ,we might  express 
the idea in a logical diagram4          
,illustration3 ,fig4 #a    ,within the  
field of ,harmony we have two distinct  
modes of ,order--,balance  and ,rhythm2 
but we have ,harmony beyond the range of
 ,balance and beyond  the range of      
,rhythm4    ,in cases where rhythms1    
corresponding in character and in       
direction  of movement1 are set side by 
side1 one on the right1 the other on the
  left1 of a vertical axis1 so that they
 balance1 one against the other1  and   
the vertical axis of the balance is the 
line of the movement1  we have the union
 of all three principles4 ,this idea1   
also1 may be  expressed in a logical    
diagram4    ,illustration3 ,fig4 #b     
,examples of this union of the three    
principles of ,order will be given      
farther on4      ,,beauty ,a ,,supreme  
,,instance ,,of ,,order    #f4 ,i       

refrain from any reference to ,beauty as
 a principle of ,design4 ,it  is not a  
principle1 but an experience4 ,it is an 
experience which defies  analysis and   
has no explanation4 ,we distinguish it  
from all other  experiences4 ,it gives  
us pleasure1 perhaps the highest        
pleasure that we  have4 ,at the same    
time it is idle to talk about it1 or to 
write about  it4 ,the less said about it
 the better4 8,it is beautiful10 you    
say4  ,then somebody asks1 8,why is it  
beautiful80 ,there is no answer to that 
question4 ,you say it is beautiful      
because it gives you pleasure3 but      
other things give you pleasure which are
 not beautiful4 ,pleasure is1           
therefore1 no criterion of ,beauty4     
,what is the pleasure which ,beauty     
gives8 ,it is the pleasure which you    
have in the sense of ,beauty4 ,that  is 
all you can say4 ,you cannot explain    
either the experience or the  kind of   
pleasure which it gives you4    ,while  
,i am quite unable to give any          

definition or explanation of  ,beauty1  
,i know where to look for it1 where ,i  
am sure to find it4 ,the  ,beautiful is 
revealed1 always1 so far as ,i know1 in 
the forms of ,order1  in the modes of   
,harmony1 of ,balance1 or of ,rhythm4   
,while there are many  instances of     
,harmony1 ,balance1 and ,rhythm which   
are not particularly  beautiful1 there  
is1 ,i believe1 nothing really beautiful
 which is not  orderly in one or the    
other1 in two1 or in all three of these 
modes4 ,in  seeking the ,beautiful1     
therefore1 we look for it in instances  
of ,order1  in instances of ,harmony1   
,balance1 and ,rhythm4 ,we shall find it
 in what  may be called supreme         
instances4 ,this is perhaps our nearest 
approach  to a definition of ,beauty3   
that it is a supreme instance of ,order1
  intuitively felt1 instinctively       
appreciated4      ,,the ,,arts ,,as     
,,different ,,modes ,,of ,,expression   
#g4 ,the ,arts are different forms or   
modes of expression3 modes of  feeling1 

modes of thought1 modes of action4      
,there are many ,arts in  which         
different terms of expression1 different
 materials1 different  methods are used4
 ,the principal ,arts are 7#a7          
,gymnastics1 including  ,dancing1 7#b7  
,music1 7#c7 ,speech1 spoken and        
written1 7#d7 ,construction  with all   
kinds of materials1 7#e7 ,sculpture1    
including ,modeling and  ,carving1 7#f7 
,drawing and ,painting4 ,these are the  
principal ,arts1 but  there are many    
others1 more or less connected with     
them4 ,design comes  into all of these  
,arts1 bringing ,order1 in some cases   
,beauty4      ,,the ,,art ,,of ,,drawing
 ,,and ,,painting    #h4 ,the ,art which
 ,i have studied and practiced1 the ,art
 in which ,i am  giving instruction1 is 
that of ,drawing and ,painting4    ,by  
the ,art of ,drawing and ,painting ,i   
mean expression in pigment-tones        
7values1 colors1 intensities of color7  
spread in different measures  or        
quantities and in different shapes3     

shapes being differences of  character  
given to a line by its straightness or  
curvature1 to a spot  or area by its    
outline or contour4 ,by ,drawing and    
,painting ,i mean1  therefore1          
expression by lines and spots of paint4 
,,two ,,modes ,,of ,,drawing ,,and      
,,painting    #i4 ,there are two modes  
of ,drawing and ,painting1 the mode of  
,pure ,design  and the mode of          
,representation4      ,,pure ,,design   
#aj4 ,by ,pure ,design ,i mean simply   
,order1 that is to say1 ,harmony1       
,balance1 and ,rhythm1 in lines and     
spots of paint1 in tones1 measures1  and
 shapes4 ,pure ,design appeals to the   
eye just as absolute ,music  appeals to 
the ear4 ,the purpose in ,pure ,design  
is to achieve ,order  in lines and spots
 of paint1 if possible1 the perfection  
of ,order1 a  supreme instance of it1   
the ,beautiful3 this with no other1 no  
further1  no higher motive2 just for the
 satisfaction1 the pleasure1 the delight
  of it4 ,in the practice of ,pure      

,design we aim at ,order and hope for   
,beauty4 ,even the motive of giving     
pleasure to others lies beyond the      
proper purpose of ,pure ,design1 though 
it constantly happens that in  pleasing 
ourselves we give others pleasure4      
,,applications ,,of ,,design    #aa4    
,the application of ,design in the      
various ,arts and ,crafts is well       
understood and appreciated4 ,we have    
many instances and examples in the  ,art
 of the ,past4 ,the possibility of ,pure
 ,design1 pure ,art1 followed for  the  
sake of ,order and ,beauty1 with no     
purpose of service or of utility1  is   
not at all understood or appreciated4 ,i
 think of ,pure ,design as ,i  think of 
,music4 ,music is the arrangement and   
composition of sounds  for the sake of  
,order and ,beauty1 to give pleasure to 
the ear of the  composer4 ,pure ,design 
is the arrangement and composition of   
lines and  spots of paint for the sake  
of ,order and ,beauty1 to give pleasure 
to  the eye of the designer4 ,i am      

prepared to admit1 however1 that as     
,music1 once created1 being appropriate 
to the occasion when it is  performed   
and to the mood of the listeners1 may   
give pleasure to many  persons1 so ,pure
 ,design1 once achieved1 being          
appropriate to the time  and the place  
of exhibition and to the mood of the    
beholders1 may give  pleasure to others 
besides the designer4 ,in that sense1 ,i
 am willing to  allow that ,pure ,design
 may be ,applied ,art1--,art applied in 
the service  of ,humanity1 its purpose  
being to bring pleasure into human      
experience4  ,the underlying motive of  
it1 however1 is found not in the service
 of  humanity1 but in the ideal of the  
artist4 ,he aims at ,order and hopes    
for ,beauty1 as the highest reward of   
his effort4 ,john ,sebastian ,bach  said
 of ,music3 8,it is for the glory of    
,god and a pleasant recreation40  ,that 
is what ,i mean4 ,the designer1 like the
 musician1 seeks first of  all to       
achieve ,order and ,beauty for the sake 

of ,order and ,beauty4 ,that  is his    
religion1--the worship of the ,ideal4   
,when the ,ideal is realized1  the      
object which has been produced may serve
 a useful purpose in giving  pleasure1  
and perhaps inspiration1 to others4     
,the principles of ,pure ,design which  
are defined and illustrated in this     
book are the principles which should be 
followed in all applications  of ,design
 in the ,arts and ,crafts4 ,in such     
applications1 however1 the  ideals of   
design are often obscured by the        
consideration of materials  and         
technical processes on the one hand1 and
 of service or utility on  the other4   
,it will be worth while1 therefore1 for 
those who wish to  bring ,design into   
their work1 whatever that is1 to study  
,design in the  abstract1 ,pure ,design1
 so that they may know1 before they     
undertake to  use it1 what ,design is4  
,it is the purpose of this book to      
explain what  it is4                    
,,representation    #ab4 ,order1 which  

in ,pure ,design is an end1 becomes in  
,representation  a means to an end2 the 
end being the ,truth of ,representation4
 ,in  ,representation we are no longer  
dealing1 as in ,pure ,design1 with      
meaningless terms1 or1 if the terms have
 meanings1 with no regard  for them4 ,in
 ,representation we are putting lines   
and spots of paint  together for the    
sake of their meanings4 ,design in      
,representation  means ,order in the    
composition or arrangement of meanings4 
,what we  aim at is the ,truth of       
,representation in a form of expression 
which  will be simple1 clear1           
reasonable1 and consistent1 as well as  
true4  ,the attention must be directed  
to what is important1 away from what is 
unimportant4 ,objects1 people1 and      
things represented must be brought  out 
and emphasized or suppressed and        
subordinated1 according to the  ,idea or
 ,truth which the artist wishes to      
express4 ,the irrelevant must  be       
eliminated4 ,the inconsistent and the   

incongruous must be avoided4  ,that is  
what ,i mean by ,design in              
,representation1 the knowledge of       
,nature and ,life presented in a        
systematic1 logical1 and orderly way4   
,,representation ,,in ,,forms ,,of      
,,design    #ac4 ,it sometimes happens  
that we have the ,truth of              
,representation in a  form of ,pure     
,design or ,pure ,design combined with  
,representation4 ,in  ,poetry we have   
the meaning of the words in the measures
 of the verse4  ,so in ,representation  
it is sometimes possible to achieve the 
,truth in  forms of ,harmony1 ,balance1 
and ,rhythm4 ,in such cases the appeal  
is  simultaneously to the love of       
,knowledge and to the sense of ,order   
and  of ,beauty1 so that we have an     
sthetic pleasure in the statement of the
  ,truth4    ,in this book ,i shall     
explain what ,i mean by ,drawing and    
,painting  in ,pure ,design4 ,later1 ,i 
hope to write another book on ,design in
  ,representation4          ,,drawing   

,,and ,,painting ,,in ,,pure ,,design   
,,positions      ,,definition ,,of      
,,positions    #ad4 ,take a pencil and a
 piece of paper4 ,with the pencil1 on   
the paper1  mark a dot or point4        
,illustration3 ,fig4 #c    ,by this dot 
7,a7 three ideas are expressed3 an idea 
of ,tone1 the tone of  lead in the      
pencil2 an idea of ,measure1 the extent 
of the space covered  by the dot2 and an
 idea of ,shape1 the character given to 
the dot by its  outline or contour4 ,the
 dot is so small that its tone1 its     
measure1  and its shape will not be     
seriously considered4 ,there is another 
idea1  however1 which is expressed by   
the dot or point1--an idea of ,position4
  ,that is its proper meaning or        
signification4 ,there is presumably a   
reason for giving the dot one position  
rather than another4      ,,positions   
,,determined ,,by ,,directions ,,and    
,,distances    #ae4 ,put another dot    
7,b7 on your paper1 not far from dot    
8,a40    ,illustration3 ,fig4 #d    ,we 

have now a relation of two              
positions1--the relation of position    
8,a0  to position 8,b40 ,the relation is
 one of ,directions and of ,distances4  
,proceeding from 8,a0 in a certain      
direction to a certain distance we      
reach 8,b40 ,proceeding from 8,b0 in a  
certain direction and to a certain      
distance we reach 8,a40 ,every position 
means two things2 a direction  and a    
distance taken from some point which may
 be described as the  premise-point4    
,,directions    #af4 ,directions may be 
referred either to the ,horizontal or to
 the  ,vertical4 ,referring them to the 
horizontal1 we say of a certain         
direction1 that it is up-to-the-left1 or
 up-to-the-right1 or  down-to-the-left1 
or down-to-the-right1 a certain number  
of degrees4  ,it may be thirty 7#cj71 it
 may be forty-five 7#de71 it may be     
sixty  7#fj71--;any number of degrees up
 to ninety 7#ij71 in which case we say  
simply that the direction is up or down4
 ,directions on the horizontal  may be  

described by the terms1 to the right or 
to the left4    ,illustration3 ,fig4 #e 
,the method of describing and defining  
different directions from any  point1 as
 a center1 is clearly explained by this 
diagram4      ,,distances    #ag4 ,the  
definition of ,distances in any         
direction is well understood4  ,in      
defining position 8,b10 in ,fig4 #d1 we 
say that it is1 in a direction  from    
8,a10 the premise-point1                
down-to-the-right forty-five degrees    
7#de71 that it is at a distance from    
8,a0 of one inch4 ,distances are  always
 taken from premise-points4             
,,positions ,,determined ,,by           
,,triangulations    #ah4 ,if we mark a  
third dot1 8,c10 on our paper and wish  
to define its  position1 we may give the
 direction and the distance from 8,a10  
or from  8,b10 or1 if we prefer1 we may 
follow the principle of ,triangulation  
and  give two directions1 one from 8,a0 
and the other from 8,b40 ,no distances  
need be given in that case4 ,the        

position of 8,c0 will be found at the   
intersection of the two directions4     
,illustration3 ,fig4 #f    ,the         
principle of ,triangulation is          
illustrated in the above diagram4       
,,intervals    #ai4 ,we shall have      
occasion to speak not only of           
,distances1 but of  ,intervals4 ,they   
may be defined as intermediate spaces4  
,the spaces  between the points 8,a0 and
 8,b10 8,a0 and 8,c10 8,b0 and 8,c10 in 
,fig4 #f1  are ,intervals4      ,,scale 
,,in ,,relations ,,of ,,positions       
#bj4 ,given any relation of positions1  
the scale may be changed by  changing   
the intervals1 provided we make no      
change of directions4 ,that  is well    
understood4    ,before proceeding to the
 considerations which follow1 ,i must   
ask the  reader to refer to the         
definitions of ,harmony1 ,balance1 and  
,rhythm  which ,i have given in the     
,introduction4      ,,the ,,order ,,of  
,,harmony    ,,in ,,positions3          
,,directions1 ,,distances1 ,,intervals  

#ba4 ,all ,positions lying in the same  
direction and at the same distance  from
 a given point1 taken as a              
premise-point1 are one4 ,there is no    
such  thing1 therefore1 as a ,harmony of
 ,positions4 ,positions in ,harmony are 
identical positions4 ,two or more       
positions may1 however1 lie in the  same
 direction from or at the same distance 
from a given point taken  as a          
premise-point4 ,in that case1 the two or
 more positions1 having a  direction or 
a distance in common1 are1 to that      
extent1 in harmony4      #bb4 ,what do  
we mean by ,harmony of ,directions8     
,illustration3 ,fig4 #g    ,this is an  
example of ,direction-,harmony4 ,all the
 points or positions  lie in one and the
 same direction from the premise-point  
8,a40 ,the  distances from 8,a0 vary4   
,there is no ,harmony of ,intervals4    
,directions being defined by angles of  
divergence1 we may have a ,harmony  of  
,directions in the repetition of similar
 angles of divergence3 in  other words1 

when a certain change of direction is   
repeated4    ,illustration3 ,fig4 #h    
,in this case the angles of divergence  
are equal4 ,there is a  ,harmony1 not   
only in the repetition of a certain     
angle1 but in the  correspondence of the
 intervals4    ,illustration3 ,fig4 #i  
,this is an example of ,harmony produced
 by the repetition of a certain         
alternation of directions4              
,illustration3 ,fig4 #aj    ,in this    
case we have ,harmony in the repetition 
of a certain relation  of directions    
7angles of divergence74 ,in these cases1
 ,fig4 #i and ,fig4  #aj1 there is      
,harmony also1 in the repetition of a   
certain relation of  intervals4    #bc4 
,two or more positions may lie at the   
same distance from a given  point taken 
as a premise-point4 ,in that case the   
positions1 having a  certain distance in
 common1 are1 to that extent1 in        
,harmony4    ,illustration3 ,fig4 #aa   
,this is an example of                  
,distance-,harmony4 ,all the points are 

equally  distant from the premise-point 
8,a40 ,the directions vary4    ,we may  
have ,distance-,harmony1 also1 in the   
repetition of a certain  relation of    
distances4    ,illustration3 ,fig4 #ab  
,this is an illustration of what ,i have
 just described4 ,the ,harmony is  of a 
certain relation of distances repeated4 
#bd4 ,intervals1 that is to say         
intermediate spaces1 are in ,harmony    
when  they have the same measure4       
,illustration3 ,fig4 #ac    ,in this    
case we have1 not only a ,harmony of    
,direction1 as in ,fig4 #g1  but also a 
,harmony of ,intervals4                 
,illustration3 ,fig4 #ad    ,in this    
case the points are in a group and we   
have1 as in ,fig4 #aa1 a  ,harmony of   
,distances from the premise-point 8,a40 
,we have also a ,harmony  of ,intervals1
 the distances between adjacent points  
being equal4 ,we  have a ,harmony of    
,intervals1 not only when the intervals 
are equal1 but  when a certain relation 
of intervals is repeated4               

,illustration3 ,fig4 #ae    ,the        
repetition of the ratio one to three in 
these intervals is  distinctly          
appreciable4 ,in the repetition we have 
,harmony1 though we  have no ,harmony in
 the terms of the ratio itself1 that is 
to say1 no  ,harmony that is appreciable
 in the sense of vision4 ,the fact that 
one  and three are both multiples of one
 means that one and three have          
something in common1 but inasmuch as the
 common divisor1 one1 cannot be         
visually appreciated1 as such 7,i feel  
sure that it cannot71 it has no         
interest or value in ,pure ,design4     
,illustration3 ,fig4 #af    ,the        
relation of intervals is1 in this case1 
the relation of  three-one-five4 ,we    
have ,harmony in the repetition of this 
relation of  intervals though there is  
no ,harmony in the relation itself1     
which is  repeated4    ,illustration3   
,fig4 #ag    ,in this case1 also1 we    
have ,interval-,harmony1 but as the     
intervals in  the vertical and          

horizontal directions are shorter than  
the intervals  in the diagonal          
directions1 the ,harmony is that of a   
relation of  intervals repeated4    #be4
 ,in moving from point to point in any  
series of points1 it will be  found     
easier to follow the series when the    
intervals are short than  when they are 
long4 ,in ,fig4 #ag it is easier to     
follow the vertical or  horizontal      
series than it is to follow a diagonal  
series1 because in  the vertical and    
horizontal directions the intervals are 
shorter4    ,illustration3 ,fig4 #ah    
,in this case it is easier to move up or
 down on the vertical than in  any other
 directions1 because the short intervals
 lie on the vertical4  ,the horizontal  
intervals are longer1 the diagonal      
intervals longer  still4                
,illustration3 ,fig4 #ai    ,in this    
case the series which lies on the       
diagonal up-left-down-right  is the more
 easily followed4 ,it is possible in    
this way1 by means of  shorter          

intervals1 to keep the eye on certain   
lines4 ,the applications  of this       
principle are very interesting4    #bf4 
,in each position1 as indicated by a    
point in these arrangements1  may be    
placed a composition of dots1 lines1    
outlines1 or areas4 ,the  dots indicate 
positions in which any of the           
possibilities of design  may be         
developed4 ,they are points from which  
all things may emerge and  become       
visible4      ,,the ,,order ,,of        
,,balance    ,,in ,,positions3          
,,directions1 ,,distances1 ,,and        
,,intervals    #bg4 ,directions balance 
when they are opposite4                 
,illustration3 ,fig4 #bj    ,the        
opposite directions1 right and left1    
balance on the point from  which they   
are taken4    #bh4 ,equal distances in  
opposite directions balance on the point
 from  which the directions are taken4  
,illustration3 ,fig4 #ba    ,the equal  
distances ,,ab and ,,ac1 taken in the   
directions ,,ab and ,,ac  respectively1 

balance on the point 8,a0 from which the
 directions are  taken4    #bi4 ,two    
directions balance when1 taken from any 
point1 they diverge at  equal angles    
from any axis1 vertical1 horizontal1 or 
diagonal4    ,illustration3 ,fig4 #bb   
,the directions ,,ab and ,,ac balance on
 the vertical axis ,,ad from which  they
 diverge equally1 that is to say1 at    
equal angles4    #cj4 ,equal distances  
balance in directions which diverge     
equally from a  given axis4             
,illustration3 ,fig4 #bc    ,the equal  
distances ,,ab and ,,ac balance in the  
directions ,,ab and ,,ac which  diverge 
equally from the axis ,,ad1 making the  
equal angles ,,cad and ,,dab4  ,both    
directions and distances balance on the 
vertical axis ,,ad4    #ca4 ,the        
positions ,b and ,c in ,fig4 #bc1       
depending on balancing directions  and  
distances1 balance on the same axis4 ,we
 should feel this balance of  the       
positions ,a and ,b on the vertical axis
 even without any indication  of the    

axis4 ,we have so definite an image of  
the vertical axis that  when it is not  
drawn we imagine it4    ,illustration3  
,fig4 #bd    ,in this case the two      
positions ,c and ,b cannot be said to   
balance1  because there is no           
suggestion1 no indication1 and no visual
 image of  any axis4 ,it is only the    
vertical axis which will be imagined    
when not  drawn4    #cb4 ,perfect       
verticality in relations of position    
suggests stability  and balance4 ,the   
relation of positions ,c-,b in ,fig4 #bd
 is one of  instability4                
,illustration3 ,fig4 #be    ,these two  
positions are felt to balance because   
they lie in a perfectly  vertical       
relation1 which is a relation of        
stability4 ,horizontality in  relations1
 of position is also a relation of      
stability4 ,see ,fig4 #bh1 p4  #ba4     
#cc4 ,all these considerations lead us  
to the definition of ,symmetry4  ,by    
,symmetry ,i mean opposite directions or
 inclinations1 opposite and  equal      

distances1 opposite positions1 and in   
those positions equal1  corresponding1  
and opposed attractions on a vertical   
axis4 ,briefly1  ,symmetry is right and 
left balance on a vertical axis4 ,this  
axis will  be imagined when not drawn4  
,in ,symmetry we have a balance which is
  perfectly obvious and instinctively   
felt by everybody4 ,all other forms  of 
,balance are comparatively obscure4     
,some of them may be described as       
occult4    ,illustration3 ,fig4 #bf     
,in this case we have a symmetry of     
positions which means opposite          
directions1 opposite and equal          
distances1 and similar and opposite     
attractions in those positions4 ,the    
attractions are black dots              
corresponding in tone1 measure1 and     
shape4    ,illustration3 ,fig4 #bg      
,in this case we have a balance of      
positions 7directions and distances7    
and attractions in those positions1 not 
only on the vertical axis  but on a     
center4 ,that means ,symmetry regarding 

the vertical axis1  ,balance regarding  
the center4 ,if we turn the figure1     
slightly1 from  the vertical axis1 we   
shall still have ,balance upon a center 
and axial  ,balance2 but ,symmetry1     
which depends upon the vertical axis1   
will be  lost4    #cd4 ,the central     
vertical axis of the whole composition  
should  predominate in symmetrical      
balances4    ,illustration3 ,fig4 #bh   
,in this case we do not feel the balance
 of attractions clearly or              
satisfactorily1 because the vertical    
axis of the whole arrangement  does not 
predominate sufficiently over the six   
axes of adjacent  attractions4 ,it is   
necessary1 in order that symmetrical    
balance shall  be instinctively felt1   
that the central vertical axis          
predominate4    ,illustration3 ,fig4 #bi
    ,the central vertical axis is       
clearly indicated in this case4         
,illustration3 ,fig4 #cj    ,here1 also1
 the central vertical axis is clearly   
indicated4    #ce4 ,all relations of    

position 7directions1 distances1        
intervals71 as  indicated by dots or    
points1 whether orderly or not1 being   
inverted on  the vertical axis1 give us 
an obvious symmetrical balance4         
,illustration3 ,fig4 #ca    ,this is a  
relation of positions to be inverted4   
,illustration3 ,fig4 #cb    ,here the   
same relation is repeated1 with its     
inversion to the right on  a vertical   
axis4 ,the result is an obvious         
symmetrical balance4 ,if this  inversion
 were made on any other than the        
vertical axis1 the result  would be     
,balance but not ,symmetry4 ,the balance
 would still be axial1  but the axis1   
not being vertical1 the balance would   
not be symmetrical4    #cf4 ,in the case
 of any unsymmetrical arrangement of    
dots1 the dots  become equal attractions
 in the field of vision1 provided they  
are  near enough together to be seen    
together4 ,to be satisfactorily seen  as
 a single composition or group they     
ought to lie1 all of them1  within a    

visual angle of thirty degrees4 ,we may1
 within these limits1  disregard the    
fact that visual attractions lose their 
force as  they are removed from the     
center of the field of vision4 ,as equal
  attractions in the field of vision1   
the dots in any unsymmetrical           
arrangement may be brought into a       
balance by weighing the several         
attractions and indicating what ,i might
 call the center of equilibrium4  ,this 
is best done by means of a symmetrical  
inclosure or frame4 ,in  ascertaining   
just where the center is1 in any case1  
we depend upon  visual sensitiveness or 
visual feeling1 guided by an            
understanding  of the principle of      
balance3 that equal attractions1        
tensions or  pulls1 balance at equal    
distances from a given center1 that     
unequal  attractions balance at         
distances inversely proportional to     
them4 ,given  certain attractions1 to   
find the center1 we weigh the           
attractions  together in the field of   

vision and observe the position of the  
center4 ,in simple cases we may be able 
to prove or disprove our visual  feeling
 by calculations and reasoning4 ,in     
cases1 however1 where the  attractions  
vary in their tones1 measures1 and      
shapes1 and where there  are qualities  
as well as quantities to be considered1 
calculations and  reasoning become      
difficult if not impossible1 and we have
 to depend  upon visual sensitiveness4  
,all balances of positions1 as indicated
 by  dots corresponding in tone1        
measure1 and shape1 are balances of     
equal  attractions1 and the calculation 
to find the center is a very simple     
one4    ,illustration3 ,fig4 #cc        
,here1 for example1 the several         
attractions1 corresponding and equal1   
lie well within the field of vision4    
,the method followed to balance  them is
 that which ,i have just described4 ,the
 center of equilibrium  was found and   
then indicated by a symmetrical framing4
 ,move the frame  up or down1 right or  

left1 and the center of the frame and   
the center  of the attractions within it
 will no longer coincide1 and the       
balance  will be lost4 ,we might say of 
this arrangement that it is a ,harmony  
of ,positions due to the coincidence of 
two centers1 the center of the          
attractions and the center of the       
framing4    #cg4 ,it will be observed   
that the force of the symmetrical       
inclosure  should be sufficient to      
overpower any suggestion of movement    
which may  lie in the attractions       
inclosed by it4    ,illustration3 ,fig4 
#cd    ,in this case the dots and the   
inclosure are about equally attractive4 
,illustration3 ,fig4 #ce    ,in this    
case the force of attractions in the    
symmetrical outline is  sufficient to   
overpower any suggestion of instability 
and movement  which may lie in the      
attractions inclosed by it4    ,there is
 another form of ,balance1 the ,balance 
of ,inclinations1 but ,i  will defer its
 consideration until ,i can illustrate  

the idea by lines4      ,,the ,,order   
,,of ,,rhythm      ,,in ,,positions3    
,,directions1 ,,distances1 ,,intervals  
#ch4 ,in any unsymmetrical relation of  
positions 7directions1 distances1       
intervals71 in which the balance-center 
is not clearly and sufficiently         
indicated1 there is a suggestion of     
movement4 ,the eye1 not being held  by  
any balance1 readily follows this       
suggestion4    ,illustration3 ,fig4 #cf 
,in this case we feel that the group of 
dots is unbalanced in character  and    
unstable in its position or attitude4   
,it is easy1 inevitable  indeed1 to     
imagine the group falling away to the   
right4 ,this is due1  no doubt1 to the  
visual habit of imagining a base-line   
when it is not  drawn4 ,our judgments   
are constantly made with reference to   
the imagined  standards of verticality  
and horizontality4 ,we seem to be       
provided with  a plumb-line and a level 
without being conscious of the fact4    
,illustration3 ,fig4 #cg    ,in this    

case there is a suggestion of falling   
down to the left due  to the feeling of 
instability4 ,a symmetrical framing     
holding the eye  at the center of       
equilibrium would prevent the feeling of
 movement1  provided the framing were   
sufficiently strong in its attractions4 
,in  the examples ,i have given 7,fig4  
#cf and ,fig4 #cg7 we have movement1 but
  no ,rhythm4    #ci4 ,there is another 
type of movement which we must          
consider1--the  type of movement which  
is caused by a gradual crowding together
 of  attractions4    ,illustration3     
,fig4 #ch    ,there is nothing in this  
series of dots but the harmony of       
corresponding attractions and intervals 
repeated in a harmony of  direction4    
,if1 instead of the repetition of equal 
intervals1 we had a  regular progression
 of intervals1 either arithmetical or   
geometrical1  we should feel a movement 
in the direction of diminishing         
intervals4    ,illustration3 ,fig4 #ci  
,in the above example the changes of    

interval are those of an  arithmetical  
progression4    ,illustration3 ,fig4 #dj
    ,in ,fig4 #dj the changes of        
interval are those of a geometrical     
progression4 ,the movement to the left  
through these sequences is1 no  doubt1  
somewhat checked or prevented by the    
habit of reading to the  right4         
,illustration3 ,fig4 #da    ,the angle  
,,fab is the angle of vision within     
which the sequence is  observed4 ,at the
 end ,f of the sequence there is a      
greater number of  attractions in a     
given angle of vision than at the end   
,b1 so the eye  is drawn towards the    
left4 ,the pull on the eye is greater at
 the end ,f  because of the greater     
number and the crowding together of     
attractions4  ,in the examples just     
given 7,figs4 #ci1 #dj71 we have not    
only movements  in certain directions1  
but movements in regular and marked     
measures4  ,the movements are1          
therefore1 rhythmical1 according to the 
definition ,i  have given of ,rhythm4   

#dj4 ,it is evident that any relation of
 positions1 balanced or  unbalanced1 may
 be substituted for the single dots or  
points in the  figures just given4 ,such
 substitutions have the following       
possibilities4    #da4 ,first4 ,when the
 points lie in a series1 at equal       
intervals1 the  substitution of a       
symmetrical group of positions at each  
point gives no  ,rhythm1 only ,harmony4 
,illustration3 ,fig4 #db    ,there is no
 movement in this series of repetitions4
 ,there is  consequently no ,rhythm4    
,disregarding the habit of reading to   
the right1  which induces the eye to    
move in that direction1 it is as easy to
 move  toward the left as toward the    
right4 ,it requires more than           
repetitions  at equal intervals to      
produce the feeling of ,rhythm4 ,there  
must be  movement1 and the movement must
 have a definite direction4    #db4     
,second4 ,the substitution at each point
 of a symmetrical group at  equal       
intervals1 as before1 but with a        

progressive change of scale1  will give 
us ,rhythm4 ,the movement will be due to
 the gradual crowding  together of      
attractions at one end of the series4   
,illustration3 ,fig4 #dc    ,in this    
case we have the repetition of a        
symmetrical relation of  positions at   
equal intervals with a gradation of     
scale in the  repetitions4 ,the result  
is a ,rhythm1 in which the movement is  
from left  to right1 owing to the       
greater crowding together of attractions
 at the  right end of the series4 ,the  
feeling of ,rhythm is no doubt somewhat 
enhanced by our habit of reading to the 
right1 which facilitates the  movement  
of the eye in that direction4    #dc4   
,third4 ,the substitution of an unstable
 group at each point of the  sequence1  
the repetitions being at equal          
intervals1 gives us a ,rhythm1  due     
simply to the movement of the group     
itself1 which is unstable4              
,illustration3 ,fig4 #dd    ,taking the 
relation of positions given in ,fig4 #cf

 and repeating it at  equal intervals1  
it will be observed that the            
falling-to-the-right  movement1 which is
 the result of instability1 is conveyed 
to the whole  series of repetitions4 ,to
 make it perfectly clear that the       
movement of  this ,rhythm is due to the 
suggestion of movement in the relation  
of  positions which is repeated1 ,i will
 ask the reader to compare it with  the 
repetition of a symmetrical group in    
,fig4 #db4 ,there is no movement  in    
that case1 therefore no ,rhythm4    #dd4
 ,fourth4 ,the movement in ,fig4 #dd may
 be increased by a diminution  of scale 
and consequent crowding together of the 
dots1 provided  the movement of the     
groups and the crowding together have   
the same  direction4    ,illustration3  
,fig4 #de    ,in this case1 as ,i have  
said1 the movement of ,fig4 #dd is      
enforced by  the presence of another    
element of movement1 that of a gradation
 of  scale and consequent crowding      
together in the groups4 ,the two        

movements  have the same direction4 ,the
 movement of the crowding is not so     
strong  as that which is caused by the  
instability of the group itself4    #de4
 ,fifth4 ,a symmetrical relation of     
positions1 being repeated in a  series  
with gradually diminishing intervals    
between the repeats1 will  give us a    
feeling of rhythmic movement4 ,it will  
be due to a gradual  increase in the    
number of attractions as the eye passes 
from one angle  of vision to another4   
,see ,fig4 #da4 ,the ,rhythm will1 no   
doubt1 be  somewhat retarded by the     
sense of successive axes of symmetry4   
,illustration3 ,fig4 #df    ,in this    
case a symmetrical group is repeated in 
a progression of  measures4 ,the        
movement is toward the greater number of
 attractions at  the right end of the   
series4 ,this increase in the number of 
attractions  is due simply to           
diminishing intervals in that direction4
 ,the eye  moves through a series of    
angles toward the angle which contains  

the  greatest number of attractions4    
,the reader can hardly fail to feel the 
successive axes of symmetry as a        
retarding element in this ,rhythm4      
#df4 ,sixth4 ,symmetrical relations of  
position may be repeated in             
progressions of scale and of intervals4 
,in that case we get two  movements1 one
 caused by a gradual increase in the    
number of  attractions in successive    
angles of vision1 the other being due to
 a  gradual crowding together and       
convergence of attractions in the same  
series of angles4    ,illustration3     
,fig4 #dg    ,comparing this ,rhythm    
with the ,rhythm of ,fig4 #dc1 the      
reader will  appreciate the force of a  
diminution of scale in connection with a
  diminution of intervals4    #dg4      
,seventh4 ,unstable groups may be       
repeated in progressions of  intervals1 
in which case the movement in the group 
is conveyed to the  whole series1 in    
which there will be1 also1 the movement 
of a gradual  increase of attractions   

from one angle of vision to another4 ,in
 all  such cases contrary motion should 
be avoided if the object is ,rhythm4    
,the several movements should have a    
harmony of direction4    ,illustration3 
,fig4 #dh    ,in this case the movement 
in the group is felt throughout the     
series1  and the force of the movement  
is enhanced by the force of a gradual   
increase of attractions from one visual 
angle to another1 in the same           
direction1 to the right4 ,by reversing  
the direction of increasing  attractions
 and so getting the two movements into  
contrary motion1 the  feeling of rhythm 
would be much diminished4 ,such contrary
 motions are  unsatisfactory unless     
,balance can be achieved4 ,in that case 
all sense  of movement and of rhythm    
disappears4    #dh4 ,eighth4 ,unstable  
groups may be repeated1 not only in a   
gradation  of intervals1 but in a       
gradation of scale1 in which case we    
have a  combination of three causes of  
movement3 lack of stability in the      

group repeated1 a gradual increase in   
the number of attractions in  the       
sequence of visual angles1 and a        
crowding or convergence of the          
attractions4 ,rhythms of this type will 
not be satisfactory unless the  three   
movements have the same direction4      
,illustration3 ,fig4 #di    ,here we    
have the repetition of an unstable group
 of attractions in a  progression of    
scale and also of intervals4 ,the       
arrangement gives us  three elements of 
movement1 all in the same direction4    
#di4 ,two or even more of such rhythms  
as ,i have described may be  combined in
 one compound rhythm1 in which the eye  
will follow two  or more distinct       
movements at the same time4 ,it is      
important in all  compound rhythms that 
there should be no opposition or        
conflict of  movements1 unless of course
 the object is to achieve a balance of  
contrary movements4 ,corresponding      
rhythms in contrary motion balance  one 
another4 ,if one of the movements is to 

the right1 the other to the  left1 the  
balance will be symmetrical4            
,,attitudes      ,,relations ,,of       
,,position ,,in ,,different ,,attitudes 
#ej4 ,given any relation of positions   
7directions1 distances1 intervals71  it 
may be turned upon a center and so made 
to take an indefinite number  and       
variety of attitudes4 ,it may be        
inverted and the inversion may be       
turned upon a center1 producing another 
series of attitudes4 ,except  in cases  
of axial balance1 the attitudes of the  
second series will be  different from   
those of the first4    ,illustration3   
,fig4 #ej    ,in this case the relation 
of positions being turned upon a center 
changes its attitude1 while the         
positions within the group remain       
relatively unchanged4 ,there is no      
change of shape4    ,illustration3 ,fig4
 #ea    ,in this case the same group has
 been inverted1 and a second series of  
attitudes is shown1 differing from the  
first series4    ,illustration3 ,fig4   

#eb    ,in this case1 however1 which is 
a case of axial balance1 the inversion  
of the group and the turning of the     
inversion on a center gives no          
additional attitudes4    #ea4 ,among all
 possible attitudes there are four which
 are principal or  fundamental1 which we
 may distinguish as follows3--          
,illustration3 ,fig4 #ec    ,these      
principal attitudes are3 ,first1 ,i1 the
 original attitude1  whatever it is2    
second1 ,,ii1 the single inversion of   
that attitude1 to  the right on a       
vertical axis2 third1 ,,iii1 the double 
inversion of the  original attitude1    
first to the right then down2 and1      
fourth1 ,,iv1 the  single inversion of  
the original position1 down across the  
horizontal  axis4      ,,the ,,order    
,,of ,,harmony ,,in ,,attitudes    #eb4 
,the repetition of any relation of      
positions without change of  attitude   
gives us ,harmony of ,attitudes4        
,illustration3 ,fig4 #ed    ,in this    
case we have not only a ,harmony in the 

repetition of a certain  relation of    
positions and of intervals1 but a       
,harmony of ,attitudes4 ,we  have1 in   
the relation of positions repeated1 a   
certain shape4 ,in the  repetition of   
the shape we have ,shape-,harmony4 ,in  
the repetition of the  shape in a       
certain attitude we have a ,harmony of  
,attitudes4    ,illustration3 ,fig4 #ee 
,in this case we have lost the ,harmony 
of ,attitudes which we had in ,fig4     
#ed1 but not the ,harmony of a certain  
shape repeated4    #ec4 ,the            
possibilities of ,harmony in the        
repetition of any relation  of positions
 in the same attitude has been          
discussed4 ,a ,harmony of  ,attitudes   
will occur1 also1 in the repetition of  
any relation of  attitudes4             
,illustration3 ,fig4 #ef    ,here we    
have ,harmony in the repetition of a    
relation of two attitudes  of a certain 
group of positions4 ,the combination of 
the two attitudes  gives us another     
group of positions and the ,harmony lies

 in the  repetition of this group4      
,,the ,,order ,,of ,,balance ,,in       
,,attitudes    #ed4 ,it is to be        
observed that single inversions in any  
direction1 for  example the relation of 
attitudes ,i and ,,ii1 ,,ii and ,,iii1  
,,iii and ,,iv1  ,,iv and ,i1 in ,fig4  
#ec1 shows an opposition and ,balance of
 ,attitudes  upon the axis of inversion4
 ,the relation of positions ,i and ,,ii 
and  ,,iii and ,,iv1 the relation of the
 two groups on the left to the two      
groups on the right1 illustrates the    
idea of ,symmetry of ,attitudes1  the   
axis of balance being vertical4 ,by     
,symmetry ,i mean1 in all cases1  right 
and left balance on a vertical axis4    
,all double inversions1  the relation of
 positions ,i and ,,iii1 and ,,ii and   
,,iv1 in ,fig4 #ec1 are                 
,attitude-,balances1 not on axes1 but on
 centers4 ,the balance of these  double 
inversions is not symmetrical in the    
sense in which ,i use the  word         
symmetry1 nor is it axial4 ,it is       

central4      ,,the ,,order ,,of        
,,rhythm ,,in ,,attitudes    #ee4 ,when 
movement is suggested by any series of  
attitudes and the  movement is regulated
 by equal or regularly progressive      
intervals1 we  have a ,rhythm of        
,attitudes4    ,illustration3 ,fig4 #eg 
,in this case the changes of attitude   
suggest a falling movement to  the right
 and down4 ,in the regular progression  
of this movement  through marked        
intervals we have the effect of ,rhythm1
 in spite of  the fact that the relation
 of positions repeated has axial        
balance4  ,the intervals in this case   
correspond1 producing                   
,interval-,harmony4  ,the force of this 
,rhythm might be increased if the       
relation of  positions repeated         
suggested a movement in the same        
direction4 ,we  should have ,rhythm1 of 
course1 in the repetition of any such   
unstable  attitude-rhythms at equal or  
lawfully varying intervals4             
,,lines      ,,definition ,,of ,,lines  

#ef4 ,taking any dot and drawing it out 
in any direction1 or in a series  or    
sequence of directions1 it becomes a    
line4 ,the line may be drawn in  any    
tone1 in any value1 color or            
color-intensity4 ,in order that the     
line may be seen1 the tone of it must   
differ from the ground-tone upon  which 
it is drawn4 ,the line being distinctly 
visible1 the question of  tone need not 
be raised at this point of our          
discussion4 ,we will study  the line1   
first1 as a line1 not as an effect of   
light4    ,the line may be drawn long or
 short1 broad or narrow4 ,as the line   
increases in breadth1 however1 it       
becomes an area4 ,we will disregard  for
 the present all consideration of       
width-measures in the line and  confine 
our attention to the possible changes of
 direction in it1 and  to possible      
changes in its length4    ,we can draw  
the line in one direction from beginning
 to end1 in which  case it will be      
straight4 ,if1 in drawing the line1 we  

change its  direction1 we can do this   
abruptly1 in which case the line becomes
  angular1 or we can do it gradually1 in
 which case it becomes curved4  ,lines  
may be straight1 angular1 or curved4    
,they may have two of these             
characteristics or all three of them4   
,the shapes of lines are of  infinite   
variety4      ,,changes ,,of ,,direction
 ,,in ,,lines      ,angles    #eg4      
,regarding the line which is drawn as a 
way or path upon which we  move and     
proceed1 we must decide1 if we change   
our direction1 whether  we will turn to 
the right or to the left1 and whether we
 will turn  abruptly or gradually4 ,if  
we change our direction abruptly we must
  decide how much of a change of        
direction we will make4 ,is it to be a  
turn of #cj or #fj or #ij or #ace8 ,how 
much of a turn shall it be8             
,illustration3 ,fig4 #eh    ,the above  
illustrations are easy to understand and
 require no  explanation4 ,an abrupt    
change of #ahj means1 of course1        

returning upon  the line just drawn4    
,curves    #eh4 ,in turning1 not        
abruptly but gradually1 changing the    
direction at  every point1 that is to   
say in making a curve1 the question is1 
how  much of a turn to make in a given  
distance1 through how many degrees  of  
the circle to turn in one inch 7#a71 in 
half an inch 771 in two  inches 7#b74   
,in estimating the relation of arcs1 as 
distances1 to  angles of curvature1 the 
angles of the arcs1 the reader will find
 it  convenient to refer to what ,i may 
call an ,arc-,meter4 ,the principle of  
this meter is shown in the following    
diagram3--    ,illustration3 ,fig4 #ei  
,if we wish to turn #cj in 1 we take the
 angle of #cj and look within  it for an
 arc of 4 ,the arc of the right length  
and the right angle  being found1 it can
 be drawn free-hand or mechanically1 by 
tracing  or by the dividers4 ,using this
 meter1 we are able to draw any curve   
or combination of curves1 approximately2
 and we are able to describe  and define

 a line1 in its curvatures1 so          
accurately that it can be  produced     
according to the definition4 ,owing1    
however1 to the difficulty  of measuring
 the length of circular arcs accurately1
 we may find it  simpler to define the  
circular arc by the length of its radius
 and the  angle through which the radius
 passes when the arc is drawn4          
,illustration3 ,fig4 #fj    ,here1 for  
example1 is a certain circular arc4 ,it 
is perhaps best  defined and described  
as the arc of a half inch radius and an 
angle  of ninety degrees1 or in writing1
 more briefly1 rad4  #ij4 ,regarding    
every curved line either as a circular  
arc or made up of a series of  circular 
arcs1 the curve may be defined and      
described by naming the arc  or arcs of 
which it is composed1 in the order in   
which they are to be  drawn1 and the    
attitude of the curve may be determined 
by starting from  a certain tangent     
drawn in a certain direction4 ,the      
direction of the  tangent being given1  

the first arc takes the direction of the
 tangent1  turning to the right of it or
 to the left4    ,illustration3 ,fig4   
#fa    ,here is a curve which is        
composed of four circular arcs to be    
drawn in  the following order3--        
,tangent up-right #de1 arc right radius 
#a #fj1 arc left radius  #ij1  arc right
 radius  #ahj4    ,two arcs will often  
come together at an angle4 ,the         
definition of the  angle must be given  
in that case4 ,it is1 of course1 the    
angle made by  tangents of the arcs4    
,describing the first arc and the       
direction 7right  or left so many       
degrees7 which the tangent of the second
 arc takes  from the tangent of the     
first arc2 then describing the second   
arc and  stating whether it turns from  
its tangent to the right or to the left1
  we shall be able to describe1 not only
 our curves1 but any angles which  may  
occur in them4    ,illustration3 ,fig4  
#fb    ,here is a curve which1 so far as
 the arcs are concerned1 of which it is 

composed1 resembles the curve of ,fig4  
#fa2 but in this case the third  arc    
makes an angle with the second4 ,that   
angle has to be defined4  ,drawing the  
tangents1 it appears to be a right      
angle4 ,the definition of  the line     
given in ,fig4 #fb will read as         
follows3--    ,tangent down right #de1  
arc left radius #a #fj1 arc right radius
   #ij1 tangent left #ij1 arc left      
#ahj4    #ei4 ,in this way1 regarding   
all curves as circular arcs or composed 
of  circular arcs1 we shall be able to  
define any line we see1 or any line     
which we wish to produce1 so far as     
changes of direction are concerned4     
,for the purposes of this discussion1 ,i
 shall consider all curves as  composed 
of circular arcs4    ,there are many    
curves1 of course1 which are not        
circular in character1  nor composed1   
strictly speaking1 of circular arcs4    
,the ,spirals are in  no part circular4 
,elliptical curves are in no part       
circular4 ,all curves  may1             

nevertheless1 be approximately drawn as 
compositions of circular  arcs4 ,the    
approximation to curves which are not   
circular may be easily  carried beyond  
any power of discrimination which we    
have in the sense  of vision4 ,the      
method of curve-definition1 which ,i    
have described1  though it may not be   
strictly mathematical1 will be found    
satisfactory  for all purposes of ,pure 
,design4 ,it is very important that we  
should be  able to analyze our lines    
upon a single general principle2 to     
discover  whether they are illustrations
 of ,order4 ,we must know whether any   
given  line1 being orderly1 is orderly  
in the sense of ,harmony1 ,balance1 or  
,rhythm4 ,it is equally important1 if we
 wish to produce an orderly as          
distinguished from a disorderly line1   
that we should have some general        
principle to follow in doing it1 that we
 should be able to produce  forms of    
,harmony or ,balance or ,rhythm in a    
line1 if we wish to do so4              

,,differences ,,of ,,scale ,,in ,,lines 
#fj4 ,having drawn a line of a certain  
shape1 either straight or angular  or   
curved1 or partly angular1 partly       
curved1 we may change the measure  of   
the line1 in its length1 without        
changing its shape4 ,that is to  say1 we
 may draw the line longer or shorter1   
keeping all changes of  direction1 such 
as they are1 in the same positions1     
relatively4 ,in that  way the same shape
 may be drawn larger or smaller4 ,that  
is what we mean  when we speak of a     
change of scale or of measure which is  
not a change  of shape4                 
,,differences ,,of ,,attraction ,,in    
,,lines    #fa4 ,a line attracts        
attention in the measure of the         
tone-contrast which  it makes with the  
ground-tone upon which it is drawn4 ,it 
attracts  attention1 also1 according to 
its length1 which is an extension of the
  tone-contrast4 ,it attracts more      
attention the longer it is1 provided it 
lies1 all of it1 well within the field  

of vision4 ,it attracts attention  also 
in the measure of its concentration4    
,illustration3 ,fig4 #fc    ,line 8a0   
would attract less attention than it    
does if the  tone-contrast1 black on a  
ground of white paper1 were diminished1 
if the line were gray1 not black4 ,in   
line 8b0 there is twice the  extension  
of tone-contrast there is in 8a40 ,for  
that reason 8b0 is more  attractive4    
,if1 however1 8a0 were black and 8b0    
were gray1 8a0 might be  more attractive
 than 8b10 because of the greater       
tone-contrast4    ,illustration3 ,fig4  
#fd    ,in this illustration the curved 
line is more attractive than the        
straight line because it is more        
concentrated1 therefore more definite4  
,the extent of tone-contrast is the     
same1 the lines being of the same       
length4    ,illustration3 ,fig4 #fe     
,in this line there is no doubt as to   
the greater attraction of the  twisted  
end1 on account of the greater          
concentration it exhibits4  ,the extent 

of tone-contrast is the same at both    
ends4 ,the force of  attraction in the  
twisted end of the line would be        
diminished if the  twisted end were made
 gray instead of black4 ,the pull of    
concentration  at one end might1        
conceivably1 be perfectly neutralized by
 the pull of  a greater tone-contrast at
 the other4    ,illustration3 ,fig4 #ff 
,in 8b0 we have a greater extension of  
tone-contrast in a given space4  ,the   
space becomes more attractive in        
consequence4    ,this might not be the  
case1 however1 if the greater extension 
of tone-contrast in one case were       
neutralized by an increase of           
tone-contrast in the other4      ,,the  
,,order ,,of ,,harmony ,,in ,,lines     
#fb4 ,harmony of ,direction means no    
change of direction4    ,illustration3  
,fig4 #fg    ,in this case we have a    
,harmony of ,direction in the line1     
because it  does not change its         
direction4    #fc4 ,harmony of ,angles4 
,we may have ,harmony in the repetition 

of a  certain relation of directions1 as
 in an angle4    ,illustration3 ,fig4   
#fh    ,the angle up #de and down #de is
 here repeated seven times4             
,illustration3 ,fig4 #fi    ,in this    
case we have a great many angles in the 
line1 but they are all  right angles1 so
 we have a ,harmony of ,angles4         
,illustration3 ,fig4 #gj    ,in this    
case we have ,harmony in the repetition 
of a certain relation  of angles1 that  
is to say1 in the repetition of a       
certain form of  angularity4    #fd4    
,equality of lengths or measures between
 the angles of a line means  a ,harmony 
of ,measures4    ,illustration3 ,fig4   
#ga    ,in this case1 for example1 we   
have no ,harmony of ,angles1 but a      
,harmony  of ,measures in the legs of   
the angles1 as they are called4    #fe4 
,we have a ,harmony of ,curvature in a  
line when it is composed wholly  of arcs
 of the same radius and the same angle4 
,illustration3 ,fig4 #gb    ,this is a  
case of ,harmony of ,curvature4 ,there  

is no change of direction  here1 in the 
sequence of corresponding arcs4         
,illustration3 ,fig4 #gc    ,here1      
again1 we have a ,harmony of ,curvature4
 ,in this case1 however1  there is a    
regular alternation of directions in the
 sequence of  corresponding arcs4 ,in   
this regular alternation1 which is the  
repetition of a certain relation of     
directions1 there is a ,harmony of      
,directions4    ,illustration3 ,fig4 #gd
    ,in this case the changes of        
direction are abrupt 7angular7 as well  
as gradual4 ,there is no regular        
alternation1 but the harmony of         
corresponding arcs repeated will be     
appreciated1 nevertheless4    #ff4 ,arcs
 produced by the same radius are in     
harmony to that extent1  having the     
radius in common4    ,illustration3     
,fig4 #ge    ,this is an example of a   
harmony of arcs produced by radii of the
 same  length4 ,the arcs vary in length4
    #fg4 ,arcs of the same angle-measure
 produced by different radii are in     

,harmony to the extent that they have an
 angle-measure in common4               
,illustration3 ,fig4 #gf    ,this is an 
example4    ,arcs having the same length
 but varying in both radius and angle   
may be  felt to be in ,measure-,harmony4
 ,it is doubtful1 however1 whether lines
  of the same length but of very        
different curvatures will be felt to    
correspond4 ,if the correspondence of   
lengths is not felt1 visually1 it  has  
no interest or value from the point of  
view of ,pure ,design4    #fh4 ,any line
 may be continued in a repetition or    
repetitions of  its shape1 whatever the 
shape is1 producing what ,i call a      
,linear  ,progression4 ,in the          
repetitions we have ,shape-,harmony4    
,illustration3 ,fig4 #gg    ,this is an 
example of ,linear ,progression4 ,the   
character of the  progression is        
determined by the shape-motive which is 
repeated in it4    #fi4 ,the repetition 
of a certain shape-motive in a line is  
not1  necessarily1 a repetition in the  

same measure or scale4 ,a repetition of 
the same shape in the same measure means
 ,measure and ,shape-,harmony in  the   
progression4 ,a repetition of the same  
shape in different measures  means      
,shape-,harmony without                 
,measure-,harmony4    ,illustration3    
,fig4 #gh    ,here we have the          
repetition of a certain shape in a line1
 in a  progression of measures4 ,that   
gives us ,shape-,harmony and a ,harmony 
of  ,proportions1 without               
,measure-,harmony4    #gj4 ,in the      
repetition of a certain shape-motive in 
the line1 the  line may change its      
direction abruptly or gradually1        
continuously or  alternately1 producing 
a ,linear ,progression with changes of  
direction4    ,illustration3 ,fig4 #gi  
,in ,fig4 #gi there is a certain change 
of direction as we pass from  one       
repetition to the next4 ,in the         
repetition of the same change  of       
direction1 of the same angle of         
divergence1 we have ,harmony4 ,if  the  

angles of divergence varied we should   
have no such ,harmony1  though we might 
have ,harmony in the repetition of a    
certain relation  of divergences4 ,any  
repetition of a certain change or       
changes of  direction in a linear       
progression gives a ,harmony of         
,directions in the  progression4        
,illustration3 ,fig4 #hj    ,in this    
case there is a regular alternation of  
directions in the  repeats4 ,the repeats
 are drawn first to the right1 then up1 
and the  relation of these two          
directions is then repeated4    #ga4 ,by
 inverting the motive of any            
progression1 in single or in double     
inversion1 and repeating the motive     
together with its inversion1 we are     
able to vary the character of the       
progression indefinitely4               
,illustration3 ,fig4 #ha    ,in this    
case we have a single inversion of the  
motive and a repetition  of the motive  
with its inversion4 ,compare this       
progression with the one  in ,fig4 #gg1 

where the same motive is repeated       
without inversion4    ,illustration3    
,fig4 #hb    ,here we have the same     
motive with a double inversion1 the     
motive  with its double inversion being 
repeated4 ,the inversion gives us       
,shape-,harmony without ,harmony of     
,attitudes4 ,we have ,harmony1 however1 
in a repetition of the relation of two  
attitudes4 ,these double  inversions are
 more interesting from the point of view
 of ,balance than  of ,harmony4         
,,the ,,order ,,of ,,balance ,,in       
,,lines    #gb4 ,we have ,balance in a  
line when one half of it is the single  
or  double inversion of the other half2 
that is1 when there is an equal         
opposition and consequent equilibrium of
 attractions in the line4 ,when  the    
axis of the inversion is vertical the   
balance is symmetrical4                 
,illustration3 ,fig4 #hc    ,there is   
,balance in this line because half of it
 is the single  inversion of the other  
half4 ,the balance is symmetrical       

because the  axis is vertical4 ,the     
balance1 although symmetrical1 is not   
likely  to be appreciated1 however1     
because the eye is sure to move along a 
line upon which there is no better      
reason for not moving than is found  in 
slight terminal contrasts4 ,the eye is  
not held at the center when  there is   
nothing to hold the eye on the center4  
,mark the center in any  way and the eye
 will go to it at once4 ,a mark or      
accent may be put at  the center1 or    
accents1 corresponding and equal1 may be
 put at equal  distances from the center
 in opposite directions4 ,the eye will  
then be  held at the center by the force
 of equal and opposite attractions4     
,illustration3 ,fig4 #hd    ,in this    
case the eye is held at the             
balance-center of the line by a  change 
of character at that point4             
,illustration3 ,fig4 #he    ,in this    
case the changes of character are at    
equal distances1 in  opposite           
directions1 from the center4 ,the center

 is marked by a break4  ,the axis being 
vertical1 the balance is a symmetrical  
one4    #gc4 ,the appreciation of       
,balance in a line depends very much    
upon the  attitude in which it is drawn4
    ,illustration3 ,fig4 #hf    ,in this
 case the balance in the line itself is 
just as good as it is  in ,fig4 #he2 but
 the axis of the balance being diagonal1
 the balance  is less distinctly felt4  
,the balance is unsatisfactory because  
the  attitude of the line is one which  
suggests a falling down to the left4    
,it is the instability of the line which
 is felt1 more than the balance  in it4 
,illustration3 ,fig4 #hg    ,in this    
case of double inversion1 also1 we have 
balance4 ,the balance  is more          
distinctly felt than it was in ,fig4    
#hf4 ,the attitude is one of  stability4
 ,this balance is neither axial nor     
symmetrical1 but central4    #gd4 ,a    
line balances1 in a sense1 when its     
inclinations are balanced4              
,illustration3 ,fig4 #hh    ,this line  

may be said to be in balance1 as it has 
no inclinations1  either to the right or
 to the left1 to suggest instability4   
,the  verticals and the horizontals1    
being stable1 look after themselves     
perfectly well4    ,illustration3 ,fig4 
#hi    ,this line has two unbalanced    
inclinations to the left4 ,it is1       
therefore1 less satisfactory than the   
line in ,fig4 #hh1 from the point  of   
view of ,balance4    ,illustration3     
,fig4 #ij    ,the two inclinations in   
this line counteract one another4 ,one  
inclination toward the left is balanced 
by a corresponding inclination  toward  
the right4    ,illustration3 ,fig4 #ia  
,in this case1 also1 there is no        
inclination toward the left which is    
not balanced by a corresponding         
inclination toward the right4           
,illustration3 ,fig4 #ib    ,in this    
line1 which is composed wholly of       
inclinations to the right  or left1     
every inclination is balanced1 and the  
line is1 therefore1  orderly in the     

sense of ,balance2 more so1 certainly1  
than it would  be if the inclinations   
were not counteracted4 ,this is the     
problem of  balancing the directions or 
inclinations of a line4    #ge4 ,a line 
having no balance or symmetry in itself 
may become balanced4  ,the line may be  
regarded as if it were a series of dots 
close together4  ,the line is then a    
relation of positions indicated by dots4
 ,it is  a composition of attractions   
corresponding and equal4 ,it is only    
necessary1 then1 to find what ,i have   
called the center of equilibrium1  the  
balance-center of the attractions1 and  
to indicate that center by a            
symmetrical inclosure4 ,the line will   
then become balanced4    ,illustration3 
,fig4 #ic    ,here is a line4 ,to find  
the center of its attractions it may be 
considered as if it were a line of dots1
 like this3--    ,illustration3 ,fig4   
#id    ,the principle according to which
 we find the balance-center is stated   
on page #bc4 ,the balance-center being  

found1 it must be indicated             
unmistakably4 ,this may be done by means
 of any symmetrical inclosure  which    
will draw the eye to the center and hold
 it there4    ,illustration3 ,fig4 #ie  
,in this case the balance-center is     
indicated by a rectangular  inclosure4  
,this rectangle is not1 however1 in     
harmony of character with  the line     
inclosed by it1 which is curved4        
,illustration3 ,fig4 #if    ,in this    
case the balance-center is indicated by 
a circle1 which1 being  a curve1 is in  
harmony of character with the inclosed  
line1 which is  also a curve4 ,i shall  
call this ,occult ,balance to           
distinguish it from  the unmistakable   
,balance of ,symmetry and other         
comparatively obvious  forms of         
,balance1 including the balance of      
double inversions4 ,as ,i  have said1 on
 page #bd1 the symmetrical framing must 
be sufficiently  attractive to hold the 
eye steadily at the center1 otherwise it
 does  not serve its purpose4      ,,the

 ,,order ,,of ,,rhythm ,,in ,,lines     
#gf4 ,the eye1 not being held on a      
vertical axis or on a balance-center1   
readily follows any suggestion of       
movement4    ,illustration3 ,fig4 #ig   
,in this case there is no intimation of 
any vertical axis or  balance-center4   
,the figure is consequently unstable4   
,there is a sense  of movement to the   
right4 ,this is due1 not only to the    
inclinations to  the right1 but to the  
convergences in that direction4         
,illustration3 ,fig4 #ih    ,in this    
case the movement is unmistakably to the
 left4 ,in such cases we  have movement1
 but no ,rhythm4    #gg4 ,rhythm        
requires1 not only movement1 but the    
order of regular and  marked intervals4 
,illustration3 ,fig4 #ii    ,in ,fig4   
#ii we have a line1 a linear            
progression1 which gives us the  feeling
 of movement1 unmistakably4 ,the        
movement1 which in the motive  itself is
 not rhythmical1 becomes rhythmical in  
its repetition at  regular1 and in this 

case equal1 intervals4 ,the intervals   
are marked by  the repetitions4    #gh4 
,it is a question of some interest to   
decide how many repetitions  are        
required in a ,rhythm4 ,in answer to    
this question ,i should say  three as a 
rule4 ,a single repetition shows us only
 one interval1 and  we do not know      
whether the succeeding intervals are to 
be equal or  progressive1 arithmetically
 progressive or geometrically           
progressive4  ,the rhythm is not defined
 until this question is decided1 as it  
will  be by two more repetitions4 ,the  
measures of the rhythm might take the   
form of a repeated relation of measures2
 a repetition1 for example1 of  the     
measures two1 seven1 four4 ,in that case
 the relation of the three  measures    
would have to be repeated at least three
 times before the  character of the     
rhythm could be appreciated4    #gi4    
,any contrariety of movement in the     
motive is extended1 of course1  to its  
repetitions4    ,illustration3 ,fig4    

#ajj    ,in this case1 for example1     
there are convergences and1             
consequently1  movements both up and    
down4 ,this contrariety of movements is 
felt  through the whole series of       
repetitions4 ,other things being equal1 
,i  believe the eye moves up more       
readily than down1 so that convergences 
downward have less effect upon us than  
corresponding convergences  upward4     
,illustration3 ,fig4 #aja    ,in this   
case1 by omitting the long vertical line
 ,i have diminished the  amount of      
convergence downward4 ,in that way ,i   
have given predominance  to the upward  
movement4 ,instead of altogether        
omitting the long  vertical line1 ,i    
might have changed its tone from black  
to gray4 ,that  would cause an          
approximate instead of complete         
disappearance4 ,it should  be remembered
 that in all these cases the habit of   
reading comes in to  facilitate the     
movements to the right4 ,it is easier   
for the eye to move  to the right than  

in any other direction1 other things    
being equal4  ,the movement back to the 
beginning of another line1 which is of  
course  inevitable in reading1 produces 
comparatively little impression upon    
us1 no more than the turning of the     
page4 ,the habit of reading to the      
right happens to be our habit4 ,the     
habit is not universal4    #hj4 ,reading
 repetitions and alternations to the    
right1 always1 ,i1 for  a long time1    
regarded such repetitions and           
alternations as rhythmical1  until      
,professor ,mowll raised the question   
whether it is necessary  to read all    
alternations to the right when there is 
nothing in the  alternations themselves 
to suggest a movement in one direction  
rather  than another4 ,why not read them
 to the left as well as to the right8   
,we at once decided that the movement in
 a ,rhythm must be determined  by the   
character of the ,rhythm itself1 not by 
any habit of reading1  or any other     
habit1 on our part4 ,it was in that way 

that we came  to regard repetitions and 
alternations as illustrations of        
,harmony  rather than of ,rhythm4       
,rhythm comes into the ,harmony of a    
,repeated  ,relation when the relation  
is one which causes the eye to move in  
one  direction rather than another1 and 
when the movement is carried on from    
repetition to repetition1 from measure  
to measure4    #ha4 ,the repetition of a
 motive at equal intervals1 when there  
is no  movement in the motive1 gives us 
no feeling of ,rhythm4    ,illustration3
 ,fig4 #ajb    ,in this case1 for       
example1 we have a repetition in the    
line of a  certain symmetrical shape4   
,as there is no movement in the shape   
repeated1 there is no ,rhythm in the    
repetition4 ,there is nothing to  draw  
the eye in one direction rather than    
another4 ,the attractions at  one end of
 the line correspond with the           
attractions at the other4    #hb4 ,the  
feeling of ,rhythm may be induced by a  
regular diminution of  measure or scale 

in the repetitions of the motive and in 
the intervals  in which the repetitions 
take place4    ,illustration3 ,fig4 #ajc
    ,in this case the shape repeated is 
still symmetrical1 but it is  repeated  
with a gradual diminution of scale and  
of intervals1 by which  we are given a  
feeling of rhythmic movement4 ,the      
change of scale and of  intervals1 to   
induce a sense of rhythmic motion1 must 
be regular4 ,to  be regular the change  
must be in the terms of one or the other
 of the  regular progressions2 the      
arithmetical progression1 which proceeds
 by  a certain addition1 or the         
geometrical1 which proceeds by a certain
  multiplication4 ,the question may     
arise in this case 7,fig4 #ajc7 whether 
the movement of the ,rhythm is to the   
right or to the left4 ,i feel1  myself1 
that the movement is to the right4 ,in  
diminishing the scale of  the motive and
 of the intervals we have1 hardly at    
all1 diminished the  extent of the      
tone-contrast in a given angle of       

vision4 ,see ,fig4 #da1  p4 #bg1 showing
 the increase of attractions from one   
visual angle to  another4 ,at the same  
time we come at the right end of the    
progression  to two or more repetitions 
in the space of one4 ,we have1          
therefore1  established the attraction  
of a crowding together at the right end 
of the series4 ,see the passage 7p4 #dc7
 on the attractiveness of a  line4 ,the 
force of the crowding together of       
attractions is1 ,i feel1  sufficient to 
cause a movement to the right4 ,it must 
be remembered1  however1 that the       
greater facility of reading to the right
 is added  here to the pull of a greater
 crowding together of attractions in the
  same direction1 so the movement of the
 ,rhythm in that direction may not  be  
very strong after all4 ,if the direction
 of any ,rhythm is doubtful1  the       
,rhythm itself is doubtful4    #hc4 ,the
 feeling of ,rhythm may be induced1 as  
,i have said1 by a gradual  increase of 
the number of attractions from measure  

to measure1 an  increase of the extent  
of tone-contrast4    ,illustration3     
,fig4 #ajd    ,increasing the extent of 
tone-contrast and the number of         
attractions in  the measures of the     
,rhythm in ,fig4 #ajc1 we are able to   
force the eye to  follow the series in  
the direction contrary to the habit of  
reading1  that is to say from right to  
left4    ,a decrease in the forces of   
attraction in connection with a decrease
  of scale is familiar to us all in the 
phenomena of perspective4 ,the  gradual 
disappearance of objects in aerial      
perspective does away  with the         
attraction of a greater crowding        
together of objects in the  distance4   
,illustration3 ,fig4 #aje    ,in this   
case the diminution of scale has been   
given up and there is  no longer any    
crowding together4 ,there is no chance  
of this rhythm  being read from left to 
right except by an effort of the will4  
,the  increase of attractions toward the
 left is much more than sufficient to   

counteract the habit of reading4    #hd4
 ,the force of a gradual coming together
 of attractions1 inducing  movement in  
the direction of such coming together1  
is noticeable in  spiral shapes4        
,illustration3 ,fig4 #ajf    ,in this   
case we have a series of straight lines 
with a constant and  equal change of    
direction to the right1 combined with a 
regular  diminution of measures in the  
length of the lines1 this in the terms  
of an arithmetical progression4 ,the    
movement is in the direction of         
concentration and it is distinctly      
marked in its measures4 ,the movement   
is therefore rhythmical4                
,illustration3 ,fig4 #ajg    ,in this   
case we have a series of straight lines 
with a constant change  of direction to 
the right2 but in this case the changes 
of measure in  the lines are in the     
terms of a geometrical progression4 ,the
 direction  is the same1 the pull of    
concentration perhaps stronger4         
,illustration3 ,fig4 #ajh    ,in this   

,rhythm there is an arithmetical        
gradation of measures  in the changes of
 direction1 both in the length of the   
legs and  in the measure of the angles4 
,the pull of concentration is1 in  this 
case1 very much increased4 ,it is       
evident that the legs may  vary         
arithmetically and the angles           
geometrically2 or the angles            
arithmetically and the legs             
geometrically4    #he4 ,if1 in the place
 of the straight lines1 which form the  
legs1 in  any of the examples given1 are
 substituted lines which in themselves  
induce movement1 the feeling of ,rhythm 
may be still further increased1         
provided the directions of movement are 
consistent4    ,illustration3 ,fig4 #aji
    ,in this case the movement is in the
 direction of increasing  concentration 
and in the direction of the             
convergences4    ,if the movement of the
 convergences be contrary to the        
movement of  concentration1 there will  
be in the figure a contrary motion which

  may diminish or even entirely prevent 
the feeling of ,rhythm4 ,if the         
movement in one direction or the other  
predominates1 we may still  get the     
feeling of ,rhythm1 in spite of the     
drawback of the other and  contrary     
movement4    ,illustration3 ,fig4 #aaj  
,in this case the linear convergences   
substituted for the straight lines  are 
contrary to the direction of increasing 
concentration4 ,the movement  is        
doubtful4    #hf4 ,corresponding        
rhythms1 set in contrary motion1 give us
 the feeling  of ,balance rather than of
 ,rhythm4 ,the balance in such cases is 
a  balance of movements4                
,illustration3 ,fig4 #aaa    ,this is an
 example of corresponding and opposed   
rhythms producing the  feeling1 not of  
,rhythm1 but of ,balance4               
,,attitudes      ,,lines ,,in           
,,different ,,attitudes    #hg4 ,any    
line or linear progression may be turned
 upon a center1 and so  made to take an 
indefinite number and variety of        

attitudes4 ,it may be  inverted upon an 
axis1 and the inversion may be turned   
upon a center  producing another series 
of attitudes which1 except in the case  
of  axial symmetry in the line1 will be 
different from those of the first       
series4    ,illustration3 ,fig4 #aab    
,in this case the line changes its      
attitude4    ,illustration3 ,fig4 #aac  
,in this case ,i have inverted the line1
 and turning the inversion upon a       
center ,i get a different set of        
attitudes4    ,illustration3 ,fig4 #aad 
,in this case1 which is a case of axial 
symmetry in the line1 the  inversion    
gives us no additional attitudes4       
,,the ,,order ,,of ,,harmony ,,in ,,the 
,,attitudes ,,of ,,lines    #hh4 ,when  
any line or linear progression is       
repeated1 without change of  attitude1  
we have a ,harmony of ,attitudes4       
,illustration3 ,fig4 #aae    ,this is an
 illustration of ,harmony of ,attitudes4
 ,it is also an  illustration of        
,interval-,harmony4    #hi4 ,we have a  

,harmony of ,attitudes1 also1 in the    
repetition of any  relation of two or   
more attitudes1 the relation of         
attitudes being  repeated without change
 of attitude4    ,illustration3 ,fig4   
#aaf    ,we have here a ,harmony of     
,attitudes due to the repetition of a   
certain  relation of attitudes1 without 
change of attitude4      ,,the ,,order  
,,of ,,balance ,,in ,,the ,,attitudes   
,,of ,,lines    #ij4 ,when a line or    
linear progression is inverted upon any 
axis or  center1 and we see the original
 line and its inversion side by side1 we
  have a ,balance of ,attitudes4        
,illustration3 ,fig4 #aag    ,the       
relation of attitudes ,i1 ,,ii1 of      
,,iii1 ,,iv1 and of ,i1 ,,ii1 ,,iii1    
,,iv1  is that of ,symmetrical ,balance 
on a vertical axis4 ,the relation of    
attitudes ,i1 ,,iv1 and of ,,ii1 ,,iii1 
is a relation of ,balance but not  of   
,symmetrical ,balance4 ,this is true1   
also1 of the relation of ,i1  ,,iii and 
of ,,ii1 ,,iv4 ,double inversions are   

never symmetrical1 but they  are        
illustrations of ,balance4 ,the balance 
of double inversions is  central1 not   
axial4 ,these statements are all        
repetitions of statements  previously   
made about positions4      ,,the ,,order
 ,,of ,,rhythm ,,in ,,the ,,attitudes   
,,of ,,lines    #ia4 ,it often happens  
that a line repeated in different       
attitudes  gives us the sense of        
movement4 ,it does this when the        
grouping of the  repetitions suggests   
instability4 ,the movement is rhythmical
 when it  exhibits a regularity of      
changes in the attitudes and in the     
intervals  of the changes4              
,illustration3 ,fig4 #aah    ,in this   
case we have a movement to the right1   
but no ,rhythm1 the  intervals being    
irregular4    ,illustration3 ,fig4 #aai 
,in this case the changes of attitude   
and the intervals of the changes  being 
regular1 the movement becomes           
rhythmical4 ,the direction of the       
rhythm is clearly down-to-the-right4    

#ib4 ,in the repetition of any line we  
have a ,harmony1 due to the  repetition4
 ,if the line is repeated in the same   
attitude1 we have a  ,harmony of        
,attitudes4 ,if it is repeated in the   
same intervals1 we have  a ,harmony of  
,intervals4 ,we have ,harmony1 also1 in 
the repetition of any  relation of      
attitudes or of intervals4    ,we have  
not yet considered the arrangement or   
composition of two or  more lines of    
different measures and of different     
shapes4      ,,the ,,composition ,,of   
,,lines    #ic4 ,by the ,composition of 
,lines ,i mean putting two or more lines
  together1 in juxtaposition1 in contact
 or interlacing4 ,our object in  the    
composition of lines1 so far as ,pure   
,design is concerned1 is to  achieve    
,order1 if possible ,beauty1 in the     
several modes of ,harmony1  ,balance1   
and ,rhythm4      ,,harmony ,,in ,,the  
,,composition ,,of ,,lines    #id4 ,we  
have ,harmony in line-compositions when 
the lines which are  put together       

correspond in all respects or in some   
respects1 when  they correspond in      
attitudes1 and when there is a          
correspondence of  distances or         
intervals4    ,illustration3 ,fig4 #abj 
,in this case the lines of the          
composition correspond in tone1 measure1
  and shape1 but not in attitude2 and   
there is no correspondence in  distances
 or intervals4    ,illustration3 ,fig4  
#aba    ,in this case the attitudes     
correspond1 as they did not in ,fig4    
#abj4  ,there is still no correspondence
 of intervals4    ,illustration3 ,fig4  
#abb    ,here we have the correspondence
 of intervals which we did not have     
either in ,fig4 #abj or in ,fig4 #aba4  
,there is not only a ,harmony of        
,attitudes and of ,intervals1 in this   
case1 but the ,harmony of a  repetition 
in one direction1 ,direction-,harmony4  
,in all these cases we  have the        
repetition of a certain angle1 a right  
angle1 and of a certain                 
measure-relation between the legs of the

 angle1 giving ,measure and             
,shape-,harmony4    #ie4 ,the repetition
 in any composition of a certain        
relation of  measures1 or of a certain  
proportion of measures1 gives           
,measure-,harmony  to the composition4  
,the repetition of the relation one to  
three in  the legs of the angle1 in the 
illustrations just given1 gives to the  
compositions the ,harmony of a          
,recurring ,ratio4 ,by a proportion ,i  
mean  an equality between ratios1 when  
they are numerically different4 ,the    
relation of one to three is a ratio4    
,the relation of one to three and  three
 to nine is a proportion4 ,we may have  
in any composition the  ,harmony of a   
,repeated ,ratio1 as in ,figs4 #abj1    
#aba1 #abb1 or we may have  a ,harmony  
of ,proportions1 as in the composition  
which follows4    ,illustration3 ,fig4  
#abc    #if4 ,to be in ,harmony lines   
are not necessarily similar in all      
respects4  ,as ,i have just shown1 lines
 may be in ,shape-,harmony1 without     

being  in any ,measure-,harmony4 ,lines 
are approximately in harmony when they  
correspond in certain particulars1      
though they differ in others4 ,the  more
 points of resemblance between them1 the
 greater the harmony4 ,when  they       
correspond in all respects we have1 of  
course1 a perfect harmony4              
,illustration3 ,fig4 #abd    ,this is a 
case of ,shape-,harmony without         
,measure-,harmony and without  ,harmony 
of ,attitudes4    ,illustration3 ,fig4  
#abe    ,in this case we have a ,harmony
 of ,shapes and of ,attitudes1 without  
,measure-,harmony or ,harmony of        
,intervals4 ,this is a good illustration
 of  a ,harmony of ,proportions4        
,straight lines are in ,harmony of      
,straightness because they are all      
straight1 however much they differ in   
tone or measure4 ,they are in  ,harmony 
of ,measure when they have the same     
measure of length4 ,the  measures of    
width1 also1 may agree or disagree4 ,in 
every agreement we  have ,harmony4      

,angular lines are in ,harmony when they
 have one or more angles in  common4    
,the recurrence of a certain angle in   
different parts of a  composition brings
 ,harmony into the composition4         
,designers are very apt  to use         
different angles when there is no good  
reason for doing so1 when  the          
repetition of one would be more orderly4
    ,illustration3 ,fig4 #abf    ,the   
four lines in this composition have     
right angles in common4 ,to  that extent
 the lines are in ,harmony4 ,there is   
also a ,harmony in  the correspondence  
of tones and of width-measures in the   
lines4  ,considerable ,harmony of       
,attitudes occurs in the form of        
parallelisms4    ,illustration3 ,fig4   
#abg    ,these two lines have simply one
 angle in common1 a right angle1 and    
the angle has the same attitude in both 
cases4 ,they differ in other  respects4 
,illustration3 ,fig4 #abh    ,in these  
three lines the only element making for 
,harmony1 except the  same tone and the 

same width1 is found in the presence in 
each line  of a certain small arc of a  
circle4 ,straightness occurs in two of  
the  lines but not in the third4 ,there 
is a ,harmony1 therefore1 between  two  
of the lines from which the third is    
excluded4 ,there is1 also1 a  ,harmony  
of ,attitude in these two lines1 in     
certain parallelisms4      ,,balance    
,,in ,,the ,,composition ,,of ,,lines   
#ig4 ,lines balance when in opposite    
attitudes4 ,we get ,balance in all      
inversions1 whether single or double4   
,illustration3 ,fig4 #abi    ,here      
similar lines are drawn in opposite     
attitudes and we get ,measure  and      
,shape-,balance4 ,in the above case the 
axis of balance is vertical4  ,the      
balance is1 therefore1 symmetrical4     
,symmetrical ,balance is obtained  by   
the single inversion of any line or     
lines on a vertical axis4 ,double       
inversion gives a ,balance of ,measures 
and ,shapes on a center4 ,we have  no   
,symmetry in double inversions4 ,all    

this has been explained4                
,illustration3 ,fig4 #acj    ,we have   
,measure and ,shape-,balance on a center
 in this case4 ,it is  a case of double 
inversion4 ,it is interesting to turn   
these double  inversions on their       
centers1 and to observe the very        
different effects  they produce in      
different attitudes4    #ih4 ,shapes in 
order to balance satisfactorily must be 
drawn in the same  measure1 as in ,fig4 
#aca which follows4    ,illustration3   
,fig4 #aca    ,illustration3 ,fig4 #acb 
,here1 in ,fig4 #acb1 we have           
,shape-,harmony without                 
,measure-,harmony4  ,it might be argued 
that we have in this case an            
illustration of  ,shape-,balance without
 ,measure-,balance4 ,theoretically that 
is so1 but  ,shape-,balance without     
,measure-,balance is never satisfactory4
 ,if we  want the lines in ,fig4 #acb to
 balance we must find the balance-center
  between them1 and then indicate that  
center by a symmetrical inclosure4  ,we 

shall then have a ,measure-,balance     
7occult7 without ,shape-,balance4       
#ii4 ,when measures correspond but      
shapes differ the balance-center may  be
 suggested by a symmetrical inclosure or
 framing4 ,when that is done  the       
measures become balanced4               
,illustration3 ,fig4 #acc    ,here we   
have ,measure-,harmony and a            
,measure-,balance without               
,shape-,harmony or ,shape-,balance4 ,the
 two lines have different shapes but    
the same measures1 lengths and widths   
corresponding4 ,the balance-center  is  
found for each line4 ,see pp4 #ed1 #ee4 
,between the two centers is  found the  
center1 upon which the two lines will   
balance4 ,this center is  then suggested
 by a symmetrical inclosure4 ,the       
balancing measures in  such cases may1  
of course1 be turned upon their centers1
 and the axis  connecting their centers 
may be turned in any direction or       
attitude1  with no loss of equilibrium1 
so far as the measures are concerned4   

,illustration3 ,fig4 #acd    ,the       
,balance of ,measures here is just as   
good as it is in ,fig4  #acc4 ,the      
attitudes are changed but not the       
relation of the three  balance-centers4 
,the change of shape in the inclosure   
makes no  difference4    #ajj4          
,measure-,balance without               
,shape-,harmony or ,shape-,balance is   
satisfactory only when the              
balance-center is unmistakably indicated
 or  suggested1 as in the examples which
 ,i have given4    #aja4 ,there is      
another form of ,balance which is to be 
inferred from what  ,i have said1 on    
page #ah1 of the ,balance of            
,directions1 but it needs to  be        
particularly considered and more fully  
illustrated4 ,i mean a ,balance  in     
which directions or inclinations to the 
right are counteracted by  corresponding
 or equivalent directions or            
inclinations to the left4 ,the  idea in 
its simplest and most obvious form is   
illustrated in ,fig4 #bb1  on page #ah4 

,in that case the lines of inclination  
correspond4 ,they do  not necessarily   
correspond except in the extent of      
contrast1 which may  be distributed in  
various ways4    ,illustration3 ,fig4   
#ace    ,the balance of inclinations in 
this case is just as good as the balance
  in ,fig4 #bb4 ,there is no symmetry as
 in ,fig4 #bb4 ,three lines balance     
against one4 ,the three lines1 however1 
show the same extent of contrast  as the
 one4 ,so far as the inclinations are   
concerned they will balance  in any     
arrangement which lies well within the  
field of vision4 ,the eye  must be able 
to appreciate the fact that a           
disposition to fall to the  right is    
counteracted by a corresponding or      
equivalent disposition to  fall to the  
left4    ,illustration3 ,fig4 #acf      
,this arrangement of the inclining lines
 is just as good as the  arrangement in 
,fig4 #ace4 ,the inclinations may be    
distributed in any  way1 provided they  
counteract one another properly4        

,illustration3 ,fig4 #acg    ,in this   
case ,i have again changed the          
composition1 and having  suggested the  
balance-center of the lines1 as         
attractions1 by a  symmetrical          
inclosure1 ,i have added                
,measure-,balance 7occult7 to           
,inclination-,balance4 ,the ,order in   
,fig4 #acg is greater than the ,order in
  ,figs4 #ace and #acf4 ,in ,fig4 #acg  
two forms of ,balance are illustrated1  
in the other cases only one4 ,the value 
of any composition lies in the  number  
of orderly connections which it shows4  
,illustration3 ,fig4 #ach    ,in this   
case ,i have taken a long angular line  
and added a sufficient  number and      
extent of opposite inclinations to make 
a balance of  inclinations4 ,the        
horizontal part of the long line is     
stable1 so it  needs no counteraction1  
but the other parts incline in various  
degrees1  to the left or to the right4  
,each inclining part requires1          
therefore1  either a corresponding line 

in a balancing direction1 or two or more
  lines of equivalent extension in that 
direction4 ,in one case ,i have set     
three lines to balance one1 but they    
equal the one in length1 that is  to    
say1 in the extent of contrast4 ,we have
 in ,fig4 #ach an illustration  of      
occult ,measure-,balance and the        
,balance of ,inclinations4 ,i have      
illustrated the idea of                 
,inclination-,balance by very simple    
examples4  ,i have not considered the   
inclinations of curves1 nor have ,i     
gone1  at all1 into the more difficult  
problem of balancing averages of        
inclination1 when the average of two or 
more different inclinations of          
different extents of contrast has to be 
counteracted4 ,in ,tone-,relations  the 
inclinations are of tone-contrasts1 and 
a short inclination with a  strong      
contrast may balance a long inclination 
with a slight one1 or  several          
inclinations of slight contrasts may    
serve to balance one of a  strong       

contrast4 ,the force of any inclining   
line may be increased by  increasing the
 tone-contrast with the ground-tone4 ,in
 tone-relations  the problem becomes    
complicated and difficult4 ,the whole   
subject of  ,inclination-,balance is one
 of great interest and worthy of a      
separate  treatise4      ,,rhythm ,,in  
,,the ,,composition ,,of ,,lines        
#ajb4 ,we will first consider the       
,measure-,rhythms which result from a   
gradual increase of scale1 an increase  
in the extent of the contrasts4  ,the   
intervals must1 in such ,rhythms1 be    
regular and marked4 ,they may be  equal2
 they may alternate1 or they may be     
regularly progressive4    ,illustration3
 ,fig4 #aci    ,in this case ,i feel    
that the direction of the ,rhythm is    
up-to-the-right  owing to the gradual   
increase of length and consequently of  
the extent  of contrast in the lines1 in
 that direction4    ,illustration3 ,fig4
 #adj    ,in this case ,i have1 by means
 of regularly diminishing intervals1    

added  the force of a crowding together 
of contrasting edges to the force  of a 
gradual extension of them4 ,the movement
 is still more strongly                 
up-to-the-right4    ,illustration3 ,fig4
 #ada    ,in this case a greater        
extension of contrasts pulls one way and
 a  greater crowding of contrasts the   
other4 ,i think that crowding has  the  
best of it4 ,the movement1 though much  
retarded1 is1 ,i feel1  down-to-the-left
 rather than up-to-the-right1 in spite  
of the fact that  the greater facility  
of reading to the right is added to the 
force of  extended contrasts4    #ajc4  
,substituting unstable for stable       
attitudes in the examples just  given1  
we are able to add the movement         
suggested by instability of  attitude to
 the movement caused by a gradual       
extension of contrasts4                 
,illustration3 ,fig4 #adb    ,the       
movement up-to-the-right in ,fig4 #aci  
is here connected with an  inclination  
of all the lines down-to-the-right4     

,illustration3 ,fig4 #adc    ,here the  
falling of the lines down-to-the-left   
counteracts the  movement in the        
opposite direction which is caused by   
the extension of  contrasting edges in  
that direction4 ,a crowding together of 
the lines1  due to the diminution of    
intervals toward the left1 adds force to
 the  movement in that direction4       
,illustration3 ,fig4 #add    ,in this   
case a movement up is caused by         
convergences1 a movement down  by       
crowding4 ,the convergences are all up1 
the crowding down4 ,i think  that the   
convergences have it4 ,i think the      
movement is1 on the whole1  up4 ,the    
intervals of the crowding down diminish 
arithmetically4    ,illustration3 ,fig4 
#ade    ,the convergences and the       
crowding of attractions are1 here1 both 
up-to-the-right4 ,the ,rhythm is much   
stronger than it was in ,fig4 #add4     
,the intervals are those of an          
arithmetical progression4               
,illustration3 ,fig4 #adf    ,the       

movement here is up-to-the-right1       
because of convergences in that         
direction and an extension of contrasts 
in that direction4    ,illustration3    
,fig4 #adg    ,in this case the two     
movements part company4 ,one leads the  
eye  up-to-the-left1 the other leads it 
up-to-the-right4 ,the movement as  a    
whole is approximately up4 ,as the      
direction of the intervals is           
horizontal1 not vertical1 this is a case
 of movement without ,rhythm4  ,the     
movement will become rhythmic only in a 
vertical repetition4 ,that  is to say1  
the direction or directions of the      
movement in any ,rhythm  and the        
direction or directions of its          
repetitions must coincide4  ,in ,fig4   
#aci1 the movement is up-to-the-right1  
and the intervals may  be taken in the  
same direction1 but in ,fig4 #adg the   
movement is up4  ,the intervals cannot  
be taken in that direction4 ,it is1     
therefore1  impossible to get any       
feeling of ,rhythm from the composition4

 ,we shall  get the feeling of ,rhythm  
only when we repeat the movement in the 
direction of the movement1 which is up4 
,illustration3 ,fig4 #adh    ,here we   
have a vertical repetition of the       
composition given in ,fig4  #adg4 ,the  
result is an upward movement in regular 
and marked intervals1  answering to our 
understanding of ,rhythm4               
,illustration3 ,fig4 #adi    ,in this   
case we have a curved movement4 ,the    
lines being spaced at  regular          
intervals1 the movement is in regular   
and marked measures4  ,its direction is 
due to an increase in the number of     
attractions1 to  crowding1 and to       
convergences4 ,the movement is1         
accordingly1 rhythmical4                
,illustration3 ,fig4 #aej    ,the       
movement of ,fig4 #adi is here partly   
destroyed by an inversion and           
opposition of attitudes and directions4 
,the movement is1 on the whole1  up1 but
 it can hardly be described as          
rhythmical1 because it has no           

repetition upwards1 as it has in the    
next illustration1 ,fig4 #aea4  ,before 
proceeding1 however1 to the             
consideration of ,fig4 #aea1 ,i want to 
call the attention of the reader to the 
fact that we have in ,fig4 #aej a  type 
of ,balance to which ,i have not        
particularly referred4 ,it is a case  of
 unsymmetrical balance on a vertical    
axis4 ,the balancing shapes and         
movements correspond4 ,they incline in  
opposite directions4 ,they diverge      
equally from the vertical axis4 ,the    
inclinations balance4 ,at the same  time
 the composition does not answer to our 
understanding of ,symmetry4  ,it is not 
a case of right and left balance on the 
vertical axis4 ,the  shapes and         
movements are not right and left and    
opposite4 ,one of the  shapes is set    
higher than the other4 ,the balance is  
on the vertical4 ,it  is obvious1 but it
 is not symmetrical4 ,it is a form of   
,balance which  has many and very       
interesting possibilities4              

,illustration3 ,fig4 #aea    ,the       
repetition1 in this case1 of somewhat   
contrary movements1 a  repetition at    
equal intervals on a vertical axis1     
gives us more ,balance  than ,rhythm4   
,we feel1 however1 a general upward     
movement through the  repetitions and1  
as this movement is regular1 it must be 
described as  rhythmical4    ,the       
feeling of upward movement in ,fig4 #aea
 is1 no doubt1 partly due  to the       
suggestion of upward growth in certain  
forms of vegetation4  ,the suggestion is
 inevitable4 ,so far as the movement is 
caused by  this association of ideas it 
is a matter1 not of sensation1 but of   
perception4 ,the consideration of such  
associations of ideas does  not belong1 
properly1 to ,pure ,design1 where we are
 dealing with  sense-impressions1       
exclusively4    #ajd4 ,rhythm is not    
inconsistent with ,balance4 ,it is only 
necessary to  get movements which have  
the same or nearly the same direction   
and  which are rhythmical in character  

to balance on the same axis and we  have
 a reconciliation of the two principles4
    ,illustration3 ,fig4 #aeb    ,here  
we have a ,rhythm1 of somewhat contrary 
movements1 with  ,balance1--,balance on 
a diagonal axis4 ,the ,balance is not   
satisfactory4  ,the ,balance of         
,inclinations is felt more than the     
,balance of ,shapes4    ,illustration3  
,fig4 #aec    ,in this case we have the 
combination of a ,rhythm of somewhat    
contrary1  but on the whole upward1     
movements with ,symmetry4    ,if the    
diverging movements of ,fig4 #aec should
 be made still more  diverging1 so that 
they become approximately contrary and  
opposite1  the feeling of a general     
upward movement will disappear4 ,the    
three  movements to the right will      
balance the three movements to the left1
  and we shall have an illustration of  
,symmetrical ,balance1 with no  ,rhythm 
in the composition as a whole4 ,it is   
doubtful whether the  balance of        
contrary and opposite movements is      

satisfactory4 ,our eyes  are drawn in   
opposite directions1 away from the axis 
of balance1  instead of being drawn     
toward it4 ,our appreciation of the     
balance must1  therefore1 be diminished4
 ,contrary and opposite movements       
neutralize  one another1 so we have     
neither rest nor movement in the balance
 of  contrary motions4    ,by bringing  
the divergences of movement together1   
gradually1 we shall  be able to         
increase1 considerably1 the upward      
movement shown in ,fig4  #aec4 ,at the  
same time1 the suggestion of an upward  
growth of vegetation  becomes stronger4 
,the increase of movement will be partly
 explained by  this association of      
ideas4    ,illustration3 ,fig4 #aed     
,here all the movements are pulled      
together into one direction4 ,the       
,rhythm is easier and more rapid4 ,the  
,balance is just as good4 ,the  movement
 in this case is no doubt facilitated by
 the suggestion of  upward growth4 ,it  
is impossible to estimate the force     

which is added by  such suggestions and 
associations4    ,illustration3 ,fig4   
#aee    ,here the movements come        
together in another way4    ,the number 
and variety of these illustrations      
might1 of course1 be  indefinitely      
increased4 ,those which ,i have given   
will1 ,i think1 serve  to define the    
principal modes of line-composition1    
when the lines are  such as we choose to
 draw4      ,,the ,,composition ,,of    
,,various ,,lines    #aje4 ,in most of  
the examples ,i have given ,i have used 
repetitions of  the same line or similar
 lines4 ,when the lines which are put   
together  are not in harmony1 when they 
are drawn1 as they may be1 without any  
regard to the exigencies of orderly     
composition1 the problem becomes  one of
 doing the best we can with our terms4  
,we try for the greatest  possible      
number of orderly connections1          
connections making for ,harmony1        
,balance1 and ,rhythm4 ,we arrange the  
lines1 so far as possible1 in  the same 

directions1 giving them similar         
attitudes1 getting1 in  details1 as much
 ,harmony of ,direction and of          
,attitudes as possible1  and            
establishing as much ,harmony of        
,intervals as possible between the      
lines4 ,by spacing and placing we try to
 get differences of character  as far as
 possible into regular alternations or  
gradations in which  there will be a    
suggestion either of ,harmony or of     
,rhythm4 ,a suggestion  of ,symmetry is 
sometimes possible4 ,occult ,balance is 
possible in  all cases1 as it depends1  
not upon the terms balanced1 but upon   
the  indication of a center of          
attractions by a symmetrical framing of 
them4    ,let us take seven lines1 with 
a variety of shape-character1 with as   
little ,shape-,harmony as possible1 and 
let us try to put these lines  together 
in an orderly way4    ,illustration3    
,fig4 #aef    ,with these lines1 which  
show little or no harmony of character1 
which  agree only in tone and in        

width-measure1 lines which would not be 
selected certainly as suitable material 
for orderly compositions1 ,i  will make 
three compositions1 getting as much     
,order into each one as ,i  can1 just to
 illustrate what ,i mean4 ,i shall not  
be able to achieve a  great deal of     
,order1 but enough1 probably1 to satisfy
 the reader that  the effort has been   
worth while4    ,illustration3 ,fig4    
#aeg    ,in this case ,i have achieved  
the suggestion of a ,symmetrical        
,balance on  a vertical axis with some  
,harmony of ,directions and of          
,attitudes and  some ,interval-,harmony4
    ,illustration3 ,fig4 #aeh    ,in    
this case1 also1 ,i have achieved a     
suggestion of ,order1 if not  ,order    
itself4 ,consider the comparative       
disorder in ,fig4 #aef1 where no        
arrangement has been attempted4         
,illustration3 ,fig4 #aei    ,here is   
another arrangement of the same terms4  
,fortunately1 in all of  these cases1   
the lines agree in tone and in          

width-measure4 ,that means  considerable
 order to begin with4    ,this problem  
of taking any terms and making the best 
possible  arrangement of them is a most 
interesting problem1 and the ability  to
 solve it has a practical value4 ,we    
have the problem to solve in  every-day 
life2 when we have to arrange1 as well  
as we can1 in the  best possible order1 
all the useful and indispensable        
articles we  have in our houses4 ,to    
achieve a consistency and unity of      
effect  with a great number and variety 
of objects is never easy4 ,it is  often 
very difficult4 ,it is particularly     
difficult when we have no  two objects  
alike1 no correspondence1 no likeness1  
to make ,harmony4  ,with the possibility
 of repetitions and inversions the      
problem  becomes comparatively easy4    
,with repetitions and inversions we have
  the possibility1 not only of ,harmony1
 but of ,balance and ,rhythm4  ,with    
inversions we have the possibility1 not 
only of ,balance1 but of  ,symmetrical  

,balance1 and when we have that we are  
not at all likely  to think whether the 
terms of which the symmetry is composed 
are in  harmony or not4 ,we feel the    
,order of ,symmetry and we are          
satisfied4    ,illustration3 ,fig4 #afj 
,in this design ,i repeat an inversion  
of the arrangement in ,fig4 #aeh4  ,the 
result is a symmetry1 and no one is     
likely to ask whether the  elements of  
which it is composed are harmonious or  
not4 ,by inversions1  single and double1
 it is possible to achieve the ,order of
 ,balance1 in  all cases4               
,illustration3 ,fig4 #afa    ,for this  
design ,i have made another arrangement 
of my seven lines4 ,the  arrangement    
suggests movement4 ,in repeating the    
arrangement at regular  and equal       
intervals1 without change of attitude1  
,i produce the effect  of ,rhythm4      
,without resorting to inversion1 it is  
difficult to make  even an approximation
 to ,symmetry with such terms 7see ,fig4
 #aeg71  but there is little or no      

difficulty in making a consistent or    
fairly  consistent movement out of them1
 which1 being repeated at regular       
intervals1 without change of attitude1  
or with a gradual change of  attitude1  
will produce the effect of ,rhythm4     
,up to this point ,i have spoken of the 
composition of lines in  juxtaposition1 
that is to say1 the lines have been     
placed near together  so as to be seen  
together4 ,i have not spoken of the     
possibilities of  ,contact and          
,interlacing4 ,the lines in any         
composition may touch one  another or   
cross one another4 ,the result will be a
 composition of  connected lines4 ,in   
certain cases the lines will become the 
outlines of  areas4 ,i will defer the   
illustration of contacts and            
interlacings until  ,i come to consider 
the composition of outlines4            
,,outlines      ,,definition ,,of       
,,outlines    #ajf4 ,outlines are lines 
which1 returning to themselves1 make    
inclosures  and describe areas of       

different measures and shapes4 ,what has
 been  said of lines may be said1 also1 
of outlines4 ,it will be worth  while1  
however1 to give a separate             
consideration to outlines1 as a         
particularly interesting and important  
class of lines4    ,as in the case of   
dots and lines1 ,i shall disregard the  
fact that the  outlines may be drawn in 
different tones1 making different       
contrasts of  value1 color1 or          
color-intensity with the ground-tone    
upon which they  are drawn4 ,i shall1   
also1 disregard possible differences of 
width in  the lines which make the      
outlines4 ,i shall confine my attention1
 here1  to the measures and shapes of   
the outlines and to the possibilities of
  ,harmony1 ,balance1 and ,rhythm in    
those measures and shapes4              
,,harmony1 ,,balance1 ,,and ,,rhythm    
,,in ,,outlines    #ajg4 ,what is       
,harmony or ,balance or ,rhythm in a    
line is ,harmony1  ,balance1 or ,rhythm 
in an ,outline4    ,illustration3 ,fig4 

#afb    ,in this outline we have        
,measure-,harmony in the angles1        
,measure-,harmony  of lengths in the    
legs of the angles1 ,measure and        
,shape-,balance on a  center and        
,symmetry on the vertical axis4 ,the    
same statement will be  true of all     
polygons which are both equiangular and 
equilateral1 when  they are balanced on 
a vertical axis4    ,illustration3 ,fig4
 #afc    ,in this case we have          
,measure-,harmony of angles but no      
,measure-,harmony  of lengths in the    
legs of the angles4 ,we have lost       
,measure and  ,shape-,balance on a      
center which we had in the previous     
example4    ,illustration3 ,fig4 #afd   
,in this case the angles are not all in 
a ,harmony of ,measure2 but we  have    
,measure-,harmony of lengths in the legs
 of the angles1 and we have  ,measure   
and ,shape-,balance on a center4 ,there 
is a certain ,harmony in  the repetition
 of a relation of two angles4           
,illustration3 ,fig4 #afe    ,in this   

case we have ,measure-,harmony in the   
angles1 which are equal1  and a ,harmony
 due to the repetition of a certain     
measure-relation in  the legs of the    
angles4 ,as in ,fig4 #afb1 we have here 
a ,measure and  ,shape-,balance on a    
center and ,symmetry on the vertical    
axis4 ,this  polygon is not equilateral1
 but its sides are symmetrically        
disposed4  ,many interesting and        
beautiful figures may be drawn in these 
terms4    ,illustration3 ,fig4 #aff     
,we have in the circle the most         
harmonious of all outlines4 ,the        
,harmony  of the circle is due to the   
fact that all sections of it have the   
same  radius and equal sections of it   
have1 also1 the same angle-measure4     
,the circle is1 of course1 a perfect    
illustration of ,measure and            
,shape-,balance on a center4 ,the       
balance is also symmetrical4 ,we have a 
,harmony of ,directions in the          
repetition of the same change of        
direction  at every point of the        

outline1 and we have a ,harmony of      
,distances in  the fact that all points 
of the outline are equally distant from 
the  balance-center1 which is           
unmistakably felt4    ,illustration3    
,fig4 #afg    ,the ,ellipse is another  
example of ,measure and ,shape-,balance 
on a  center4 ,in this attitude it is   
also an illustration of ,symmetry4      
,illustration3 ,fig4 #afh    ,in this   
case we still have balance but no       
symmetry4 ,the attitude  suggests       
movement4 ,we cannot help feeling that  
the figure is falling  down to the left4
 ,a repetition at equal intervals would 
give us ,rhythm4    ,illustration3 ,fig4
 #afi    ,in this case we have an       
outline produced by the single inversion
  of a line in which there is the       
repetition of a certain motive  in a    
gradation of measures4 ,that gives      
,shape-,harmony without                 
,measure-,harmony4 ,this is a case of   
,symmetrical ,balance4 ,it is also  a   
case of rhythmic movement upward4 ,the  

movement is mainly due to  convergences4
    ,illustration3 ,fig4 #agj    ,in    
this case1 also1 the shapes repeated on 
the right side and on the  left side of 
the outline show movements which become 
in repetitions  almost rhythmical4 ,the 
movement is up in spite of the fact that
 each  part of the movement is1 in its  
ending1 down4 ,we have in these examples
  symmetrical balance on a vertical axis
 combined with rhythm on the same  axis4
 ,it may be desirable to find the       
balance-center of an outline  when only 
the axis is indicated by the character  
of the outline4 ,the  principle which we
 follow is the one already described4   
,in ,fig4 #afi we  have a symmetrical   
balance on a vertical axis1 but there is
 nothing to  indicate the               
balance-center4 ,it lies on the axis    
somewhere1 but there  is nothing to show
 us where it is4 ,regarding the outline 
as a line  of attractions1 the eye is   
presumably held at their balance-center1
  wherever it is4 ,exactly where it is  

is a matter of visual feeling4 ,the     
balance-center being ascertained1 it may
 be indicated by a symmetrical  outline 
or inclosure1 the center of which cannot
 be doubtful4    ,illustration3 ,fig4   
#aga    ,the balance-center1 as         
determined by visual feeling1 is here   
clearly  indicated4 ,in this case       
besides the balance on a center we have 
also  the ,symmetry which we had in     
,fig4 #afi4    ,illustration3 ,fig4 #agb
    ,the sense of ,balance is1 in this  
case1 much diminished by the change of  
attitude in the balanced outline4 ,we   
have our balance upon a center1  all the
 same2 but the balance on the vertical  
axis being lost1 we have  no longer any 
,symmetry4 ,it will be observed that    
balance on a center is  not inconsistent
 with movement4 ,if this figure were    
repeated at equal  intervals without    
change of attitude1 or with a gradual   
change1 we  should have the ,rhythm of a
 repeated movement4    ,in some outlines
 only certain parts of the outlines are 

orderly1 while  other parts are         
disorderly4    ,illustration3 ,fig4 #agc
    ,in the above outline we have two   
sections corresponding in measure and   
shape-character and in attitude4 ,we    
have1 therefore1 certain elements  of   
the outline in harmony4 ,we feel        
movement but not rhythm in the  relation
 of the two curves4 ,there is no balance
 of any kind4    ,we ought to be able to
 recognize elements of order as they    
occur in any  outline1 even when the    
outline1 as a whole1 is disorderly4     
,illustration3 ,fig4 #agd    ,in order  
to balance the somewhat irregular       
outline given in ,fig4 #agc1  we follow 
the procedure already described4 ,the   
effect1 however1 is  unsatisfactory4    
,the composition lacks stability4       
,illustration3 ,fig4 #age    ,the       
attitude of the figure is here made to  
conform1 as far as possible1  to the    
shape and attitude of the symmetrical   
framing3 this for the sake  of ,shape   
and ,attitude-,harmony4 ,the change of  

attitude gives greater  stability4      
,,interior ,,dimensions ,,of ,,an       
,,outline    #ajh4 ,a distinction must  
be drawn between the measures of the    
outline1  as an outline1 and the        
measures of the space or area lying     
within the  outline3 what may be called 
the interior dimensions of the outline4 
,illustration3 ,fig4 #agf    ,in this   
case we must distinguish between the    
measures of the outline  and the        
dimensions of the space inclosed within 
it4 ,when we consider  the measures--not
 of the outline1 but of the space or    
area inside of the  outline--we may look
 in these measures1 also1 for ,harmony1 
for ,balance1  or for ,rhythm1 and for  
combinations of these principles4       
,,harmony ,,in ,,the ,,interior         
,,dimensions ,,of ,,an ,,outline        
#aji4 ,we have ,harmony in the interior 
dimensions of an outline when  the      
dimensions correspond or when a certain 
relation of dimensions is  repeated4    
,illustration3 ,fig4 #agg    ,in this   

case we have an outline which shows a   
,harmony in the  correspondence of two  
dimensions4    ,illustration3 ,fig4 #agh
    ,in this case we have ,harmony in   
the correspondence of all vertical      
dimensions1 ,harmony in the             
correspondence of all horizontal        
dimensions1  but no relation of ,harmony
 between the two4 ,it might be argued1  
from  the fact that the interval in one 
direction is twice that in the other1   
that the dimensions have something in   
common1 namely1 a common divisor4  ,it  
is very doubtful1 however1 whether this 
fact is appreciable in the  sense of    
vision4 ,the recurrence of any relation 
of two dimensions  would1 no doubt1 be  
appreciated4 ,we should have1 in that   
case1  ,shape-,harmony4                 
,illustration3 ,fig4 #agi    ,in this   
circle we have a ,measure-,harmony of   
diameters4    ,illustration3 ,fig4 #ahj 
,in this case we have a ,harmony due to 
the repetition of a certain ratio  of   
vertical intervals3 #a3c1 #a3c1 #a3c4   

#aaj4 ,any gradual diminution of the    
interval between opposite sides  in an  
outline gives us a convergence in which 
the eye moves more or  less rapidly     
toward an actual or possible contact4   
,the more rapid the  convergence the    
more rapid the movement4                
,illustration3 ,fig4 #aha    ,in this   
case we have not only symmetrical       
balance on a vertical axis  but         
movement1 in the upward and rapid       
convergence of the sides ,,ba and  ,,ca 
toward the angle ,a4 ,the question may  
be raised whether the movement1  in this
 case1 is up from the side ,,bc to the  
angle ,a or down from the  angle ,a     
toward the side ,,bc4 ,i think that the 
reader will agree that  the movement is 
from the side ,,bc into the angle ,a4   
,in this direction  the eye is more     
definitely guided4 ,the opposite        
movement from ,a toward  ,,bc is a      
movement in diverging directions which  
the eye cannot follow  to any distance4 
,as the distance from ,,bc toward ,a    

decreases1 the  convergence of the sides
 ,,ba and ,,ca is more and more helpful 
to the eye  and produces the feeling of 
movement4 ,the eye finds itself in a    
smaller  and smaller space1 with a more 
and more definite impulse toward ,a4    
,it is a question whether the movement  
from ,,bc toward ,a is rhythmical  or   
not4 ,the movement is not connected with
 any marked regularity of  measures4 ,i 
am inclined to think1 however1 that the 
gradual and even  change of measures    
produces the feeling of equal changes in
 equal  measures4 ,if so1 the movement  
is rhythmical4    ,when the movement of 
the eye in any convergence is a movement
 in  regular and marked measures1 as in 
the example which follows1 the  movement
 is rhythmical1 without doubt4          
,illustration3 ,fig4 #ahb    ,the upward
 movement in this outline1 being        
regulated by measures which  are marked 
and equal1 the movement is certainly    
rhythmical1 according  to our           
understanding and definition of ,rhythm4

 ,comparing ,fig4 #aha with  ,fig4 #ahb1
 the question arises1 whether the       
movement in ,fig4 #ahb is felt  to be   
any more rhythmical than the movement in
 ,fig4 #aha4 ,the measures  of the      
movement in ,fig #aha are not marked1   
but ,i cannot persuade myself  that they
 are not felt in the evenness of the    
gradation4 ,the movement  in ,fig4 #aha 
is easier than it is in ,fig4 #ahb1 when
 the marking of the  measures interferes
 with the movement4    ,illustration3   
,fig4 #ahc    ,in this case we have     
another illustration like ,fig4 #ahb1   
only the  measures of the rhythm are    
differently marked4 ,the force of the   
convergence is greatest in ,fig4 #aha4  
,it is somewhat diminished by the       
measure-marks in ,fig4 #ahb4 ,it is     
still further diminished1 in ,fig4 #ahc1
  by the angles that break the measures4
    ,illustration3 ,fig4 #ahd    ,in    
this case the movement is more rapid    
again1 the measures being  measures of  
an arithmetical progression4 ,there is a

 crowding together  of attractions in   
the direction of the convergence1 and   
the movement  is easier than it is in   
,fig4 #ahc1 in spite of the fact that   
the lines  of convergence are more      
broken in ,fig4 #ahd4 ,there is an      
arithmetical  diminution of horizontal  
as well as of vertical lines in ,fig4   
#ahd4    ,illustration3 ,fig4 #ahe      
,in this case the measures of the rhythm
 are in the terms of a  geometrical     
progression4 ,the crowding together of  
attractions is still  more rapid in this
 case and the distance to be traversed  
by the eye is  shorter4 ,the            
convergence1 however1 is less           
compelling1 the lines of the            
convergence being so much               
broken--unnecessarily4    ,the movement 
will be very much retarded1 if not      
prevented1 by having  the movement of   
the crowding and the movement of the    
convergence  opposed4    ,illustration3 
,fig4 #ahf    ,there is no doubt that in
 this example1 which is to be compared  

with  that of ,fig4 #ahd1 the upward    
movement is almost prevented4 ,there are
  here two opposed movements3 that of   
the convergence upward and that  of a   
crowding together of attractions        
downward4 ,the convergence is  stronger1
 ,i think1 though it must be remembered 
that it is probably  easier for the eye 
to move up than down1 other things being
 equal4    #aaa4 ,the movements in all  
of these cases may be enhanced by       
substituting for the straight lines     
shapes which are in themselves  shapes  
of movement4    ,illustration3 ,fig4    
#ahg    ,here1 for example1 the movement
 of ,fig4 #ahd is facilitated and       
increased by a change of shape in the   
lines1 lines with movement being        
substituted for lines which have no     
movement1 beyond the movement of  the   
convergence4    ,illustration3 ,fig4    
#ahh    ,in ,fig4 #ahh all the shapes   
have a downward movement which          
contradicts  the upward movement of     
convergence4 ,the movement down almost  

prevents  the movement up4    #aab4 ,the
 movement of any convergence may be     
straight1 angular1 or  curved4          
,illustration3 ,fig4 #ahi    ,in this   
case the movement of the convergence is 
angular4 ,it should  be observed that   
the movement is distributed in the      
measures of an  arithmetical            
progression1 so that we have1 not only  
movement1 but  rhythm4    ,illustration3
 ,fig4 #aij    ,in this case the        
movement of convergence is in a curve4  
,the stages of  the movement1 not being 
marked1 the movement is not rhythmical1 
unless  we feel that equal changes are  
taking place in equal measures4 ,i am   
inclined to think that we do feel that4 
,the question1 however1 is one  which ,i
 would rather ask than answer1          
definitely4    ,illustration3 ,fig4 #aia
    ,in this case the movement is1      
unquestionably1 rhythmical1 because  the
 measures are clearly marked4 ,the      
measures are in an arithmetical         
progression4 ,they diminish gradually in

 the direction of the  convergence1     
causing a gradual crowding together of  
attractions in that  direction4         
,substituting1 in the measures1 shapes  
which have movement1 the movement  of   
the rhythm may be considerably          
increased1 as is shown in the example   
which follows4    ,illustration3 ,fig4  
#aib    ,this is a case in which the    
movement is1 no doubt1 facilitated by an
  association of ideas1 the suggestion  
of a growth4    #aac4 ,the more obvious 
the suggestion of growth1 the more      
inevitable is  the movement in the      
direction of it1 whatever that direction
 is4 ,it  must be understood1 however1  
that the movement in such cases is due  
to  an association of ideas1 not to the 
pull of attractions in the sense of     
vision4 ,the pull of an association of  
ideas may or may not be in the          
direction of the pull of attractions4   
,illustration3 ,fig4 #aic    ,in ,fig4  
#aic we have an illustration of a       
rhythmic movement upward4 ,the  upward  

movement is due quite as much to an     
association of ideas1 the  thought of a 
growth of vegetation1 as it is to mere  
visual attractions4  ,it happens that   
the figure is also an illustration of   
,symmetrical  ,balance4 ,as we have     
,harmony in the similarity of the       
opposite sides1  the figure is an       
illustration of combined ,harmony1      
,balance1 and ,rhythm4    ,there is     
another point which is illustrated in   
,fig4 #aic4 ,it is this3  that we may   
have rhythmic movement in an outline1   
or1 indeed1 in any  composition of      
lines1 which shows a gradual and regular
 change from  one shape to another2     
which shows a gradual and regular       
evolution or  development of            
shape-character2 provided the changes   
are distributed  in regular and marked  
measures and the direction of the       
changes1 the  evolution1 the            
development1 is unmistakable2 as it is  
in ,fig4 #aic4 ,the  changes of shape in
 the above outline are changes which are

 gradual and  regular and suggest an    
upward movement unmistakably4 ,the      
movement1  however1 involves a          
comparison of shape with shape1 so it is
 as much  a matter of perception as of  
sensation4 ,evolutions and developments 
in ,space1 in the field of vision1 are  
as interesting as evolutions  and       
developments in the duration of ,time4  
,when the changes in such  movements are
 regular1 when they take place in       
regular and marked  measures1 when we   
must take them in a certain order1 the  
movements are  rhythmical1 whether in   
,time or in ,space4      ,,the          
,,attitudes ,,of ,,outlines    #aad4    
,any outline1 no matter what dimensions 
or shape it has1 may be  turned upon a  
center and in that way made to take a   
great number and  variety of attitudes4 
,not only may it be turned upon a center
 but  inverted upon an axis4 ,being     
inverted1 the inversion may be turned   
upon  a center and made to take another 
series of attitudes1 and this second    

series of attitudes will be different   
from the first series1 except  in cases 
of axial symmetry in the outline or     
area4 ,it must be clearly  understood   
that a change of attitude in any outline
 or area is not a  change of shape4     
#aae4 ,what has been said of ,harmony1  
,balance1 and ,rhythm in the  attitudes 
of a line applies equally well to       
outlines and to the spaces  defined by  
them4      ,,the ,,arrangement ,,and    
,,composition ,,of ,,outlines    #aaf4  
,by the composition of outlines ,i mean 
putting two or more  outlines in        
juxtaposition1 in contact or            
interlacing4 ,in all cases of           
interlacing1 of course1 the             
shape-character of the interlacing      
outlines  is lost4 ,the outlines become 
the outlines of other areas and of a    
larger number of them4 ,our object in   
putting outlines together is1 in  ,pure 
,design1 to illustrate the orders of    
,harmony1 ,balance1 and ,rhythm1  to    
achieve ,order1 as much as we can1 if   

possible ,beauty4    ,i will now give a 
series of examples with a brief analysis
 or  explanation of each one4           
,illustration3 ,fig4 #aid    ,in this   
case we have ,shape-,harmony in the     
outlines and also a ,harmony  of        
,attitudes4    ,illustration3 ,fig4 #aie
    ,here we have another illustration  
of the ,harmony of ,shapes and of       
,attitudes1 with a ,harmony of          
,intervals1 which we did not have in    
,fig4  #aid4    ,illustration3 ,fig4    
#aif    ,in this case we have a ,harmony
 of ,attitudes and of ,intervals 7the   
,harmony of a repeated ,relation of     
,intervals7 in what may be called an    
,all-,over ,repetition4                 
,illustration3 ,fig4 #aig    ,in this   
case we have a ,harmony of ,attitudes in
 the repetition of  a relation of two   
opposite attitudes2 this with           
,shape-,harmony and  ,interval-,harmony4
    ,illustration3 ,fig4 #aih    ,in    
this case we have a ,symmetry of        
,attitudes1 with ,shape-,harmony and    

,interval-,harmony4 ,turning the        
composition off the vertical axis we    
should have ,balance but no ,symmetry4  
,the balance-center will be felt in  all
 possible attitudes of this composition4
    ,illustration3 ,fig4 #aii    ,in    
this case ,i have repeated a certain    
outline1 which gives me the  ,harmony of
 a repetition1--this in connection with 
a progression in  scale1 so that the    
,harmony is ,shape-,harmony1 not        
,measure-,harmony4 ,we  have in the     
attitude of this repetition a           
,symmetrical ,balance4 ,the  movement is
 rhythmical and the direction of the    
rhythm is up4    ,the movement in ,fig4 
#aii might be indefinitely increased by 
the  introduction into it of a gradation
 of attractions1 increasing in  number4 
,that means that the extent of          
contrasting edges is increased  from    
measure to measure4    ,illustration3   
,fig4 #bjj    ,the addition of details1 
increasing in number from measure to    
measure  upward1 increases the movement 

of the rhythm in that direction4        
,illustration3 ,fig4 #bja    ,taking the
 arrangement of ,fig4 #aii and repeating
 it six times at  diverging angles of   
sixty degrees1 we get what may be called
 a radial  balance upon the basis of a  
hexagon4    ,outlines may be drawn one  
inside of the other or several inside of
 one4    ,illustration3 ,fig4 #bjb      
,this is a case of                      
outlines-within-outlines and of         
,shape-,harmony without                 
,measure-,harmony4 ,there is1 also1 a   
,harmony of ,attitudes1 but no ,harmony 
of ,intervals4    ,interesting results  
may be produced by drawing a series of  
outlines  similar in shape1 the second  
inside of the first1 the third inside of
  the second1 and so on4                
,illustration3 ,fig4 #bjc    ,in this   
case1 for example1 we have the outlines 
drawn one inside of the  other4 ,the    
outlines have all the same shape1 but   
different measures4  ,it is a case of   
,shape-,harmony and ,harmony of         

,attitudes1 without  ,measure-,harmony1 
and without any ,harmony of ,intervals4 
,this is a very  interesting and        
important form of ,design which has many
 applications4    ,illustration3 ,fig4  
#bjd    ,in this case1 also1 we have    
,shape-,harmony without                 
,measure-,harmony4 ,we  have a ,harmony 
of ,attitudes and also of ,intervals1   
the spaces between  the outlines        
corresponding4    ,illustration3 ,fig4  
#bje    ,here we have the ,harmony of an
 alternation of ,attitudes repeated1    
with  ,shape-,harmony1 without          
,measure-,harmony4    ,in all forms of  
design in which we have the concentric  
repetition  of a certain outline we     
have1 in connection with the feeling of 
a  central balance1 the feeling of a    
movement or movements toward the        
center4 ,these movements are due to     
convergences4 ,movements carrying  the  
eye away from the center1 in opposite   
directions1 interfere with  the feeling 
of balance4 ,the feeling is enhanced1   

however1 when the  movements converge   
and come together4    ,we may have not  
only an alternation of attitudes in     
these cases1 but an  alternation of     
shape-character4    ,illustration3 ,fig4
 #bjf    ,the repetition of             
outlines-within-outlines may be         
concentric or  eccentric4 ,the          
repetition is concentric in ,fig4 #bjd4 
,it is eccentric in  the example which  
follows4    ,illustration3 ,fig4 #bjg   
,in all eccentric repetitions like this 
we have a lack of balance and  the      
suggestion of movement4 ,the direction  
of the movement is determined  by the   
direction of convergences and of the    
crowding together of  attractions4 ,the 
movement in ,fig4 #bjg is               
up-to-the-left1 unmistakably4           
,repeating the composition of ,fig4     
#bjg1 at regular intervals and without  
change of attitude1 the movement        
up-to-the-left would be extended to  the
 repetitions and the movement would be  
rhythmical4 ,the movement is  rhythmical

 in the composition itself1 as shown in 
,fig4 #bjg1 because the  movement in the
 composition is regular in character1   
regular in its  measures1 and           
unmistakable in direction4              
,illustration3 ,fig4 #bjh    ,this is   
another example of eccentric repetition 
in  outlines-within-outlines4 ,as in    
,fig4 #bjg1 we have movement1 and the   
movement is rhythmical4    ,in the      
examples ,i have given there have been  
no contacts and no  interlacings4       
,contacts and interlacings are possible4
    ,illustration3 ,fig4 #bji    ,here1 
for an example1 is an instance of       
contact1 with ,harmony of  ,attitudes   
and a ,symmetrical ,balance on a        
vertical axis4    ,illustration3 ,fig4  
#baj    ,in this case we have contacts1 
with no ,harmony of ,attitudes4 ,the    
balance which is central as well as     
axial is in this attitude of the  figure
 symmetrical4    ,illustration3 ,fig4   
#baa    ,here we have a similar         
composition with interlacings4    ,when 

the outlines have different shapes as   
well as different measures1             
particularly when the outlines are      
irregular and the shapes to be put      
together are1 in themselves1 disorderly1
 the problem of composition  becomes    
more difficult4 ,the best plan is to    
arrange the outlines in  a group1 making
 as many orderly connections as         
possible4 ,taking any  composition of   
outlines and repeating it in the        
different ways which  ,i have described1
 it is generally possible to achieve    
orderly if not  beautiful results4      
,illustration3 ,fig4 #bab    ,here are  
five outlines1 very different in        
shape-character4 ,let us see  what can  
be done with them4 ,a lot of experiments
 have to be tried1  to find out what    
connections1 what arrangements1 what    
effects are  possible4 ,the             
possibilities cannot be predicted4      
,using tracing-paper1 a  great many     
experiments can be tried in a short     
time1 though it may take  a long time to

 reach the best possible results4       
,illustration3 ,fig4 #bac    ,in this   
example ,i have tried to make a good    
composition with my five  outlines4 ,the
 problem is difficult4 ,the outlines to 
be combined  have so little ,harmony4   
,the only ,harmony we can achieve will  
be the  ,harmony of the same arrangement
 of shapes repeated1 which amounts to   
,shape-,harmony4 ,inversions will give  
us the satisfaction of ,balance4        
,inversions on a vertical axis will give
 us the satisfaction of  ,symmetry4 ,in 
the design above given ,i have achieved 
simply the ,harmony  of a relation of   
shapes repeated1 with ,rhythm4 ,the     
,rhythm is due to  the repetition of a  
decidedly unbalanced group of elements  
with a  predominance of convergences in 
one direction4 ,the movement is on  the 
whole up1 in spite of certain downward  
convergences4 ,the upward  convergences 
predominate4 ,there are more            
inclinations to the right  than to the  
left1 but the composition which is      

repeated is unstable in  its attitude   
and suggests a falling away to the left4
 ,the resultant of  these slight        
divergences of movement is a general    
upward movement4    ,illustration3 ,fig4
 #bad    ,in this case ,i have less     
difficulty than in ,fig4 #bac1 having   
left out  one of my five outlines1 the  
one most difficult to use with the      
others4  ,there is a great gain of      
,harmony4 ,there is a ,harmony of       
,intervals and  a ,harmony in the       
repetition of the same grouping of      
outlines4 ,in the  outlines themselves  
we have a ,harmony of curved character1 
and the  curves fit one another very    
well1 owing to a correspondence of      
measure  and shape-character in certain 
parts4 ,in such cases we are able to    
get considerable ,harmony of ,attitudes 
into the composition4 ,there is  a      
,harmony of ,attitudes in the repeats1  
as well as in certain details4          
,comparing ,fig4 #bad with ,fig4 #bac1  
,i am sure the reader will agree that   

we have in ,fig4 #bad the larger measure
 of ,harmony4    ,illustration3 ,fig4   
#bae    ,in ,fig4 #bae ,i have used     
inversions and repetitions of the rather
  disorderly outline which gave me so   
much difficulty when ,i tried to        
combine it with the other outlines4     
,whatever merit the composition  has is 
due solely to the art of composition1 to
 the presence of  ,attitude-,harmony1   
,interval-,harmony1 and to the          
inversions and  repetitions2 inversions 
giving ,balance1 repetitions giving     
,harmony4    ,while it is important to  
recognize the limitation of the terms in
 this  problem1 it is important to yield
 to any definite impulse which you may  
feel1 though it carries you beyond your 
terms4 ,the value of a rule is  often   
found in breaking it for a good and     
sufficient reason2 and there  is no     
better reason than that which allows    
you1 in ,design1 to follow  any impulse 
you may have1 provided that it is       
consistent with the  principles of      

,order4    ,illustration3 ,fig4 #baf    
,in this case an effort has been made to
 modify the terms already used  so as to
 produce a more rapid and consistent    
movement4 ,advantage has  been taken of 
the fact that the eye is drawn into all 
convergences1 so  all pointing down has 
been1 so far as possible1 avoided4 ,the 
movement  is distinctly rhythmical4     
,in the previous examples ,i have       
avoided contacts and interlacing4 ,it   
was not necessary to avoid them4        
,illustration3 ,fig4 #bag    #aag4 ,what
 is done1 in every case1 depends upon   
the designer who does  it4 ,he follows  
the suggestions of his imagination1 not1
 however1 with  perfect license4 ,the   
imagination acts within definite        
limitations1  limitations of terms and  
of principles1 limitations of certain   
modes in  which terms and principles are
 united4 ,in spite of these limitations1
  however1 if we give the same terms1   
the same principles1 and the same  modes
 to different people1 they will produce 

very different results4  ,individuality 
expresses itself in spite of the        
limitation of terms and  modes1 and the 
work of one man will be very different  
from the work of  another1 inevitably4  
,we may have ,order1 ,harmony1 ,balance1
 or ,rhythm  in all cases1 ,beauty only 
in one case1 perhaps in no case4 ,it    
must be  remembered how1 in the practice
 of ,pure ,design1 we aim at ,order and 
hope for ,beauty4 ,beauty is found only 
in supreme instances of ,order1         
intuitively felt1 instinctively         
appreciated4 ,the end of the practice of
  ,pure ,design is found in the love of 
the ,beautiful1 rather than in the      
production of beautiful things4         
,beautiful things are produced1 not by  
the practice of ,pure ,design1 but out  
of the love of the ,beautiful which  may
 be developed by the practice4          
,,areas    #aah4 ,i have already        
considered the measures of areas1 in    
discussing  the interior dimensions of  
outlines1 and in discussing the outlines

  themselves ,i have considered the     
shapes of areas4 ,it remains for  me to 
discuss the tones in which the areas may
 be drawn and the  tone-contrasts by    
which they may be distinguished and     
defined--in their  positions1 measures1 
and shapes4      ,,linear ,,areas       
#aai4 ,before proceeding1 however1 to   
the subject of tones and                
tone-relations1 ,i must speak of a      
peculiar type of area which is  produced
 by increasing or diminishing the width 
of a line4 ,i have  postponed the       
discussion of measures of width in lines
 until now4    ,a line may change its   
width in certain parts or passages4 ,it 
may  become wider or narrower as the    
case may be4 ,the wider it is the more  
it is like an area4 ,if it is           
sufficiently wide1 the line ceases to be
  a line1 and becomes an area4 ,the line
 may change its width abruptly  or      
gradually4 ,the effect of the line is by
 these changes indefinitely  varied4    
,the line of ,design is not the line of 

,geometry4    #abj4 ,considerable       
interest may be given to what ,i have   
called ,linear  ,progressions by        
changing the width of the line at       
certain points1 in  certain passages1   
and more or less abruptly4 ,the changes 
will be like  accents in the line1      
giving variety and1 possibly1 an added  
interest4    ,illustration3 ,fig4 #bah  
,let us take this line as the motive of 
a linear progression4 ,we can  give it a
 different character1 perhaps a more    
interesting character1 by  widening all 
the vertical passages1 as follows3--    
,illustration3 ,fig4 #bai    ,this is   
what we get for a motive by widening all
 the vertical passages4                 
,illustration3 ,fig4 #bbj    ,this is   
what we get for a motive by widening all
 the horizontal  passages4              
,illustration3 ,fig4 #bba    ,compare   
this ,progression1 in which ,i have used
 the motive of ,fig4  #bai1 with that of
 ,fig4 #gg1 p4 #dg4 ,the accents1 which 
in ,fig4 #bba  occur in every repetition

 of the motive1 might occur only in     
certain  repetitions1 at certain        
intervals4    ,illustration3 ,fig4 #bbb 
,it is not necessary that the changes in
 the width of the line be  abrupt1 as in
 the examples just given4 ,the width of 
the line may  increase or diminish      
gradually1 in which case we may have1   
not only  accents in the line1 but      
movements due to gradations of          
dimension1  to convergences1 or to an   
increase or gradual crowding together of
  attractions in a series of visual     
angles4    ,illustration3 ,fig4 #bbc    
,in this case we have a gradual increase
 followed by a diminution of  the width 
of the line in certain parts1 and these 
changes occur at  equal intervals4 ,a   
certain amount of rhythmic movement is  
given to  the progression by such       
accents1 provided the direction of      
movement  is unmistakable1 which it is  
not in this case4 ,it is not at all     
clear  whether the movement is          
down-to-the-right or up-to-the-left4 ,it

 seems  to me about as easy to move in  
one direction as in the other4          
,illustration3 ,fig4 #bbd    ,in this   
case there is less doubt about the      
movement4 ,it seems to  be              
down-to-the-right4 ,the eye is pulled   
through an increase of  width-measures  
toward a greater extension and crowding 
together of  contrasting edges4         
,illustration3 ,fig4 #bbe               
,substituting outlines for areas in the 
previous illustration1 we are           
surprised1 perhaps1 to find that the    
movement is reversed4 ,we go            
up-to-the-left in this case1 not        
down-to-the-right4 ,the pull of a       
greater extension of tone-contrast in a 
given area was1 in ,fig4 #bbd1          
sufficient to overcome the pull of a    
less evident convergence in the  other  
direction4    ,by increasing or         
diminishing the width of lines1 doing it
 gradually  or abruptly1 we are able to 
control the movement of the eye to an   
indefinite extent4 ,this is one of the  

important resources of the  designer's  
art4 ,its use is not limited to forms of
 ,linear ,progression1  but may be      
extended to all forms of ,design in     
which lines are used4    ,illustration3 
,fig4 #bbf    ,in this case1 for        
example1 the eye follows the direction  
of  convergences1 but we can easily     
force it to turn and move in the        
opposite direction1 by widening the     
lines in that direction1 thus           
increasing the extent of contrasting    
edge until it more than  outbalances the
 convergences2 as in the following      
illustration3--    ,illustration3 ,fig4 
#bbg      ,,the ,,arrangement ,,and     
,,composition ,,of ,,areas    #aba4     
,what has been said about the           
composition of ,lines and ,outlines     
applies equally well to the composition 
of ,areas1 so far as they  are          
distinguished and defined by outlines4  
,we will now proceed to  consider areas 
as distinguished and defined1 not by    
outlines1 but by  tone-contrasts4 ,the  

composition of lines and outlines is one
 thing1  the composition of tones in    
different positions1 measures1 and      
shapes  is another4 ,in putting lines   
and outlines together we draw4 ,the     
point  of view is that of drawing4 ,in  
putting tones in different positions1   
measures1 and shapes we paint4 ,the     
point of view is that of the  painting4 
,,tones ,,and ,,tone-,,relations        
#abb4 ,up to this point ,i have avoided 
the consideration of ,tones and         
,tone-,relations4 ,i have spoken of     
possible changes of tone in dots and  in
 lines2 changes of value1 of color1 of  
color-intensity2 but it is not  in dots 
nor in lines that these changes call for
 particular attention4  ,our interest   
has been in the positions1 measures1    
shapes1 and  attitudes of dots and      
lines1 and in the possibilities of      
arrangement  and composition4 ,when it  
comes to the consideration of areas and 
area-systems1 however1 the subject of   
tone-relations becomes one of the       

greatest interest1 because areas are    
defined and distinguished1 not  only by 
their outlines1 but quite as much by    
differences of tone2 that  is to say1 by
 tone-contrasts4      ,,the ,,process   
,,of ,,painting ,,as ,,distinguished    
,,from ,,drawing    #abc4 ,the first    
thing to consider is the tone of the    
surface upon  which you are going to    
paint4 ,you then take a tone differing  
from the  ground-tone1 in value1 in     
color1 or in color-intensity1 you put it
 in a  certain position1 and you spread 
it over a certain extent of space4 ,in  
so doing you give to the space a certain
 shape4 ,this is the process of         
,painting1 as distinguished from the    
process of ,drawing4 ,in ,drawing we    
think of lines and outlines first4 ,in  
,painting we think of ,tones first1  of 
positions1 measures1 and shapes         
afterwards4      ,,definition ,,of ,,the
 ,,word ,,tone    #abd4 ,in producing   
tones we use1 necessarily1 certain      
pigment-materials  and mixtures of these

 materials4 ,the effect of light        
produced by any  particular material or 
mixture we call its tone4 ,though ,i    
have been  using the word ,tone ,i have 
not yet defined its meaning4 ,i will now
 do  that4                              
,,tone-,,analysis1--,,value1 ,,color1   
,,intensity1 ,,neutrality    #abe4 ,in  
every tone we have to distinguish two   
elements1 the quantity  of light in     
it--what we call its value--and the     
quality of the light  in it--its color2 
and the color1 whatever it is1--,red1   
,orange1 ,yellow1  ,green1 ,blue1 or    
,violet1--may be intense or neutral4 ,by
 intensity ,i  mean the quality of a    
color in its highest or in a very high  
degree4  ,by the intensity of ,red ,i   
mean ,red when it is as red as possible4
 ,the  mixture of ,vermilion and ,rose  
,madder1 for example1 gives us a ,red of
  great intensity4 ,that is about the   
strongest ,red which we are able to     
produce with the pigment-materials which
 we use4 ,intensity must not be         

confounded with value nor value with    
intensity4 ,by value ,i mean more or    
less light4 ,by intensity ,i mean a     
great purity and brilliancy of color4   
,intensity stands in opposition to      
neutrality1 in which no color can be    
distinguished4 ,the more color we have  
in any tone the more intensity we  have4
 ,the less the intensity the less color1
 and the absence of color  means        
neutrality or grayness4 ,neutrality or  
grayness1 though it is the  negation of 
color1 the zero of color1 so to speak1  
must be classed  as a color because upon
 analysis it proves to be a result of   
color  combination or mixture4 ,when ,i 
speak1 as ,i shall from time to time1 of
  the neutral as a color1 it will be    
understood that ,i am speaking of a     
combination or mixture of colors in     
which no particular color can be        
distinguished4 ,i speak of the neutral  
as a color just as ,i speak of  zero as 
a number4 ,we use zero as a number      
though it is no number1 and  counts for 

nothing4      ,,study ,,of ,,tones ,,and
 ,,tone-,,relations    #abf4 ,the study 
of tones and tone-relations means the   
study of  pigment-materials and their   
effects1 to find out what quantities  of
 light we can produce1 what qualities of
 color1 what intensities  of color1 what
 neutralizations4 ,that is the problem  
of tones and  tone-relations4 ,we cannot
 know much about tones and              
tone-relations  until we have had       
experience in the use of                
pigment-materials4 ,we must  be able to 
distinguish tones1 however slight the   
differences of value  or of color or of 
color-intensity1 and we must be able to 
produce tones  according to our         
discriminations3 this with exact        
precision4 ,in order  to think in       
tone-relations we must have definite    
ideas of tone and of  tone-relations1 in
 the form of visual images4 ,in order to
 express our  ideas we must be able to  
paint4 ,we must have practice in        
painting and  a great deal of it4 ,i    

propose to describe this practice in    
tones and  tone-relations3 what it ought
 to be1 what forms it should take4      
,,pigment-,,materials    #abg4 ,of      
pigments ,i use these3 ,blue ,black1    
,madder ,lake 7,deep71 ,rose  ,madder1  
,indian ,red1 ,venetian ,red1           
,vermilion1 ,burnt ,sienna1 ,cadmium    
,orange1 ,yellow ,ochre1 ,pale ,cadmium1
 ,aureolin1 ,cremnitz ,white1           
8,emeraude0 ,green 7,green ,oxide of    
,chromium1 transparent71 ,cobalt ,blue1 
,french ,ultramarine ,blue4 ,these are  
the pigments which ,i suggest for       
oil-painting4 ,in water-color painting  
,i should substitute ,charcoal  ,gray   
for ,blue ,black4 8,emeraude ,green0 is 
often called ,viridian in the  form in  
which it is used in water-color4 ,for   
,cremnitz ,white ,i should  substitute1 
in water-color painting1 ,chinese       
,white4 ,these are the                  
pigment-materials which ,i use myself   
and recommend to others4 ,there  are1 of
 course1 many other pigments which may  

be used1 but these will1  ,i think1 be  
found sufficient for all purposes4      
,provided with these  pigments1 with a  
palette upon which to put them1 with    
brushes and other  materials necessary  
for painting1 we are prepared to take up
 the study  of tones and tone-relations4
      ,,the ,,scale ,,of ,,values       
#abh4 ,it is evident that we have in    
black paint the least quantity of  light
 which we can produce4 ,black is the    
lowest of all values4 ,it is  equally   
evident that in white paint we have the 
greatest possible  quantity of light4   
,white is the highest of all values4    
,mixing ,black  and ,white in different 
proportions we can produce an indefinite
 number  of intermediates4 ,we do not   
want1 however1 to be indefinite in our  
terms2 on the contrary we want to be as 
definite as possible4 ,let us1          
therefore1 establish1 between ,black and
 ,white1 a ,middle ,value 7,m72  between
 ,black and ,middle ,value an           
intermediate ,dark 7,d72 between ,middle

  ,value and ,white an intermediate     
,light 7,lt71 and between these five    
values the intermediates1 ,low ,dark    
7,,ld71 ,high ,dark 7,,hd71 ,low ,light 
7,l,lt71 and ,high ,light 7,h,lt74      
,further intermediates 7eight7 may be   
established1 but to these we need not   
give any particular names4 ,if  we have 
occasion to refer to any one of them we 
can say that it lies  between certain   
quantities or values of light for which 
we have names4  ,we can speak1 for      
example1 of the intermediate between    
,middle and ,high  ,dark1 and it may be 
described in writing by the formula     
,m-,,hd4 ,with this  terminology we     
shall be able to describe the principal 
quantities or  values of light both in  
speech and in writing4    ,in order to  
study the principal quantities or values
 of light and the  possibilities of     
contrast which they afford it is wise to
 avoid all  differences of color and    
color-intensity4 ,to do that we produce 
our  ,scale of ,values in terms of      

perfect neutrality1 in which no color   
can  be distinguished4 ,when we use the 
names of different values it is         
understood that they are values of      
,neutrality4 ,the term ,m1 for example1 
stands for ,neutral ,middle1 ,d for     
,neutral ,dark1 ,lt for ,neutral ,light4
      ,,contrasts ,,of ,,the ,,scale    
,,of ,,values    #abi4 ,having produced 
a scale of nine neutral values1         
including ,white  and ,black1 the       
question arises as to the number of     
contrasts which it  affords1 and it is  
easy to see that the number is          
thirty-six4    ,the vertical lines in   
the following diagram indicate the      
possible  contrasts of value in the     
,scale of ,values4 ,counting the lines1 
we see  that the number of contrasts is 
thirty-six4 ,producing these contrasts1 
we shall see what each one amounts to4  
,illustration3 ,diagram #a              
,,definition ,,of ,,value-,,relations   
#acj4 ,the best method of describing and
 distinguishing these  value-contrasts  

will be to use the value-names in a form
 of fractions4  ,for example1 ,lt_/,d   
would mean a contrast of ,dark on       
,light1 ,d_/,lt would  mean a contrast  
of ,light on ,dark1 ,wt_/,blk would mean
 a contrast of ,black  on ,white4 ,that 
is to say1 ,white is subdivided or      
crossed by ,black4 ,when  we wish to    
describe several contrasts in           
combination1 we set the value  of the   
ground-tone above the line1 always1 the 
value of the tone or  tones put upon it 
below1 thus3--           ,lt            
-----------     ,wt      ,blk    ,this  
formula means1 spots of ,white and      
,black on a ground of ,light4           
,lt     --------------      ,wt         
,blk     ---      ,m    ,this formula   
means spots of ,white and ,black on a   
ground-tone of ,light1  with a spot of  
,middle on the ,white1 the ,middle being
 altogether  separated from the ,light  
by the ,white4    ,there is no definite 
thinking except in definite terms1 and  
without  some such terminology as ,i    

have devised and described1 it will be  
impossible to enter upon an experimental
 practice in value-relations  with the  
hope of definite results4 ,with definite
 terms1 however1 we can  take up the    
practice in value-relations with a good 
chance of learning1  in the course of   
time1 all that there is to be learned4  
,,scales ,,of ,,colors ,,in ,,different 
,,values    #aca4 ,we must now proceed  
to the consideration of the qualities of
  light beyond the ,scale of ,neutral   
,values1 in the region of colors and    
color-intensities1--a region of tones   
which we have not yet explored4    ,it  
is evident that no color can exist      
either in the value of ,black or  in the
 value of ,white1 but in every other    
value we have the possibility  of all   
colors4 ,that is to say1 we may have    
,red 7,r7 or ,orange 7,o7 or  ,yellow   
7,y7 or ,green 7,g7 or ,blue 7,b7 or    
,violet 7,v7 or any of the colors  lying
 intermediate between them1--,red       
,orange 7,,ro71 ,orange ,yellow 7,,oy71 

,yellow ,green 7,,yg71 ,green ,blue     
7,,gb71 ,blue ,violet 7,,bv71 or ,violet
 ,red  7,,vr73 all these1 in any value  
of the ,scale of ,values1 except in the 
value of ,black and in the value of     
,white4 ,the possibilities of value  and
 color1 in tones1 are exhibited in the  
following diagram3--      ,,diagram ,,of
 ,,values ,,and ,,colors       ,wt      
,wt       ,h,lt  ,r  ,,ro  ,o  ,,oy  ,y 
,,yg  ,g  ,,gb  ,b  ,,bv  ,v  ,,vr      
,h,lt       ,lt   ,r  ,,ro  ,o  ,,oy  ,y
  ,,yg  ,g  ,,gb  ,b  ,,bv  ,v  ,,vr    
,lt       ,l,lt  ,r  ,,ro  ,o  ,,oy  ,y 
,,yg  ,g  ,,gb  ,b  ,,bv  ,v  ,,vr      
,l,lt       ,m    ,r  ,,ro  ,o  ,,oy  ,y
  ,,yg  ,g  ,,gb  ,b  ,,bv  ,v  ,,vr  ,m
       ,,hd   ,r  ,,ro  ,o  ,,oy  ,y    
,,yg  ,g  ,,gb  ,b  ,,bv  ,v  ,,vr  ,,hd
       ,d    ,r  ,,ro  ,o  ,,oy  ,y     
,,yg  ,g  ,,gb  ,b  ,,bv  ,v  ,,vr  ,d  
,,ld   ,r  ,,ro  ,o  ,,oy  ,y  ,,yg  ,g 
,,gb  ,b  ,,bv  ,v  ,,vr  ,,ld          
,blk                                    
,blk                          ,diagram  

#b      ,,definition ,,of ,,the         
,,color-,,terms    #acb4 ,it is         
important that the words which we use   
for the different  colors should be well
 understood1 that in using them we use  
them with  the same meanings4 ,by ,red  
,i mean the only positive color which   
shows  no element either of ,yellow or  
of ,blue4 ,it is the color which we     
often  describe by the word crimson1 and
 we produce it by the mixture of  ,rose 
,madder and ,vermilion4 ,by ,yellow ,i  
mean the only positive color  which     
shows no element either of ,red or      
,blue4 ,it is the color of the  primrose
 which may be produced by the pigment   
,aureolin4 ,by ,blue ,i mean  the only  
positive color which shows no element   
either of ,yellow or of  ,red4 ,blue is 
seen in a clear sky after rain and in   
the pigment ,cobalt4  ,by ,orange ,i    
mean a positive color showing equal     
elements of ,red and  of ,yellow4 ,by   
,green ,i mean a positive color showing 
equal elements of  ,yellow and of ,blue4

 ,by ,violet ,i mean a positive color   
showing equal  elements of ,blue and    
,red4 ,the character of the             
intermediates is clearly  indicated by  
their several names4 ,in each one we see
 the adjacents in  equal measures4 ,this
 definition of the colors is only       
approximate4  ,it does not pretend to be
 scientific1 but it may help to bring us
 to  a common understanding4 ,to carry  
these definitions farther1 ,i should    
have to produce examples4 ,this ,i can  
do in my class-room1 producing  each    
color according to my idea1 exactly4 ,i 
might reach the same result             
approximately by color-printing1 but the
 result would not1 probably1  be        
permanent4 ,the samples produced by     
hand1 for use in the class-room1  can be
 reproduced from time to time when they 
no longer answer to the  ideas which    
they are intended to express4 ,in this  
treatise ,i shall  use a terminology    
instead of colored illustrations which  
would not be  satisfactory1 or1 if      

satisfactory1 not so permanently4       
,,color-,,intensities ,,in ,,different  
,,values    #acc4 ,if we proceed to     
carry out the idea of ,diagram #b1      
producing all  the twelve colors in all 
of the seven values intermediate between
  the extremes of ,black and ,white1    
making the colors1 in every case1  as   
strong1 as intense1 as is possible with 
the pigment-materials we  have chosen to
 use1 we shall discover that the twelve 
colors reach  their greatest intensities
 in different values2 that is to say1 in
  different quantities of light4 ,red   
reaches its greatest intensity in  the  
value ,high ,dark1 ,orange in ,low      
,light1 ,yellow in ,high ,light1 ,green 
in ,low ,light1 ,blue in ,high ,dark1   
,violet in ,low ,dark1 approximately2   
and the intermediate colors reach their 
greatest intensities in the             
intermediate values1 approximately4 ,in 
order to indicate this fact  in our     
diagram1 we will mark the positions of  
greatest intensity by  putting the color

 signs in larger type4    ,,diagram ,,of
 ,,values1 ,,colors1 ,,and              
,,color-,,intensities       ,wt         
,wt       ,h,lt  ,r  ,,ro  ,o  ,,oy ,y  
,,yg  ,g  ,,gb  ,b  ,,bv  ,v  ,,vr  ,,hl
       ,lt   ,r  ,,ro  ,o ,,oy ,y ,,yg  
,g  ,,gb  ,b  ,,bv  ,v  ,,vr  ,lt       
,l,lt  ,r  ,,ro ,o ,,oy  ,y  ,,yg ,g    
,,gb  ,b  ,,bv  ,v  ,,vr  ,l,lt       ,m
    ,r ,,ro ,o  ,,oy  ,y  ,,yg  ,g ,,gb 
,b  ,,bv  ,v  ,,vr  ,m       ,,hd  ,r   
,,ro  ,o  ,,oy  ,y  ,,yg  ,g  ,,gb ,b   
,,bv  ,v  ,,vr  ,,hd       ,d    ,r     
,,ro  ,o  ,,oy  ,y  ,,yg  ,g  ,,gb  ,b  
,,bv ,v ,,vr ,d       ,,ld   ,r  ,,ro   
,o  ,,oy  ,y  ,,yg  ,g  ,,gb  ,b  ,,bv  
,v ,,vr  ,,ld       ,blk                
,blk                                    
,diagram #c      ,,tones ,,of ,,the     
,,spectrum ,,and ,,of ,,pigments        
#acd4 ,it is probable that we have in   
the ,spectrum an indication of  the     
natural value-relations of the different
 colors when in their  highest          
intensities4 ,owing to the limitations  

of pigment-material1  however1 it is    
impossible to reproduce the intensities 
of the ,spectrum  satisfactorily4 ,an   
approximation is all that we can achieve
 in painting4      ,,the ,,spectrum     
,,sequence ,,and ,,the ,,circuit ,,of   
,,the ,,colors    #ace4 ,having produced
 the scale of twelve colors in the      
values of  their greatest intensities1  
and as intense as possible1 we get an   
approximation to the ,spectrum with this
 difference1 that the color             
,violet-,red 7,purple7 which we get in  
pigments and mixtures of pigments  does 
not occur in the ,spectrum and1 so far  
as we know1 does not belong  in the     
,spectrum4 ,we have in the ,spectrum a  
sequence which begins  with ,red and    
ends with ,violet4 ,it is a sequence1   
not a circuit4 ,in  pigment-mixtures1   
however1 we have a circuit1 clearly     
enough1 and  ,violet-,red is a          
connecting link between ,violet and     
,red4      ,,the ,,complementaries      
#acf4 ,considering the circuit of the   

colors which we are able to produce     
with our pigment-materials1 the question
 arises1 ,what contrasts of  color are  
the strongest8 what interval in the     
,scale of ,colors gives  us the         
strongest possible color-contrast8      
,producing the twelve colors  in the    
values of their greatest intensities1   
and as intense as  possible1 and setting
 the tones in a circuit and in their    
natural and  inevitable order1 you will 
observe that the greatest color-contrast
  is the contrast between colors at the 
interval of the seventh3 for  example1  
the contrasts of ,red and ,green1 or    
,orange and ,blue1 or ,yellow  and      
,violet4 ,the colors at the interval of 
the sixth are less strong  in contrast4 
,the contrast diminishes gradually as we
 pass from the  interval of the seventh 
to the interval of the second4 ,the     
contrast of  colors at the interval of  
the seventh1 the greatest possible      
contrast1  is called the contrast of the
 complementaries4 ,in estimating        

intervals  we count the colors between  
which the intervals occur4      ,a      
,,general ,,classification ,,of ,,tones 
#acg4 ,taking each color in the value of
 its greatest intensity 7as  shown in   
the ,spectrum71 and as intense as       
possible1 the color may be  neutralized 
in the direction of ,black 7neutral     
darkness7 or ,white  7neutral light7 or 
in the direction of any value of        
neutrality  intermediate between ,black 
and ,white1 including the value of the  
color in its greatest intensity4 ,if we 
think of five degrees of                
neutralization1 including the extremes  
of ,intensity and ,neutrality1  we shall
 get as definite a terminology for      
color-intensities and                   
color-neutralizations as we have for    
colors and for values4 ,the  choice of  
five degrees is arbitrary4 ,it is a     
question how far the  classification    
shall go1 what it shall include4 ,we are
 dealing with  infinity1 and our        
limitations are necessarily arbitrary4  

,in ,diagram #c we have a general       
classification of tones as to value1    
color1 color-intensity1 and             
color-neutralization4 ,of values we have
  nine4 ,of colors we have twelve4 ,of  
degrees of intensity and of             
neutralization we have five4            
,,color-,,intensities ,,and             
,,color-,,neutralizations    #ach4 ,it  
is important to distinguish between     
degrees of intensity and  degrees of    
neutralization4 ,the degrees of         
color-intensity and of                  
color-neutralization1 in any value1 are 
described by fractions4 ,the  formula   
,d-,r means1 value ,dark1 color ,red1   
intensity three quarters4  ,the formula 
,d-,r1 ,n means1 value ,dark1 color     
,red1 three quarters  neutralized4 ,the 
formula ,m-,o means1 value ,middle1     
color ,orange1  intensity one half4 ,the
 formula ,m-,o1 ,n means1 value ,middle1
 color  ,orange1 half neutralized4      
,m-,o1 ,n is a tone somewhat less       
intense  in color than ,m-,o1 as may be 

seen on the diagram4 ,the degree of     
neutralization has reference1 in all    
cases1 to the maximum intensity  for the
 given value4 ,what that is1            
theoretically1 may be seen by  referring
 to the triangle of the color1 in which 
the possibilities of  intensity1 in     
different values1 are clearly indicated4
      ,,the ,,definition ,,of           
,,particular ,,tones    #aci4 ,to define
 any tone1 in this classification1 we   
must name its  value1 its color1 and the
 degree of color-intensity or           
neutralization4      ,,the              
,,classification ,,of ,,tones           
,,necessarily ,,theoretical    #adj4    
,the general classification of tones in 
which is shown  all the possibilities of
 value1 color1 color-intensity1 and     
color-neutralization1 in reflecting     
pigments1 is necessarily  theoretical1  
or rather ideal1 because the degrees of 
intensity  obtainable in any value      
depend upon the pigment-materials we    
have to  use1 or choose to use4 ,no very

 great intensity of ,yellow1 even in the
  value of ,high ,light1 can be obtained
 if we choose to use a mixture of       
,yellow ,ochre with ,ultramarine ,blue  
and ,white to produce it4 ,it is only   
when we use the most brilliant          
pigments--the ,madders1 ,vermilion1 the 
,cadmiums1 ,aureolin1 and ,cobalt       
,blue--that we can approximate toward   
the  highest intensities1 as indicated  
in our diagram and exhibited in the     
,spectrum4      ,,the ,,definition ,,of 
,,particular ,,tone-,,relations    #ada4
 ,the number of                         
tone-contrasts--contrasts of value1 of  
color1 and of  color-intensity or       
neutralization--is1 evidently1 beyond   
calculation4    ,the method of          
describing any particular contrast or   
contrasts is easy  to understand4 ,we   
have only to define the tones and to    
indicate how  they cross one another4   
,,ro1 ,n     ---------        ,,vr      
,this formula means that a spot of      
,violet-,red 7,dark1 full intensity7 is 

put on a ground-tone of ,middle         
,red-,orange1 half neutralized4         
,,ro     ----------     ,,vr      ,wt   
--     ,,yg    ,this formula means that 
spots of ,low ,dark ,violet-,red 7full  
intensity7 and ,white are put on a      
ground-tone of ,middle ,red-,orange1    
half intensity1 and that on the spot of 
,low ,dark ,violet-,red 7full           
intensity71 as a ground-tone1 is put a  
spot of ,light ,yellow-,green  7full    
intensity74 ,it is not necessary to name
 the value when the  color occurs in the
 value of its greatest intensity1 and it
 is not  necessary to describe the      
intensity1 in any value1 when the       
greatest  intensity possible to that    
value is meant4 ,in the first case the  
value  is understood1 in the second case
 the intensity--the greatest for the    
value--is understood4                   
,,sequences ,,of ,,values ,,and ,,colors
      #adb4 ,when1 in view of all       
possible tones1 as indicated in the     
general classification of tones1        

according to value1 color1 and          
color-intensity1 or color-neutralization
 7,diagram of the ,triangles71  we try  
to think what tones we shall use1 what  
contrasts of tone we  shall produce1 we 
are sure to be very much 8at sea10      
because of the  great number and variety
 of possibilities4 ,even when we        
disregard  differences of intensity and 
consider simply the possibilities of    
value and of color1 as shown in the     
general classification of tones         
according to value and color 7,diagram  
of ,values and ,colors1 p4 #acg71  we   
have still too many possibilities to    
consider1 and our choice of  tones is   
determined by accident or habit rather  
than by clear vision or  deliberate     
preference4 ,we shall find it worth     
while to limit our range  in each       
experiment to some particular sequence  
of values and colors1 or  to some       
particular combination of sequences4    
,instead of trying to think  in the     
range of all values1 all colors1 we     

ought to limit our thinking1  in each   
case1 to the range of a few values and a
 few colors1--a few  definite tones with
 which we can become perfectly familiar 
and of which  we can have definite      
visual images4 ,it is only when we can  
imagine  tones vividly that we can think
 satisfactorily in tone-relations4 ,we  
shall achieve this power of thinking in 
tones and tone-relations best  through  
self-imposed limitations4    #adc4 ,we  
ought to begin our study of ,tones and  
,tone-,relations with the  ,scale of    
,neutral ,values 7see p4 #ace74 ,we     
ought to work with the nine  tones of   
this scale or sequence until we know    
them well1 until we can  visualize them 
clearly1 and until we can produce them  
accurately2 until  we can readily       
produce any single tone of the scale and
 any of the  thirty-six possible        
contrasts which the scale affords4      
,besides the ,scale of ,neutral ,values 
there are three types of ,value and     
,color ,sequence which we may use4      

#add4 ,first4 ,we have the sequences    
which may be described as those of  the 
,vertical2 sequences which may be       
indicated by vertical lines drawn       
across the ,diagram of ,values and      
,colors4 ,in each of these sequences1   
twelve in number1 we have one color in  
all the values of the ,scale of         
,values1 except ,black and ,white4      
,these sequences of the ,vertical1 as ,i
  shall call them1 are of very little   
use in ,pure ,design4 ,they give us     
value-contrasts and contrasts of        
color-intensity 7intensities of one     
color71 but no color-contrasts1 no      
differences of color4 ,the tones in     
these sequences are monotonous in color4
    #ade4 ,second4 ,we have the         
sequences which may be described as     
those of  the ,horizontal2 sequences    
which may be indicated by horizontal    
lines  drawn across the ,diagram of     
,values and ,colors4 ,in these sequences
 we  have differences of color and      
color-intensity1 but all in one value4  

,these sequences give us color-contrasts
 7different colors in different  degrees
 of intensity71 but no value-contrasts4 
,the tones in these  sequences are      
monotonous in value4 ,the sequences of  
one horizontal are  of very little use4 
#adf4 ,third4 ,we have the sequences    
which may be described as those  of the 
,diagonal2 sequences which may be       
indicated by lines drawn  diagonally    
across the ,diagram of ,values and      
,colors4 ,in drawing these  sequences   
the reader must not forget that the     
,scale of ,colors is a  circuit1 so when
 he reaches the end of the diagram he   
returns and  continues from the other   
end4 ,the diagram might1 for convenience
 in  drawing these sequences1 be        
extended to several repetitions of the  
,scale of ,colors4 ,in the sequences of 
the ,diagonal we have contrasts  both of
 value and of color4 ,the color in these
 sequences changes from  value to value 
through the ,scale of ,values4 ,each    
sequence gives us  certain colors in    

certain values1 and in no case have we  
two colors  in the same value4 ,to these
 sequences of the ,diagonal we must give
  our particular attention4 ,they are   
the sequences which we shall use        
constantly1 in ,representation as well  
as in the practice of ,pure ,design4    
#adg4 ,the sequences of the ,diagonal   
fall into two divisions4 ,first1  there 
are the sequences which we draw through 
the ,diagram of ,values  and ,colors    
from ,black up-to-the-right to ,white4  
,i shall call these the  ,sequences of  
the ,right ,mode 7,sign 74 ,second1     
there are the sequences  which we draw  
from ,black up-to-the-left to ,white4 ,i
 shall call these  the ,sequences of the
 ,left ,mode 7,sign 74    ,taking the   
lowest color in the sequence as the     
keynote1 we have for the  ,right ,mode1 
in the ,scale of ,twelve ,colors1 twelve
 distinct sequences of  which this which
 follows is an example4       ,seq4     
,,ld-,,bv1  #b;ds            ,wt        
,h,lt  -  ,,oy     ,lt   -  ,o     ,l,lt

  -  ,,ro     ,m    -  ,r     ,,hd   -  
,,vr     ,d    -  ,v     ,,ld   -  ,,bv 
,blk    ,in this sequence the colors are
 taken at the interval of the second4   
,that is what is meant by the           
abbreviation #b;ds4    ,taking the      
lowest color of the sequence as its     
keynote1 as before1 we  have for the    
,left ,mode twelve distinct sequences1  
of which that which  follows is an      
example4       ,seq4 ,,ld-,,oy1  #b;ds  
,wt     ,h,lt  -  ,,bv     ,lt   -  ,v  
,l,lt  -  ,,vr     ,m    -  ,r     ,,hd 
-  ,,ro     ,d    -  ,o     ,,ld   -    
,,oy         ,blk    ,in this sequence1 
as in the one previously given1 the     
colors are taken  at the interval of the
 second4    #adh4 ,the colors in these  
diagonal sequences may be taken not only
 at  intervals of the second1 but at    
intervals of the third1 the fourth1 the 
fifth1 the sixth1 and the seventh4      
,taking the colors at these different   
intervals we have1 for each interval1   
twenty-four distinct sequences2  twelve 

for the ,right ,mode1 twelve for the    
,left ,mode2 in all one hundred  and    
forty-four different sequences4    #adi4
 ,among the sequences of the ,diagonal  
those in which the colors are  taken at 
the interval of the fifth are           
particularly interesting4 ,the  colors  
taken at the interval of the fifth fall 
into four triads1--the  first1 ,r-,y-,b1
 the second1 ,,ro-,,yg-,,bv1 the third1 
,o-,g-,v1 the fourth1  ,,oy-,,gb-,,vr4  
,taking the colors in any of these      
triads in the two modes1  the ,right and
 the ,left1 we get six sequences of     
different colors in  different values   
for each triad4 ,of these               
,triad-,sequences ,i will give  one as  
an example4       ,seq4 ,,ld-,r1  #eths 
,wt     ,h,lt  -  ,r     ,lt   -  ,y    
,l,lt  -  ,b     ,m    -  ,r     ,,hd   
-  ,y     ,d    -  ,b     ,,ld   -  ,r  
,blk    ,the ,triad-,scales1 whether in 
the ,right ,mode or in the ,left ,mode1 
are of great interest both in ,pure     
,design and in ,representation4 ,in     

,representation1 however1 the number of 
tones between the limits of  ,black and 
,white would1 as a rule1 be increased1  
as in the extended  diagram given       
farther on4    #aej4 ,instead of taking 
the colors at a certain interval in one 
mode or  the other1 it is possible to   
take the colors in a certain relation of
  intervals repeated2 this in either    
mode4 ,the relation of a third to a     
fifth1 for instance1 being repeated1 in 
one mode or the other1 gives us  some   
very interesting sequences4 ,the one    
which follows is an example4            
,,ld-,v1  #eth-#c;d           ,wt       
,h,lt  -  ,y               #c;d     ,lt 
-  ,o               #eth     ,l,lt  -   
,v               #c;d     ,m    -  ,b   
#eth     ,,hd   -  ,y               #c;d
     ,d    -  ,o               #eth     
,,ld   -  ,v         ,blk    ,the       
relation of a seventh followed by two   
fifths1 when repeated1 in  either mode1 
gives a large number of sequences of    
very great interest1  particularly for  

,representation4    #aea4 ,any two of   
the sequences which ,i have described as
 those of the  ,vertical1 or more than  
two1 may be combined and used together4 
,in  that case we have two or more      
colors to a value4 ,the monotony which  
is inevitable in any single vertical    
sequence is avoided in the  combination 
of two or more such sequences4          
,seq4 ,r and ,seq4 ,y              ,wt  
,r   ,h,lt   ,y       ,r    ,lt   ,y    
,r   ,l,lt   ,y       ,r    ,m    ,y    
,r    ,,hd   ,y       ,r    ,d    ,y    
,r    ,,ld   ,y           ,blk    ,this 
is an example of the combination of two 
vertical sequences--the  sequence of    
,red and the sequence of ,yellow4 ,i    
have not found  the sequences of this   
type very interesting4 ,in using them in
  ,representation ,i have found it      
desirable to have the intensities       
increase gradually toward white1 or1    
what amounts to the same thing1  to have
 each color neutralized as it loses     
light4 ,that happens1  constantly1 in   

,nature4    #aeb4 ,any two of the       
sequences which ,i have described as of 
the  ,horizontal1 or even more than two1
 may be combined and used together4     
,seq4 ,lt and ,d1 #c;ds       ,lt   ,r  
,o   ,y   ,g   ,b   ,v     ,d    ,r   ,o
   ,y   ,g   ,b   ,v    ,this scale     
gives us a variety of color-contrasts   
with one  value-contrast4 ,the colors   
are taken at the interval of the third4 
,they  might be taken at any interval up
 to that of the seventh1 in which  case 
we should have a contrast of            
complementary colors in two values1     
each color occurring in each value4 ,the
 monotony of value which is  inevitable 
in any single horizontal sequence is in 
the combination of  two or more such    
sequences avoided4 ,i have used the     
,red-,yellow-,blue  triad in three and  
in five values with satisfaction4 ,each 
value  represents a plane of light in   
which certain differences of color are  
observed4    #aec4 ,any two of the      
sequences which ,i have described as of 

the ,diagonal  may be combined1 in two  
ways4 ,first1 two sequences of the same 
mode may  be combined4 ,second1 two     
sequences of different modes1 one of the
 ,right  ,mode and one of the ,left     
,mode1 may be combined4       ,,ld-,,gb 
#c;ds with ,,ld-,,ro  #c;ds             
,wt         ,,gb  ,h,lt  ,,ro           
,,bv  ,lt   ,,oy         ,,vr  ,l,lt    
,,yg         ,,ro   ,m   ,,gb           
,,oy  ,,hd   ,,bv         ,,yg   ,d     
,,vr         ,,gb  ,,ld   ,,ro          
,blk    ,in this case we have a         
combination of two diagonal sequences of
 the  ,left ,mode in which the colors   
are taken at the interval of the third4 
,changing the mode of these two         
sequences we get them inverted1 thus3-- 
,,ld-,,gb  ,,ld-,,ro  #c;ds             
,wt       ,,gb  ,h,lt  ,,ro       ,,yg  
,lt   ,,vr       ,,oy  ,l,lt  ,,bv      
,,ro   ,m   ,,gb       ,,vr  ,,hd   ,,yg
       ,,bv   ,d   ,,oy       ,,gb  ,,ld
   ,,ro           ,blk    ,here the mode
 is changed and the combined sequences  

inverted4 ,the  combined sequences may  
be both in the same mode or in different
 modes4  ,when the modes are different  
the sequences come into contact1 and in 
some cases cross one another4           
,,ld-,v  #b;ds with ,,ld-,v  #b;ds      
,wt              ,y           ,,oy      
,,yg            ,o    ,g           ,,ro 
,,gb            ,r    ,b           ,,vr 
,,bv              ,v             ,blk   
,in this case we have a combination of  
two diagonal sequences4 ,one of  the    
sequences is in the ,right1 the other is
 in the ,left ,mode4 ,the  colors are in
 the values of their greatest           
intensities4       ,seq4 ,,ld-,,gb      
#c;ds with ,,ld-,,gb  #c;ds             
,wt                  ,,gb               
,,yg    ,,bv               ,,oy    ,,vr 
,,ro               ,,vr    ,,oy         
,,bv    ,,yg                  ,,gb      
,blk    ,in this case the combined      
sequences cross one another in the tone 
of  ,m-,,ro4 ,the combined sequences    
have three tones in common4 ,it may     

happen  that the sequences combined will
 have no tones in common4 ,this is shown
  in the sequence which follows3--      
,,ld-,o  #eths with ,,ld-,b  #eths      
,wt              ,o  ,h,lt   ,b         
,g   ,lt   ,y              ,v  ,l,lt    
,r              ,o   ,m    ,b           
,g   ,,hd   ,y              ,v   ,d     
,r              ,o   ,,ld   ,b          
,blk    #aed4 ,instead of having two    
colors to a value in the combination of 
two  vertical sequences1 we may have an 
alternation of colors in the values1    
giving one color to a value1 thus3--    
,wt     ,r  ,h,lt         ,lt   ,y      
,r  ,l,lt         ,m    ,y     ,r   ,,hd
         ,d    ,y     ,r   ,,ld         
,blk    ,it has seemed to me that the   
sequences in which we have one color to 
a value give better results than those  
in which we have two or more  colors to 
a value4    #aee4 ,instead of having    
each color in two values in the         
combination  of two horizontal          
sequences1 we may have the colors1 taken

 at equal  intervals1 occurring         
alternately first in one value and then 
in the  other4       ,lt  ,r  4  ,y  4  
,b  4     ,d   4  ,o  4  ,g  4  ,v      
#aef4 ,these alternating sequences may  
proceed1 not only vertically and        
horizontally1 but diagonally across the 
diagram4 ,in that case the  alternations
 will be between different              
value-intervals in a series of  equal   
color-intervals or between different    
color-intervals in a series  of equal   
value-intervals4        ,wt     ,h,lt   
,,vr      ,lt                    ,,bv   
,l,lt               ,,gb        ,v      
,m          ,,yg       ,b      ,,hd     
,,oy       ,g       ,d        ,y        
,,ld  ,o     ,blk    ,in this case the  
alternation is between different        
value-intervals  through the ,scale of  
,colors4 ,the movement being1 as a      
whole1  up-to-the-right1 is in the      
,right ,mode4 ,i have not used any of   
the  sequences1 of this type1 in which  
the value-intervals alternate1 first  in

 one mode then in the other1 with a     
constant color-interval1 but ,i  have   
used1 frequently1 the alternation of two
 different color-intervals  in a series 
of equal value-intervals4 ,the sequences
 produced in this  way are among the    
most interesting of all the many ,i have
 used4 ,i will  give several examples4  
,wt     ,h,lt  ,y             #gth      
,lt   ,v             #eth     ,l,lt  ,o 
#gth      ,m   ,b             #eth      
,,hd   ,r             #gth      ,d   ,g 
#eth     ,,ld   ,v         ,blk    ,in  
this case the alternation is from the   
keynote1 ,low ,dark ,violet1 up  first  
in the ,left ,mode a fifth1 then up in  
the ,right ,mode a seventh1  then in the
 ,left ,mode a fifth1 and so on up to   
,white4 ,this particular  alternation   
might be described as the relation of a 
fifth and a seventh  repeated1 in the   
,left ,mode4            ,wt     ,h,lt   
,y             #gth     ,lt   ,v        
#eth     ,l,lt  ,g             #gth     
,m   ,r             #eth     ,,hd   ,b  

#gth      ,d   ,o             #eth      
,,ld   ,v         ,blk    ,in the       
sequence just given the alternation is1 
from the keynote ,low  ,dark ,violet1   
first in the ,right ,mode a fifth1 then 
in the ,left ,mode a  seventh3 this     
through the ,scale of ,values up to     
,white4 ,the order of the  previous     
sequence is inverted4 ,this particular  
alternation might be  described as the  
relation of a fifth and seventh repeated
 in the ,right  ,mode4    ,the          
alternation of intervals of the fifth   
with intervals of the third  gives some 
interesting sequences1 in which the     
alternation of intervals  is1           
necessarily1 an alternation of modes4   
,wt     ,h,lt  ,y             #c;d      
,lt   ,g             #eth     ,l,lt  ,o 
#c;d      ,m   ,y             #eth      
,,hd   ,r             #c;d      ,d   ,o 
#eth     ,,ld   ,v         ,blk    #aeg4
 ,i have by no means exhausted the      
possibilities of value and color        
combination1 but ,i have indicated a    

sufficient number to serve the  purposes
 of experimental practice in            
tone-relations1 for a long time  to     
come4 ,the sequences which ,i have found
 most interesting1 in my own            
experiments1 have been the diagonal     
sequences of the two modes1 using       
intervals of the fifth1 and the diagonal
 sequences in which with equal          
value-intervals there is an alternation 
of certain color-intervals1--the        
seventh and the fifth1 and the seventh  
and two fifths4 ,it may very well  be   
that these particular sequences interest
 me because ,i have used them  more than
 others and consequently think in them  
more easily4    #aeh4 ,for the purposes 
of ,pure ,design the ,scale of ,nine    
,values1  including ,black and ,white1  
will be found sufficient2 but when it   
comes  to the combination of ,design    
with ,representation1 and particularly  
to ,representation in ,full ,relief1 it 
will be necessary to introduce          
intermediates into the ,scale of        

,values4 ,with this purpose in view  ,i 
give one more diagram in which          
intermediates of value have been        
introduced4 ,for convenience in drawing 
out the different sequences upon  this  
diagram ,i have repeated the ,scale of  
,colors showing the connection  of      
,violet-,red with ,red4 ,this diagram   
7#e7 is simply an extension of the      
,diagram of ,values and ,colors given on
 p4 #acg4    #aei4 ,we may use the      
various sequences ,i have described     
without mixing  the tones1 using the    
tones one at a time as they may be      
required2 but  if we choose we may mix  
adjacents or thirds or even threes4 ,in 
that  way the tone-possibilities of each
 sequence may be very much extended4    
,it may be well to show what the        
extension amounts to by giving one of   
the sequences with an indication of the 
result of mixtures within the  limits   
described4       ,seq4 ,,ld-,r  #eths   
,wt          ,h,lt   ,r           ,lt   
,y          ,l,lt   ,b           ,m     

,r          ,,hd    ,y           ,d     
,b          ,,ld    ,r          ,blk    
,this is the sequence in which we decide
 to mix adjacents1 thirds1 and  threes4 
,a ,,diagram ,,of ,,values ,,and        
,,colors       ,wt                      
,wt            ,r ,,ro ,o ,,oy ,y ,,yg  
,g ,,gb ,b ,,bv ,v ,,vr ,r ,,ro ,o ,,oy 
,y ,,yg ,g ,,gb ,b ,,bv ,v ,,vr         
,h,lt  ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb  
,b ,,bv ,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg 
,g ,,gb ,b ,,bv ,v ,,vr  ,h,lt          
,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb ,b ,,bv 
,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb 
,b ,,bv ,v ,,vr       ,lt   ,r ,,ro ,o  
,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v ,,vr ,r 
,,ro ,o ,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v 
,,vr  ,lt            ,r ,,ro ,o ,,oy ,y 
,,yg ,g ,,gb ,b ,,bv ,v ,,vr ,r ,,ro ,o 
,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v ,,vr    
,l,lt  ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb  
,b ,,bv ,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg 
,g ,,gb ,b ,,bv ,v ,,vr  ,l,lt          
,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb ,b ,,bv 
,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb 

,b ,,bv ,v ,,vr       ,m    ,r ,,ro ,o  
,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v ,,vr ,r 
,,ro ,o ,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v 
,,vr  ,m            ,r ,,ro ,o ,,oy ,y  
,,yg ,g ,,gb ,b ,,bv ,v ,,vr ,r ,,ro ,o 
,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v ,,vr    
,,hd   ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb  
,b ,,bv ,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg 
,g ,,gb ,b ,,bv ,v ,,vr  ,,hd           
,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb ,b ,,bv 
,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb 
,b ,,bv ,v ,,vr       ,d    ,r ,,ro ,o  
,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v ,,vr ,r 
,,ro ,o ,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v 
,,vr  ,d            ,r ,,ro ,o ,,oy ,y  
,,yg ,g ,,gb ,b ,,bv ,v ,,vr ,r ,,ro ,o 
,,oy ,y ,,yg ,g ,,gb ,b ,,bv ,v ,,vr    
,,ld   ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb  
,b ,,bv ,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg 
,g ,,gb ,b ,,bv ,v ,,vr  ,,ld           
,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb ,b ,,bv 
,v ,,vr ,r ,,ro ,o ,,oy ,y ,,yg ,g ,,gb 
,b ,,bv ,v ,,vr       ,blk              
,blk                                    
,diagram #e                    #b;ds    

#c;ds  #cs     ,wt       ,h,lt   ,r     
,o     ,lt    ,y         ,v    ,n       
,g     ,l,lt   ,b         ,o    ,n      
,v     ,m     ,r         ,g    ,n       
,o     ,,hd    ,y         ,v    ,n      
,g     ,d     ,b         ,o    ,n       
,v     ,,ld    ,r       ,blk    ,this   
diagram shows the results of mixing     
seconds1 thirds1 and threes4  ,it is    
evident that in mixing the tones of any 
sequence in this way  we go beyond the  
strict limitations of the sequence1     
particularly in  mixing thirds and      
threes4 ,the results obtained are fairly
 definite1  however1 and the tones      
obtainable are still within the range of
  definite thinking4 ,if we should go   
farther1 to the mixture of tones  beyond
 the interval of the third1 we should   
get into the region of  indefinite      
possibilities4    #afj4 ,it must be     
clearly understood that our object in   
using these  sequences and more or less 
restricted mixtures is to limit our     
thinking  so that it may gain in        

definiteness what it loses in extent4   
,when  we limit our thinking in any case
 to a few tones1--certain colors in     
certain values1--we come to know those  
tones so well that we can imagine  any  
one of them vividly1 without seeing it4 
,it is only when we have in  mind       
definite tone-images that we begin to   
think in tone-relations and  rise to the
 possibilities of imaginative           
composition in tones4    ,in using the  
sequences which ,i have described the   
tones must be  carefully mixed and      
prepared upon the palette and set there 
in the  order of the sequence1 whatever 
it is4 ,that gives the painter certain  
colors in certain values4 ,that is to   
say1 he has a certain number  of tones  
to consider and to use4 ,he takes one of
 the tones into his  brush and gives it 
a position1 a measure1 and a shape4     
,that done1 he  takes another tone and  
gives to that a position1 measure1 and  
shape4  ,proceeding in this way he      
creates a certain relationship of tones1

  positions1 measures1 and shapes1 the  
terms of which relationship are         
perfectly definite4 ,he repeats what he 
finds satisfactory4 ,he avoids  what he 
finds unsatisfactory4 ,experimenting in 
this way1 in such  definite terms1 he   
ought to make a sure and steady progress
 toward the  discovery of what is       
orderly and beautiful4 ,the use of any  
particular  sequence of values and      
colors is like the use1 by the musician1
 of a  well-tuned instrument4 ,it is at 
once a definition of terms and a source 
of suggestion and of inspiration4       
,there is nothing occult or sacred about
 these sequences and  combinations of   
sequences4 ,in using them we are in no  
way safeguarded  against error4 ,using  
these sequences1 we can produce bad     
effects of  light and of color as well  
as good ones4 ,whether the results of   
using  these sequences are good or bad  
depends upon the user--what his thinking
  amounts to4 ,it will be a grave       
mistake to regard any of these sequences

  as recipes for righteousness1 when    
they are simply modes of thought4  ,they
 are nothing more than the sections or  
divisions of a general  classification  
of tones4 ,in using any particular      
sequence we observe  that the same value
 and color-relations recur repeatedly4  
,that is  always desirable from the     
point of view of ,design4 ,it means     
,harmony4    #afa4 ,the beauty of any   
scheme of values and colors depends1 not
 only  upon the pigment-materials used1 
upon the sequence of values and colors  
chosen and upon the particular tones    
produced1 but quite as much  upon the   
relative positions and juxtapositions   
given to the tones1  the quantities or  
measures in which they are used1 and1   
lastly1 the  way in which the paint is  
handled4 ,to find out what tones to use 
as  ground-tones1 what tones to put upon
 these ground-tones1 and in what        
quantities or measures1 is a matter of  
experimental practice and of  visual and
 imaginative discrimination4    ,having 

defined the word tone and its elements1 
value1 color1 and  color-intensity1 and 
having established a general            
classification of  tones to show the    
possibilities of tone1 ,i must go on to 
describe what  will be orderly in       
tone-relations4 ,order and ,beauty in   
tone-relations  will be found in        
,tone-,harmonies1 ,tone-,balances1 and  
,tone-,rhythms4                         
,,tone-,,harmony      #afb4 ,by         
,tone-,harmony ,i mean a relation of    
likeness in tones4 ,tones  are in       
,harmony when they resemble one another 
in all or in certain  respects4 ,to be  
in ,harmony two or more tones must have 
at least  something in common1 either   
value or color4 ,if they have the same  
color they may be in the same degree of 
intensity1 giving a ,harmony  of        
,intensities4 ,tone-,harmony resolves   
itself into ,value-,harmony1            
,color-,harmony1 and the ,harmony of    
,intensities4 ,the ,harmony of          
,intensities lies between tones of the  

same color1 when they are  equally      
neutralized or neutralized in           
approximately the same degree4  ,when   
different colors are neutralized we have
 the ,harmony of a common  neutrality or
 grayness of color4    #afc4 ,tones may 
be harmonized on the palette before they
 are used1 that  is to say1 before any  
positions1 measures1 and shapes are     
given to  them on paper or canvas1 or   
they may be harmonized after positions1 
measures1 and shapes have been given to 
them4 ,to harmonize tones on  the       
palette1 as to value1 we must bring them
 approximately to the same  value1 with 
as little change of color as possible4  
,to harmonize tones  on the palette as  
to color we must bring them             
approximately to the same  color1 with  
as little change of value as possible4  
,if two or more tones  have the same    
color they may be intensified or        
neutralized until they  are brought     
approximately to the same degree of     
intensity4 ,the tones of  ,red showing a

 ,harmony of ,intensities would lie on a
 vertical line drawn  through the       
triangle of ,red in the ,diagram of the 
,triangles4    ,as the tone-effect which
 we produce depends very largely upon   
the  positions1 measures1 and shapes    
which we give to our tones1 we may not  
be satisfied with an effect which has   
been produced with previously  prepared 
and harmonized tones4 ,we may wish to   
change the effect1  to achieve a still  
greater ,harmony4 ,given a certain      
arrangement or  composition of tones1   
certain tones in certain positions1     
measures1 and  shapes1 and given the    
problem to harmonize those tones1 what  
do we do8    #afd4 ,suppose it is       
,value-,harmony which we want2 what is  
our procedure8           ,wt     ,h,lt  
-  ,b      ,lt  -  ,v     ,l,lt  -  ,y  
,m   -  ,,ro     ,,hd   -  ,g      ,d   
-  ,o     ,,ld   -  ,,vr         ,blk   
,here1 let us say1 are the tones of a   
design1 certain colors in  certain      
values4 ,what shall we do with these    

tones to bring them into                
,value-,harmony8    ,illustration3      
,wt     ,h,lt  -  ,b      ,lt  -  ,v    
,l,lt  -  ,y      ,m   -  ,,ro     ,,hd 
-  ,g      ,d   -  ,o     ,,ld   -  ,,vr
         ,blk    ,diagram #f    ,for    
,value-,harmony we must diminish the    
range of values toward one  value4 ,in  
the above diagram ,i have shown a       
diminution of the range of  values      
toward ,high ,light3 this in several    
degrees4    ,illustration3           ,wt
     ,h,lt  -  ,b      ,lt  -  ,v       
,l,lt  -  ,y      ,m   -  ,,ro     ,,hd 
-  ,g      ,d   -  ,o     ,,ld   -  ,,vr
         ,blk    ,diagram #g            
,following the indications of this      
diagram1 we pull the colors together    
toward ,light in one case 7,b71 toward  
,middle in another 7,a71 toward  ,dark  
in a third 7,c74 ,as we do this we      
increase the ,value-,harmony4 ,in       
reproducing the tones in a diminished   
range of values1 raising the  colors in 
value or lowering them1 we are not      

obliged to change the  colors except in 
cases where they become1 possibly1      
confounded with  ,black or with ,white4 
,it will often happen1 however1 that the
 intensity  of a color has to be        
diminished when the value is changed4   
,for example1  if ,red ,orange1 in the  
illustration given1 is in its greatest  
intensity1  the color may remain        
unchanged in ,system 8,a10 but its      
intensity will  be1 necessarily1        
diminished in ,system 8,b10 or ,system  
8,c40 ,see ,diagram  of the ,triangles4 
,for the sake of ,value-,harmony we     
diminish the range of values1 making  as
 little changes of color as possible1   
and only those changes  of              
color-intensity which are inevitable4 ,a
 complete and perfect  ,value-,harmony  
is1 as a rule1 undesirable because it   
means that all  the colors are reduced  
to one value which gives a monotony of  
value4  ,approximate ,harmony of ,values
 is generally sufficient4 ,the range of 
values is narrowed1 the contrasts are   

diminished1 and an even tonality  is    
secured4 ,that is all we require1 in    
most cases1 an approximation to  one    
value4    #afe4 ,suppose it is          
,color-,harmony which we want to        
achieve3 what  procedure shall we       
follow8       ,wt     ,b     ,v     ,y  
,r     ,g     ,o     ,blk    ,here are  
certain tones1 certain colors in certain
 values4 ,what shall we  do with these  
tones to get ,color-,harmony8 ,we must  
diminish the range  of color-contrasts  
by giving predominance to one color1    
either to one  of the colors to be      
harmonized or to some other4 ,that may  
be done by  mixing one color into all   
our tones4        ,wt                   
,wt       ,b                            
,v       ,v                             
,,vr       ,y    ,giving predominance to
 ,red1 we get3    ,o       ,r           
,r       ,g                             
,n       ,o                             
,,ro     ,blk                           
,blk                      ,diagram #h   

,the range of color-contrast is in this 
way diminished to the intervals  between
 ,violet1 ,orange1 and ,neutral4 ,the   
process1 so far as color is  concerned1 
disregarding value-relations1 is fully  
explained in the  following diagram3--  
,illustration3 ,diagram #i    ,suppose1 
instead of giving predominance to ,red1 
as in the example  above1 we give       
predominance to ,blue1 taking the same  
range of colors4        ,wt             
,wt       ,b                            
,b       ,v                             
,,bv       ,y    ,giving predominance to
 ,blue we get3    ,g       ,r           
,v       ,g                             
,,gb       ,o                           
,n     ,blk                             
,blk        ,diagram #aj    ,the range  
of color-contrast is in this way        
diminished to the intervals  between    
,green1 ,violet1 and ,neutral4 ,the     
process1 so far as color is  concerned1 
is fully explained in the following     
diagram3--    ,illustration3 ,diagram   

#aa    ,in the diagrams which ,i have   
given the predominance is in the        
measure of one half4 ,that is to say1   
the mixtures are half and  half1        
theoretically speaking4 ,the theoretical
 result is a range of  intermediate     
colors4 ,the predominance is not        
necessarily in the measure  of one half4
 ,it may be in any measure4 ,the        
presence of ,red or ,blue in  all the   
tones may be hardly noticeable or it may
 amount to a general  redness or        
blueness in which other colors are      
distinguished with more  or less        
difficulty4    #aff4 ,suppose it is the 
harmony of grayness1 a ,harmony of      
,neutralization1 which we want4 ,what is
 the procedure to follow8               
,illustration3 ,diagram #ab    ,the     
procedure is shown in this diagram4 ,we 
see here what is meant by a  ,harmony of
 ,neutralization1 without changes of    
value4 ,the neutralization  is in the   
measure of one half in each case4 ,red  
,orange and ,green  are the only colors 

which exist in their maximum            
intensities4 ,their  intensities are    
diminished to the half-point1 without   
change of  value1--from ,,ro to ,,ro in 
one case1 and from ,g to ,g in the      
other4 ,the  other colors are reduced in
 their intensities proportionally4 ,the 
value  in each case remains unchanged4  
#afg4 ,having considered the methods of 
getting ,value-,harmony and             
,color-,harmony separately1 ,i must now 
describe the method of getting the      
combination of ,value-,harmony with the 
,harmony of ,neutralization4 ,to do     
this we must set the colors in positions
 regarding the ,scale of ,neutral       
,values1 which will indicate their      
several values1 and in each case  the   
degree of intensity4 ,we must then      
decide whether to neutralize  the       
several tones toward ,black or ,white1  
or toward some neutral value  between   
these extremes4    ,illustration3       
,diagram #ac    ,this illustrates the   
method of a neutralization toward ,black

 in the  measures of one quarter1 one   
half1 and three quarters4               
,illustration3 ,diagram #ad    ,this    
illustrates the method of a             
neutralization toward ,white in the     
measures of one third and two thirds4   
,illustration3 ,diagram #ae    ,this    
illustrates the method of a             
neutralization toward the ,middle       
,neutral1 between ,black and ,white1 a  
neutralization in the measures of  one  
quarter1 one half1 and three quarters4  
,in bringing tones into harmony1 by one 
or another or all of these  various     
methods1 we must remember that when we  
have diminished the  contrast of value  
and of color beyond a certain point the 
result is  monotony1 a monotony which   
may be undesirable4 ,it is easy to get  
into a  state of mind in which we       
dislike all contrasts4 ,in this state of
 mind  we find no sthetic satisfaction  
except in monotony4 ,such a state of    
mind should be avoided4 ,monotony is the
 ,nirvana of stheticism4    #afh4 ,we   

may have a ,harmony in the repetition   
and recurrence of two or  more          
contrasting1 even strongly contrasting1 
tones4 ,we may have ,harmony  in the    
repetition and recurrence of a contrast 
in which there is  perhaps no ,harmony4 
,for example3 ,i may repeat the contrast
 ,orange-,blue any number of times  in a
 certain composition4 ,there is no      
,harmony of ,value or of ,color in  the 
contrast1 but in repeating the contrast 
,i have the ,harmony of a  ,repetition1 
just as ,i have a ,harmony in the       
repetition of a certain  line or outline
 in which there is no order of any kind4
 ,the ,harmony  lies solely in the      
repetition or recurrence4 ,in this way  
,i may repeat1  at equal intervals all  
over a certain space1 the various       
contrasts  indicated by the following   
diagram3--    ,illustration3 ,diagram   
#af    ,there is no ,harmony in the     
relation of tones here indicated1 but we
  shall get ,harmony in the repetition  
of this relation4    ,illustration3     

,diagram #ag    ,the ,harmony here      
indicated will lie in the repetition of 
certain  contrasts in which there is no 
,harmony4    ,the ,harmony of a repeated
 contrast1 or contrasts1 is a very      
important  form of ,tone-,harmony4 ,it  
means that a certain effect of light due
 to  the juxtaposition or association of
 certain tones recurs repeatedly1  let  
us say at equal or approximately equal  
intervals1 all over a  certain space4   
,the result is sure to be harmonious1 no
 matter how  strong the tone-contrasts  
are in the group or series1 provided    
that the  repetitions are well within   
the range of vision so that they may be 
compared1 and the recurrence of the same
 effect of light appreciated4  ,we must 
not be too near to the arrangement1 for 
in that case the  contrasts of the      
repeated group will be more noticeable  
than the even  tonality of the all-over 
repetition4 ,every even1 all-over effect
 of  light1 no matter what the contrasts
 are which produce it1 gives us the     

feeling of ,harmony4    #afi4 ,in such  
compositions as the one indicated in    
,diagram #ag  predominance may be given 
to one tone by having it recur in larger
  spots in each group or in a greater   
number of spots1 two or more in  each   
group4 ,in this way1 in a composition of
 many colors in different  values1      
predominance may be given to ,middle    
,blue or ,light ,orange or  ,dark       
,blue-,violet1 or any other particular  
tone4 ,predominance may be  given to    
neutral gray of a certain value1 by     
having it recur in larger  spots or in  
numerous small spots4    #agj4 ,neutral 
gray may be made to predominate in      
another way2 by so  composing the tones1
 in the group to be repeated1 that they 
neutralize  one another at a certain    
distance1--the point of view of the     
observer4       ------------------      
,y  ,g  ,y  ,g  ,y  ,g                  
------------------      ,r  ,v  ,r  ,v  
,r  ,v      ------------------      ,y  
,g  ,y  ,g  ,y  ,g                      

------------------      ,r  ,v  ,r  ,v  
,r  ,v      ------------------          
,diagram #ah    ,in this case ,yellow   
and ,violet will neutralize one another 
and ,red will  neutralize ,green4 ,the  
effect of the repetition of these       
complementary  oppositions ought to be1 
at a certain distance1 a very lively    
neutral4    ,it has been the idea of    
certain painters of our time to subject 
every  tone-impression to analysis1 and 
to produce the effect of the tone by  an
 arrangement or composition of its      
elements4 ,many interesting and  some   
beautiful results have been produced in 
this way4    ,illustration3 ,diagram #ai
    ,in this case we have a repetition  
of the triad ,red-,yellow-,blue1 which1 
at a certain distance1 ought to produce 
the effect of a middle neutral4  ,the   
principle of these arrangements is one  
of the most important in                
tone-composition4    #aga4 ,there is    
another consideration which ought to    
keep us from any  morbid interest in    

harmonious monotonies1 which ought to   
reconcile  us to contrasts1 even strong 
contrasts1 and to a great variety in    
tones4 ,harmony is only one principle of
 composition in ,design2 we  have two   
others which are equally important1--the
 principle of ,balance  and the         
principle of ,rhythm4 ,the principles of
 ,balance and ,rhythm  are consistent   
with the greatest possible contrasts of 
tone4 ,the  tone-contrasts in forms of  
,balance and ,rhythm may be strong1 even
  harsh1 and the appreciation and       
enjoyment of the ,balance or of the     
,rhythm in no degree diminished4    ,we 
will now proceed to the consideration of
 ,tone-,balance and  ,tone-,rhythm4     
,,tone-,,balance      #agb4 ,tones1     
simply as tones1 disregarding the       
positions1 measures1 and  shapes which  
may be given to them1 balance1 when the 
contrasts which  they make with the     
ground-tone upon which they are placed  
are equal4 ,we  have an indication of   
such a balance of tones1 simply as      

tones1 in the  following formula3--     
,,ld - ,v     --------------------      
,h,lt - ,y      ,h,lt - ,y    ,two spots
 of ,high ,light ,yellow occur on a     
ground-tone of ,low ,dark  ,violet4 ,the
 two spots of ,yellow make equal        
contrasts with the  ground-tone1 and for
 that reason balance as tones1 no matter
 what  positions1 measures1 and shapes  
are given to them4 ,the value-contrast  
is that of the interval of the seventh  
in the ,scale of ,values2 the           
color-contrast is that of the interval  
of the seventh in the ,scale of         
,colors4 ,we must assume that the       
intensities are so adjusted as not to   
disturb the balance4              ,m -  
,v     -----------------     ,lt - ,o   
,d - ,o    ,in this case the values     
making the contrasts differ4 ,the       
contrasts  are1 nevertheless1 equal     
because the value-intervals are         
equivalent  intervals4 ,the value       
difference between ,light and ,middle is
 equivalent  to the value difference    

between ,dark and ,middle4 ,though the  
contrasting  elements differ1 the       
contrasts are equal4 ,in this case the  
contrasting  colors are the same and the
 color-contrasts correspond4 ,we must   
assume  that the intensities are so     
adjusted as not to disturb the balance4 
,,ld - ,v     --------------------      
,l,lt - ,o      ,l,lt - ,g    ,in this  
case the contrasting colors differ1 but 
the contrasts are  equal because the    
color-interval between ,orange and      
,violet is the  same as the             
color-interval between ,green and       
,violet4 ,in this case the              
value-contrasts correspond4 ,we must    
assume here1 as before1 that there  is  
no difference of color-intensity to     
disturb the balance4              ,d -  
,r     ------------------     ,,hd - ,o 
,,ld - ,v    ,in this case the two tones
 which balance on the ground-tone differ
 both  in value and in color4 ,they     
balance1 nevertheless1 because both the 
value and the color-contrasts are of the

 interval of the third4 ,again  we must 
assume that there is no disparity of    
intensities to disturb the  balance4    
#agc4 ,the reader will find the ,diagram
 of ,values and ,colors 7,no4  #e7 very 
useful in making calculations for       
tone-balances1 so far  as               
value-contrasts and color-contrasts are 
concerned1 leaving out  considerations  
of color-intensity4    ,taking any tone 
indicated on the ,diagram as a          
ground-tone1 any tones  at equal        
distances in balancing directions will  
balance on that  ground-tone4           
,illustration3 ,diagram #bj    ,the     
various types of tone-balance are shown 
in the above diagram4 ,the  tones which 
balance1 one against the other1 on the  
ground-tone of  ,blue-,violet1 are the  
tones marked by the same number4    ,the
 value and color-balances being         
achieved1 the intensities may be        
adjusted1 increased or diminished1 until
 the balance is perfect4    #agd4 ,as   
you increase the color-intensity in any 

tone it attracts more  attention1 and   
unless you increase the intensity in the
 opposite tones  there will be a        
disparity which will disturb your       
balance4 ,when the  intensity in any    
tone is too great1 you can increase the 
color-contrast  or the value-contrast of
 the opposite tones until the balance is
  achieved4    #age4 ,up to this point  
,i have been speaking of ,tone-,balance 
in the  abstract1 of ,tone-,balance as  
such4 ,i have spoken of ,tone-,balance  
as  something apart from ,position1     
,measure1 and ,shape-,balance1 as if    
tones could balance without having any  
positions1 measures1 or shapes  assigned
 to them4 ,the fact is that a tone does 
not exist until you give  it a position1
 a measure1 and a shape4 ,it follows    
that ,tone-,balance is1  in all cases1  
more or less complicated by             
considerations of position1  measure1   
and shape4    #agf4 ,the principle of   
balance being that equal attractions    
balance  at equal distances and unequal 

attractions at distances inversely      
proportional to them1 it follows1 that  
if the attraction of a tone  is         
increased by quantity1 the attraction of
 quantity may be balanced  against the  
attraction of contrast4 ,the calculation
 of such balances  may be made on the   
,diagram of ,values and ,colors4        
,illustration3 ,diagram #ba    ,in this 
case1 for example1 we have the          
indication of a possible balance  of two
 parts of ,light ,red and one part of   
,dark ,green on a ground-tone  of       
,middle ,violet1 the difference of      
contrast in one case making up for  a   
difference of quantity and of           
contrasting edge in the other4    #agg4 
,so far as ,tone-,balance depends upon  
positions1 measures1  and shapes1 the   
problem is the problem of ,position1    
,measure1 and  ,shape-,balance1 which we
 have already considered4    ,given     
certain tones in certain measures and   
shapes1 the inversion of  the measures  
and shapes involves an inversion of the 

tones1 so we have  a ,tone-,balance as  
well as a ,measure and ,shape-,balance4 
,the inversion in  any case may be      
single or double4    ,illustration3     
,diagram #bb    ,in this case we have an
 instance of single inversion1 which    
gives us a  ,symmetrical ,balance1 of   
tones1 as well as of measures and       
shapes4    ,illustration3 ,diagram #bc  
,in this case we have an instance of    
double inversion of tones1 as well  as  
of measures and shapes4    #agh4 ,the   
tones and tone-contrasts on one side of 
a center or axis  are not necessarily   
the same as those on the other side4 ,we
 may have  a ,tone-,balance in which    
very different tones and tone-contrasts 
are  opposed to one another4 ,this      
brings us to the consideration of       
,occult  ,balance in ,tones1 ,measures1 
and ,shapes4    ,a balance of any tones 
and of any tone-contrasts1 in any       
measures and  in any shapes1 is obtained
 when the center of tone-attractions is 
unmistakably indicated1 either by the   

symmetrical character of the  balance or
 by a symmetrical inclosure which will  
indicate the center4  ,given any        
combination of tones1 measures1 and     
shapes1 and the problem  to find the    
balance-center1 how shall we solve the  
problem8 ,it cannot  very well be done  
by reasoning4 ,it must be done by visual
 feeling4 ,the  principle of ,balance   
being clearly understood1 finding the   
center of  any tone-contrasts is a      
matter of experimental practice in which
 those  persons succeed best who are    
most sensitive to differences of tone1  
and  who make the greatest effort to    
feel the centers and to indicate them   
accurately4 ,experience and practice are
 necessary in all cases4                
,illustration3 ,fig4 #bbh    ,here1     
within this circle1 are the attractions 
to be balanced4 ,the  problem is to find
 the balance-center1 and to indicate    
that center  by a symmetrical inclosure 
which will bring the tones1 measures1   
and  shapes into a ,balance4 ,the center

 is here indicated by the circle4       
,whether it is correctly indicated is a 
matter of judgment in which  there may  
be a difference of opinion4 ,there is a 
center somewhere upon  which the        
attractions are balancing4 ,the question
 is1 where is it8 ,the  illustration    
which ,i have given is in the terms of  
the ,scale of ,neutral  ,values4        
,differences of color and               
color-intensity would complicate the    
problem1 but would not in any way affect
 the principle involved4 ,i  know of no 
more interesting problem or exercise    
than this3 to achieve  ,tone-,balance   
where there is no ,tone-,symmetry4      
#agi4 ,it will sometimes happen1 that a 
gradation of tones or measures  will    
draw the eye in a certain direction1    
toward the greater contrast1  while a   
larger mass or measure of tone1 on the  
other side1 will be  holding it back4   
,in such a case we may have a mass      
balancing a motion4    ,illustration3   
,fig4 #bbi    ,in this case the eye is  

drawn along1 by a gradation of values1  
to the  right1 toward the edge of       
greater contrast1 away from a large dark
  mass of tone in which there is no     
movement4 ,the tendency of the dark     
mass is to hold the eye at its center4  
,the problem is to find the             
balance-center between the motion and   
the mass4 ,i have done this1 and  the   
balance-center is indicated by the      
symmetrical outline of the  diagram4    
#ahj4 ,some shapes hold the eye with    
peculiar force1 and in such cases  the  
attractions of tone or measure or shape 
on the other side have  to be increased 
if we are to have a balance4            
,symmetrical shapes have  a tendency to 
hold the eye at centers and on axes4    
,given certain  attractions on the other
 side1 we must be sure that they are    
sufficient  to balance the force of the 
symmetry in addition to the force of its
  tone-contrasts1 whatever they are4    
,illustration3 ,fig4 #bcj    ,in this   
case we have an approximate balance in  

which the force of a  symmetry1 with    
contrasting edges1 on one side1 is      
balanced by contrasts  and certain      
movements on the other4 ,if ,i should   
turn down the upper  spot on the right1 
we would feel a loss of balance due to  
the turning  of two movements1 which    
combine to make one movement to the     
right1 into  two movements down to the  
right4 ,if ,i should increase the force 
of the  symmetry1 by filling in the     
center with black1 it would be necessary
  either to move the symmetry nearer to 
the center or to move the  opposite     
attractions away from it4 ,an unstable  
attitude in the symmetry  would have to 
be counteracted1 in some way1 on the    
other side4    ,intricate shapes from   
which the eye cannot easily or quickly  
escape  often hold the eye with a force 
which must be added to that of their    
tone-contrasts4    ,illustration3 ,fig4 
#bca    ,in this case the shape on the  
right requires a pretty strong dark spot
  to balance its contrasts and its      

intricacy4    ,the problem is further   
complicated when there are1 also1       
inclinations1  to the right or to the   
left1 to be balanced4    ,illustration3 
,fig4 #bcb    ,in this case ,i have     
tried to balance1 on the center of a    
symmetrical  inclosure1 various         
extensions and inclinations of          
tone-contrast1 the  movement of a       
convergence1 and the force of a somewhat
 intricate and  unstable symmetry4      
,these occult forms of ,balance are not 
yet well understood1 and ,i feel        
considerable hesitation in speaking of  
them4 ,we have certainly a great  deal  
to learn about them4 ,they are far      
better understood by the ,chinese  and  
by the ,japanese than by us4    #aha4   
,when any line or spot has a meaning1   
when there is any symbolism  or         
representation in it1 it may gain an    
indefinite force of attraction4  ,this1 
however1 is a force of attraction for   
the mind rather than  for the eye4 ,it  
affects different persons in different  

measures4  ,the consideration of such   
attractions1 suggestions1 meanings1 or  
significations does not belong to ,pure 
,design but to ,symbolism or to         
,representation4                        
,,tone-,,rhythm      #ahb4 ,the idea of 
,tone-,rhythm is expressed in every     
regular and perfect  gradation of       
,tones2 of values1 of colors or of      
color-intensities1  provided the eye is 
drawn through the gradation in one      
direction or  in a series or sequence of
 directions4 ,this happens when there is
 a  greater tone-contrast at one end of 
the gradation than at the other4  ,when 
the terminal contrasts are equal there  
is no reason why the  eye should move   
through the gradation in any particular 
direction4  ,according to our definition
 of ,rhythm1 the gradation should be    
marked in its stages or measures1 and   
the stages or measures should  be       
regular4 ,that is certainly true1 but in
 all regular and perfect  gradations ,i 
feel that corresponding changes are     

taking place in  corresponding measures1
 and ,i get the same feeling from such a
  gradation that ,i get from it when it 
is marked off in equal sections4        
,though the measures in regular and     
perfect gradations are not marked1  they
 are1 it seems to me1 felt4 ,they seem  
sufficiently marked by  the regularity  
and perfection of the gradation1 any    
irregularity  or imperfection being     
appreciable as a break in the measure4  
,i am  inclined1 therefore1 to say of   
any regular and perfect gradation that  
it is rhythmical provided the direction 
of movement is unmistakable4  ,the      
direction1 as ,i have said1 depends upon
 the relation of terminal  contrasts4   
,the eye is drawn toward the greater    
contrast1 whatever that  is and wherever
 it is4 ,a few examples will make this  
clear4                       ,m         
-----------------------------------     
,blk  ,,ld  ,d  ,,hd  ,m  ,l,lt  ,lt    
,h,lt  ,wt    ,in this case we have the 
gradation of the ,scale of ,values set  

on a  ground-tone of the middle value4  
,here there are two opposed gradations  
with equal contrasts at the opposite    
ends4 ,the result is ,balance1 not      
,rhythm4                       ,wt      
-----------------------------------     
,blk  ,,ld  ,d  ,,hd  ,m  ,l,lt  ,lt    
,h,lt  ,wt    ,in this case we have a   
gradation of values beginning with      
,white on  ,white1 no contrast at all1  
and reaching ultimately the contrast of 
,black and ,white4 ,the eye is drawn    
through the tones of this gradation  in 
the direction of this contrast1 that is 
to say1 from right to left4  ,it is a   
clear case of ,rhythm4 ,if1 instead of  
white1 we had black1 as  a ground-tone1 
the movement of the rhythm would be in  
the opposite  direction1--from left to  
right4       ,wt  ,h,lt  ,lt  ,l,lt  ,m 
,,hd   ,d   ,,ld  ,blk                  
-------------------------------------   
,blk  ,,ld  ,d   ,,hd   ,m  ,l,lt  ,lt  
,h,lt  ,wt    ,in this case1 as in the  
first1 we have equally great contrasts  

at the  ends and no contrast at the     
middle4 ,the result is ,balance1 not    
,rhythm4                ,v              
-------------------     ,y  ,,yg  ,g    
,,gb  ,b  ,,bv    ,in this case1        
disregarding possible differences of    
value and  color-intensities1 there will
 be a color-rhythm proceeding from      
right to left4 ,the contrast to which   
the eye will be drawn is the            
color-contrast of ,yellow and ,violet4  
,,ld-,v                                 
-------------------------------------   
,d-,y  ,,hd-,,yg  ,m-,g  ,l,lt-,,gb     
,lt-,b  ,h,lt-,,bv    ,in this case1    
disregarding possible differences of    
intensity1 there  will be a rhythm of   
color moving from right to left and a   
rhythm  of values moving from left to   
right4 ,assuming that we are equally    
attracted by corresponding value and    
color-contrasts1 these two  rhythms1    
when produced1 will neutralize one      
another and we shall  have an           
illustration of ,tone-,balance rather   

than ,tone-,rhythm4 ,if  corresponding  
color and value-contrasts are not       
equally attractive we  shall have an    
unequal tug-of-war between the two      
rhythms4                        ,,ld-,v 
-------------------------------------   
,h,lt-,y  ,lt-,,yg  ,l,lt-,g  ,m-,,gb   
,,hd-,b  ,d-,,bv    ,in this case we    
have two rhythms1 one of values and one 
of colors1 in a  ,harmony of ,direction4
 ,the direction of movement will be from
 right to  left4                        
,h,lt-,y                                
----------------------------------------
---------------     ,h,lt-,y  ,h,lt-,y  
,h,lt-,y_/  ,h,lt-,y  ,h,lt-,y_/        
,h,lt-,y    ,in this case we have no    
change of color and no change of value1 
but a  rhythm of the intensities of one 
color1 in one value4 ,the movement will 
be from right to left4 ,the ground-tone 
might be ,neutral ,high ,light1 the     
zero-intensity of ,yellow4 ,that would  
not change the direction of the         
movement4                               

,,ld-,y                                 
----------------------------------------
---------     ,h,lt-,y  ,lt-,y          
,l,lt-,y_/  ,m-,y  ,,hd-,y_/  ,d-,y     
,in this case ,i have indicated a       
combined movement of values and         
color-intensities4 ,the direction of the
 movement will be from right to  left4  
,the tone-rhythms which ,i have         
described are based upon the repetition 
at regular intervals of a certain change
 of value1 of color or of               
color-intensity4 ,we have ,harmony1 of  
course1 in the repetition of equal      
changes1 though the changes are not the 
same changes4 ,the change of  value from
 ,middle to ,low ,light is equal to the 
change from ,low ,light to  ,light1     
though these changes are not the same   
changes4 ,the ,harmony is1  therefore1  
the ,harmony of equivalent contrasts    
which are not the same  contrasts4      
#ahc4 ,we have more or less movement in 
every composition of tones  which is    
unbalanced1 in which the eye is not held

 between equivalent  attractions1 either
 upon a vertical axis or upon a center4 
,in all such  cases1 of tones           
unbalanced1 the movement is in the      
direction of the  greatest contrast4    
,unless the movement is regular and     
marked in its  measures1 as ,i think it 
is in all regular and perfect           
gradations1 the  movement is not        
rhythmical4 ,we get ,rhythm1 however1 in
 the repetition  of the movement1       
whatever it is1 in equal or lawfully    
varying measures1  provided the         
direction of the movement remains the   
same or changes  regularly or gradually4
 ,if the line of the movement is        
up-to-the-right  forty-five degrees we  
have rhythm in the repetition of the    
movement at  equal or lawfully varying  
intervals1 without changes of direction2
 but  we should have ,rhythm1 also1 if  
the direction of the movement1 in its   
repetitions1 were changed1 regularly or 
gradually2 if1 for example1  the        
direction were changed first from       

up-right forty-five degrees to  up-right
 forty degrees1 then to up-right        
thirty-five degrees1 then  to up-right  
thirty degrees1 this at equal or at     
lawfully varying  intervals4 ,in this   
way the movement of the composition     
repeated may  be carried on and         
gradually developed in the movement of  
the series4  ,a reference to ,fig4 #afa1
 p4 #id1 and to ,fig4 #aai1 p4 #fh1 will
 help the  reader to understand these   
statements4    #ahd4 ,when any          
unbalanced composition of tones is      
singly inverted upon  a vertical axis   
and the movement of the composition     
follows the axis1  either up or down1   
and this movement1 up or down1 is       
repeated1 up or  down1 we get forms of  
,tone-,rhythm which are also forms of   
,symmetrical  ,balance4 ,in the         
inversions and repetitions of the       
tone-composition  we have               
,tone-,harmony4 ,as the tones in the    
repeated composition have  certain      
positions1 measures1 and shapes1 the    

,harmony1 the ,balance1 and  the ,rhythm
 are of ,positions1 ,measures1 and      
,shapes as well as of ,tones2  so we get
 the combination of all the terms of    
,design in all the three  modes of      
,design4          ,,composition         
,,three ,,general ,,rules      #ahe4 ,it
 is quite impossible for me1 in this    
discussion of terms  and principles1 to 
indicate1 in any measure1 the           
possibilities of  composition1 in lines 
and spots of paint1 in tones1 measures1 
and  shapes4 ,this is in no sense a     
,book of ,designs4 ,all ,i have         
undertaken to  do is to give a few very 
simple examples and to indicate the kind
 of  reasoning to be followed1          
recommending the same kind of reasoning 
in  all cases4 ,there are three general 
rules1 however1 which ,i must state4    
,first4 ,given a certain outline and    
certain tones1 measures1 and shapes  to 
be put into it1 it is the ,problem of   
,pure ,design to do the best we  can1   
getting as many connections making unity

 as possible4 ,the process  is one of   
experimenting1 observing1 comparing1    
judging1 arranging and  rearranging1    
taking no end of time and pains to      
achieve ,order1 the  utmost possible    
,order1 if possible the ,beautiful4     
,second4 ,when only an outline is given 
and we can put into it lines and  spots 
of paint1--tones1 measures1 and         
shapes1--ad libitum1 we must be  sure   
that in the addition and multiplication 
of features we do not get  less ,order  
than we had in the simple outline with  
which we started1  when it had nothing  
in it4 ,as we proceed to add features we
 must be  sure that we are not          
diminishing the order of the composition
 as a  whole4 ,if the composition as a  
whole is orderly1 we do not want to make
  it less so by cutting it up and       
introducing additional attractions      
which may be disorderly and confusing4  
,it may be harder to achieve  ,order    
with a greater number and variety of    
terms4 ,we may deserve credit  for      

overcoming this difficulty1 but it is a 
difficulty which confronts  us only when
 the terms are given and we have to make
 the best of them4  ,when no terms are  
given1 only a perfectly orderly outline1
 we should  hesitate before we put      
anything into it4 ,if we add anything we
 must be  sure that it does not         
diminish1 in the slightest degree1 the  
order we  had before1 when we had       
nothing but the outline4 ,the order of  
the whole  must never be diminished4    
,third4 ,when we have an outline with   
certain tones1 measures1 and shapes  in 
it1 the question is3 whether we can     
increase the order by adding  other     
tones1 other measures1 or other shapes4 
,illustration3 ,fig4 #bcc               
,arrangement 8a0 is less orderly than   
arrangement 8b10 so ,i have acted       
wisely in adding the other outlines4    
,illustration3 ,fig4 #bcd    ,in this   
case1 however1 ,i have added features   
without achieving any  increase of      
,order in the composition4 ,the order is

 less than it was  before4 ,the         
additions have no interest from the     
point of view of ,pure  ,design4 ,i may 
add features for the sake of variety or 
novelty1 to  give a change of feeling1 a
 new sensation1 but such motives are not
  the motives of ,pure ,design4 ,in     
,pure ,design our motive is1 always1 to 
achieve ,order1 in the hope that in so  
doing we may achieve a supreme  instance
 of it which will be beautiful4         
,illustration3 ,fig4 #bce    ,consider  
these illustrations4 ,arrangement 8b0 is
 more orderly than  arrangement 8a10 so 
,i am justified in making the additions4
 ,the  additions have brought occult    
balance into the composition with       
,direction and ,interval-,harmony4      
,arrangement 8c0 is less orderly than   
8b10 less orderly than 8a40 ,it has1    
therefore1 no value for us4 ,there  is  
no merit in the multiplication of       
features which it exhibits4  ,the       
surface is 8enriched0 at the expense of 
,direction-,harmony1                    

,interval-,harmony1 and ,shape-,harmony4
 ,there may be an approximation  to an  
occult balance in arrangement 8c10 but  
you cannot feel it  unmistakably as you 
do in 8b40 ,its value is1 therefore1    
less4    #ahf4 ,i object to the word    
8decoration10 as commonly used by       
designers1  because it implies that     
additions are likely to be improvements1
 that  to multiply features1 to enrich  
surfaces1 is worth while or desirable4  
,the fact is1 that additions are1 as a  
rule1 to be avoided4 ,there is no  merit
 in the mere multiplication of features4
 ,it is a mistake4 ,the rule  of ,pure  
,design1 and it is the rule for all     
,design1 is simplification  rather than 
complication4 ,as designers we ought to 
avoid additions1 if  possible4    ,we   
ought to make them only when in so doing
 we are able to increase the  order of  
the whole4 ,we make additions1 indeed1  
to achieve the greater  simplicity of   
,order1 and for no other reason4 ,our   
object in all cases  is to achieve      

,order1 if possible a supreme instance  
of ,order which will  be beautiful4 ,we 
aim at ,order and hope for ,beauty4     
,,the ,,study ,,of ,,order ,,in ,,nature
 ,,and ,,in ,,works ,,of ,,art          
#ahg4 ,in connection with the practice  
of ,pure ,design1 as ,i have  described 
it1--the composition and arrangement of 
lines and spots of  paint2 of tones1    
measures1 and shapes3 this in the modes 
of ,harmony1  ,balance1 and ,rhythm1 for
 the sake of ,order and in the hope of  
,beauty1--the student should take up the
 study of ,order in its three  modes1 as
 revealed in ,nature and achieved in    
,works of ,art4    #ahh4 ,the method of 
study should be a combination of        
analysis with  synthetic reproduction4  
,taking any instance of ,order1 whether 
in  ,nature or in some work of ,art1 the
 first thing to do is to consider  its  
terms1--its positions1 its lines1 its   
areas1 its measure and  space-relations1
 its tones and tone-relations1--bringing
 every element  to separate and exact   

definition4 ,the next thing to do is to 
note  every occurrence of ,harmony1 of  
,balance1 of ,rhythm1--every connection 
making for consistency1 unity1 ,order4  
,in that way we shall get an exact      
knowledge of the case4 ,we shall know   
all the facts1 so far as the  terms and 
the principles of ,design are concerned4
 ,that is what ,i mean  by analysis4 ,by
 a synthetic reproduction ,i mean a     
reproduction of the  effect or design1  
whatever it is1 following the images    
which we have  in mind as the result of 
our analysis4 ,the reproduction should  
be made  without reference to the effect
 or design which has been analyzed4     
,there should be no direct imitation1 no
 copying4 ,we must not depend  so much  
upon the memory as upon the imagination4
 ,having reproduced  the effect or      
design in this way1 following the       
suggestions of the  imagination1 the    
reproduction should be brought into     
comparison with  the effect or design   
reproduced and the differences noted4   

,differences  should be carefully       
observed and the previous analysis      
should be  reviewed and reconsidered4   
,when this is done another attempt at   
reproduction should be made4 ,this      
process should be repeated until the    
effect or design is thoroughly          
understood and imaginatively grasped4   
,the evidence of understanding and      
comprehension will be seen in the       
reproduction which is made1 which ought 
to have an essential but not  a literal 
correspondence with the original4       
,analysis should precede2  synthesis    
should follow4    ,i hope1 in another   
book or books1 to be published later1 to
 give some  examples of ,order in       
natural objects or effects1 also        
examples of  ,order in ,works of ,art1  
with a careful analysis of each one1    
showing  how the points1 lines1 and     
areas1 the measure and the              
space-relations1  the tones and         
tone-relations come together in the     
forms of ,harmony1  ,balance1 and       

,rhythm1 in the modes of ,order1 in     
instances of ,beauty4  ,in the mean     
time1 as the methods of analytic study  
and of synthetic  practice are clearly  
indicated in the preceding pages1 the   
student who  has taken pains to         
understand what he has read will find   
himself well  prepared for the work4 ,he
 can take up the study of ,order in     
,nature and  of ,design in ,works of    
,art without further assistance4        
,,conclusion      #ahi4 ,it does not    
follow1 even when our minds1 in         
consequence of the  study and the       
practice which ,i have described1 are   
richly stored with  the terms and the   
motives of ,design1 that we shall       
produce anything  important or          
remarkable4 ,important work comes only  
from important  people4 ,what we        
accomplish1 at best1 is merely the      
measure and  expression of our own      
personalities4 ,nevertheless1 though we 
may not  be able to produce anything    
important1 it is something to appreciate

  and enjoy what is achieved by others4 
,if our studies and our work bring  us  
to the point of visual discrimination1  
to sthetic appreciation  and enjoyment1 
and no farther1 we are distinguished    
among men4 ,the  rarest thing in the    
world is creative genius1 the faculty   
which creates  great works4 ,next to    
that comes the faculty of appreciation4 
,that1  too1 is rare4 ,we must not      
believe that appreciation is easy4 ,it  
is  true that the recognition of ,order 
is instinctive and spontaneous1 but     
untrained people recognize it only in a 
few simple and obvious forms4  ,order in
 its higher forms--the order of a great 
number and variety  of terms and of     
different principles in                 
combination--lies altogether  beyond the
 appreciation of untrained people4 ,it  
is only as we are  trained1 exercised1  
and practiced in the use of terms and in
 following  principles that we rise to  
the appreciation of great achievements4 
,the  sense of order1 which we all have1

 in a measure1 needs to be exercised    
and developed4 ,the spontaneity of      
undeveloped faculty does not count  for 
much4 ,it carries us only a little way4 
,let no one believe that  without study 
and practice in ,design he can recognize
 and appreciate  what is best in        
,design4    ,appreciation and enjoyment 
are the rewards of hard thinking with   
hard work4 ,in order to appreciate the  
masterpiece we must have some  knowledge
 of the terms which the artist has used 
and the principles  which he has        
followed4 ,we know the terms only when  
we have ourselves  used them1 and the   
principles when we have tried to follow 
them4 ,the  reason why the appreciation 
of excellence in speech and in writing  
is so widespread is due to the fact that
 we all speak and write1  constantly1   
and try1 so many of us1 to speak and    
write well4 ,the reason  why there is so
 little appreciation of excellence in   
other forms of  art is due to the fact  
that the terms are not in general use   

and the  principles are not understood1 
as they should be1 in the light of      
personal experience and effort4 ,it is  
for this reason that ,i am anxious  to  
see the teaching and practice of ,design
 introduced into the schools1  public   
and private1 everywhere1 and into our   
colleges as well as our  schools4 ,i    
have no idea that many able designers   
will be produced1  but what ,i expect1  
as a result of this teaching1 is a more 
general  understanding of ,design1 more 
interest in it1 and more appreciation   
and  enjoyment of its achievements4     
,among the many who will appreciate and 
enjoy will be found the few who will    
create and produce4    ,the purpose of  
what is called art-teaching should be   
the production1  not of objects1 but of 
faculties1--the faculties which being   
exercised  will produce objects of ,art1
 naturally1 inevitably4 ,instead of     
trying  to teach people to produce ,art1
 which is absurd and impossible1 we     
must give them a training which will    

induce visual sensitiveness with        
sthetic discrimination1 an interest in  
the tones1 measures1 and  shapes of     
things1 the perception and appreciation 
of ,order1 the sense  of ,beauty4 ,in   
these faculties we have the causes of   
,art4 ,inducing  the causes1 ,art will  
follow as a matter of course4 ,in       
exercising and  developing the faculties
 which ,i have named1 which naturally   
and  inevitably produce ,art1 we are    
doing all that can be done by teaching4 
,there is no better training for the    
visual and sthetic faculties  than is   
found in the practice of ,pure ,design1 
inducing1 as it does1  discrimination in
 tones1 measures1 and shapes1 and the   
appreciation  of what is orderly and    
beautiful4 ,the result of the practice  
will be  a wide spread of visual and    
sthetic faculty which will have1 as its 
natural and inevitable result1 the      
appreciation and the production of      
,works of ,art4    ,our object1 then1 in
 the study and practice of ,pure ,design

 is1 not so  much the production of     
,works of ,art1 as it is to induce in   
ourselves  the art-loving and           
art-producing faculties4 ,with these    
faculties we  shall be able to discover 
,order and ,beauty everywhere1 and life 
will  be happier and better worth       
living1 whether we produce ,works of    
,art1  ourselves1 or not4 ,we shall have
 an impulse which will lead us to       
produce ,works of ,art if we can4 ,at   
the same time we shall have the         
judgment which will tell us whether what
 we have done is or is not  beautiful4  
,,paragraph ,,index           #a1 p4    
#a4 ,the ,meaning of ,design4       #b1 
p4   #a4 ,the ,order of ,harmony4       
#c1 p4   #a4 ,the ,order of ,balance4   
#d1 p4   #b4 ,the ,order of ,rhythm4    
#e1 p4   #b4 ,relations of ,harmony1    
,balance1 and ,rhythm4       #f1 p4     
#d4 ,beauty a supreme instance of       
,order4       #g1 p4   #d4 ,the ,arts as
 different modes of ,expression4        
#h1 p4   #e4 ,drawing and ,painting4    

#i1 p4   #e4 ,two modes of ,drawing and 
,painting4      #aj1 p4   #e4 ,pure     
,design4      #aa1 p4   #f4 ,applied    
,design4      #ab1 p4   #g4             
,representation4      #ac1 p4   #g4     
,representation in ,forms of ,design4   
#ad1 p4   #i4 ,the ,definition of       
,positions4      #ae1 p4   #i4 ,the     
,relation of ,directions and ,distances4
      #af1 p4  #aj4 ,directions defined4
      #ag1 p4  #aa4 ,distances defined4 
#ah1 p4  #aa4 ,positions determined by  
,triangulations4      #ai1 p4  #aa4     
,intervals4      #bj1 p4  #ab4 ,scale in
 ,relations of ,position4      #ba1 p4  
#ab4 ,harmony of ,positions4      #bb1  
p4  #ab4 ,harmony of ,directions4       
#bc1 p4  #ac4 ,harmony of ,distances4   
#bd1 p4  #ad4 ,harmony of ,intervals4   
#be1 p4  #af4 ,intervals in any series  
of ,positions4      #bf1 p4  #ag4       
,positions and their possibilities4     
#bg1 p4  #ag4 ,balance of opposite      
,directions4      #bh1 p4  #ag4 ,balance
 of ,distances in opposite ,directions4 

#bi1 p4  #ah4 ,balance of ,directions   
not opposite4      #cj1 p4  #ah4        
,balance of ,distances in ,directions   
not opposite4      #ca1 p4  #ai4        
,positions in ,balance4      #cb1 p4    
#ai4 ,stable equilibrium of vertical and
 horizontal                  directions4
      #cc1 p4  #bj4 ,symmetry defined4  
#cd1 p4  #ba4 ,the central axis should  
predominate in symmetrical              
,balances4      #ce1 p4  #bb4 ,balance  
in ,relations of ,position1 when        
inverted4      #cf1 p4  #bb4 ,finding   
the center of equilibrium in unbalanced 
relations of position4 ,indication of   
centers by                  symmetrical 
inclosures4      #cg1 p4  #bd4 ,tendency
 of symmetrical inclosures1 when        
sufficiently                            
attractive1 to prevent movement4        
#ch1 p4  #be4 ,how unstable equilibrium 
suggests movement4      #ci1 p4  #bf4   
,rhythmic movement in a gradual increase
 in the number of                       
attractions through a series of visual  

angles4      #dj1 p4  #bg4 ,the         
possibilities of rhythmic movement in   
relations of                  position4 
#da1 p4  #bg4 ,balanced attractions at  
equal intervals give no                 
movement1 consequently no ,rhythm4      
#db1 p4  #bh4 ,the gradual increase of  
attractions in a series of              
visual angles1 as produced by gradual   
changes of scale1                       
causes rhythmic movement4      #dc1 p4  
#bh4 ,how unbalanced groups of positions
 being repeated at                      
equal intervals produce rhythmic        
movement4      #dd1 p4  #bi4 ,rhythmic  
movements produced by the repetition of 
unbalanced relations of position and by 
a gradual                  diminution of
 scale4      #de1 p4  #cj4 ,rhythmic    
movements produced by the repetition of 
a                  balanced relation of 
positions with a gradual diminution     
of intervals1 causing a gradual increase
 of attractions                  through
 a series of visual angles4      #df1 p4

  #cj4 ,rhythmic movements produced by  
the repetition of a                     
balanced relation of positions with     
diminution of                  intervals
 and of scale4      #dg1 p4  #ca4       
,rhythmic movements produced by the     
repetition of an                        
unbalanced relation of positions with a 
crowding due                  to gradual
 diminution of intervals4      #dh1 p4  
#ca4 ,rhythmic movements produced by the
 repetition of an                       
unbalanced relation of positions with a 
diminution of                  measure  
in the intervals and of scale in the    
groups4                  ,the           
combination of two or more rhythms4     
#di1 p4  #cb4 ,the combination of two or
 more rhythms4      #ej1 p4  #cb4       
,relations of position in different     
attitudes4      #ea1 p4  #cc4 ,principal
 ,attitudes4      #eb1 p4  #cd4 ,harmony
 in ,attitudes4      #ec1 p4  #ce4      
,harmony in the repetition of any       
relation of attitudes4      #ed1 p4     

#ce4 ,balance in ,attitudes4      #ee1  
p4  #cf4 ,rhythm in ,attitudes4         
#ef1 p4  #cg4 ,the ,line4      #eg1 p4  
#cg4 ,changes of ,direction in a line4  
,angles4      #eh1 p4  #ch4 ,gradual    
changes of ,direction in a line4        
,curves4      #ei1 p4  #da4 ,curves     
regarded as compositions of circular    
arcs4      #fj1 p4  #db4 ,differences of
 scale in lines4      #fa1 p4  #db4     
,differences of attractive force in     
lines4      #fb1 p4  #dd4 ,harmony of   
,direction in lines4      #fc1 p4  #dd4 
,harmony of ,angles in lines4      #fd1 
p4  #de4 ,harmony in ,legs of ,angles4  
#fe1 p4  #de4 ,harmony in ,curvatures4  
#ff1 p4  #df4 ,harmony in ,arcs when    
they have the same radius4      #fg1 p4 
#df4 ,harmony in ,arcs when they have   
the same angle4      #fh1 p4  #dg4      
,linear ,progressions4      #fi1 p4     
#dg4 ,variations of scale in ,linear    
,progressions4      #gj1 p4  #dh4       
,changes of ,direction in ,linear       
,progressions4      #ga1 p4  #di4       

,inversions in ,linear ,progressions4   
#gb1 p4  #ej4 ,balance in a ,line4      
#gc1 p4  #ea4 ,appreciation of ,balance 
in a line depends very much on          
its attitude4      #gd1 p4  #eb4        
,balance of ,inclinations in a line4    
#ge1 p4  #ed4 ,finding the center of    
equilibrium of a line and               
indicating that center by a symmetrical 
inclosure4      #gf1 p4  #ef4 ,rhythm in
 a ,line4      #gg1 p4  #ef4 ,rhythm    
requires more than movement4 ,the       
movement must be                  in    
regular and marked measures4      #gh1  
p4  #eg4 ,the number of repetitions     
required in a ,rhythm4      #gi1 p4     
#eg4 ,contrary movements in ,rhythms4   
#hj1 p4  #eh4 ,regular alternations in  
space not necessarily                   
rhythmical4 ,that depends upon the      
character of the                        
motive4      #ha1 p4  #ei4 ,repetition  
and alternation without ,rhythm4        
#hb1 p4  #ei4 ,rhythm due to gradation  
of scale4      #hc1 p4  #fj4 ,rhythm due

 to the gradual increase in the number  
of                  attractions from    
measure to measure4      #hd1 p4  #fa4  
,rhythm in ,spiral ,concentrations4     
#he1 p4  #fc4 ,direct and ,contrary     
,motion in ,spiral lines4      #hf1 p4  
#fd4 ,the ,balance of corresponding but 
opposed ,rhythms4      #hg1 p4  #fd4    
,lines in different ,attitudes4         
#hh1 p4  #fe4 ,harmony in ,attitudes of 
lines4      #hi1 p4  #ff4 ,harmony in   
the repetition of any relation of       
attitudes4      #ij1 p4  #ff4 ,balance  
in ,attitudes of ,lines4      #ia1 p4   
#fg4 ,rhythm in ,attitudes of ,lines4   
#ib1 p4  #fh4 ,recapitulation4      #ic1
 p4  #fh4 ,the ,composition of ,lines4  
#id1 p4  #fi4 ,harmony in the           
,composition of ,lines4      #ie1 p4    
#gj4 ,measure-,harmony of ratios and of 
proportions4      #if1 p4  #gj4         
,elements making for ,harmony in        
dissimilar lines4      #ig1 p4  #gc4    
,balance in the ,composition of ,lines4 
#ih1 p4  #gd4 ,shape-,harmony without   

,measure-,harmony4      #ii1 p4  #gd4   
,measure-,balance without               
,shape-,balance4     #ajj1 p4  #gf4 ,the
 centers of equilibrium in mere         
measure-balances                  should
 be indicated by symmetrical inclosures4
     #aja1 p4  #gf4 ,balance of         
,inclinations4     #ajb1 p4  #gi4       
,measure-,rhythm in the ,composition of 
,lines4     #ajc1 p4  #hj4 ,the         
combination of various types of rhythmic
 movement4     #ajd1 p4  #hf4 ,rhythm   
not necessarily inconsistent with       
,balance4     #aje1 p4  #hi4 ,the       
,composition of various lines4     #ajf1
 p4  #if4 ,outlines4     #ajg1 p4  #if4 
,harmony1 ,balance1 and ,rhythm in      
,outlines4     #ajh1 p4 #ajb4 ,interior 
,dimensions of an ,outline4     #aji1 p4
 #ajb4 ,harmony of ,interior            
,dimensions4     #aaj1 p4 #ajd4         
,convergence as a cause of movement4    
#aaa1 p4 #ajh4 ,rhythm of ,convergence4 
,contrary ,motion in ,convergences4     
#aab1 p4 #aji4 ,changes of ,direction in

 ,convergences4     #aac1 p4 #aaj4      
,ideas of association in rhythmic       
movements4 ,rhythm in                   
changes of shape4     #aad1 p4 #aab4    
,outlines in different ,attitudes4      
#aae1 p4 #aab4 ,harmony1 ,balance1 and  
,rhythm in the ,attitudes of            
,outlines4     #aaf1 p4 #aab4 ,the      
,composition of ,outlines4     #aag1 p4 
#abd4 ,the purpose of designing to      
induce the sense of ,beauty             
which is the cause of all that is fine  
in ,design4     #aah1 p4 #abe4 ,areas4  
#aai1 p4 #abe4 ,linear ,areas4     #abj1
 p4 #abe4 ,changes of width-measure in  
,linear ,progressions4     #aba1 p4     
#abi4 ,areas defined by outlines1 and   
also by tone-contrasts4     #abb1 p4    
#aca4 ,the ,composition of ,areas as    
defined by tone-contrasts4     #abc1 p4 
#aca4 ,difference between drawing and   
painting1 if there                  is  
any4     #abd1 p4 #aca4 ,definition of  
the word ,tone4     #abe1 p4 #acb4      
,tone-,analysis4     #abf1 p4 #acb4 ,the

 study of ,tones and ,tone-,relations4  
#abg1 p4 #acc4 ,pigment-,materials4     
#abh1 p4 #acc4 ,the ,scale of ,neutral  
,values4     #abi1 p4 #acd4 ,contrasts  
of the ,scale of ,values4     #acj1 p4  
#ace4 ,definition of ,value-,relations4 
#aca1 p4 #acf4 ,scales of ,colors in    
,different ,values4     #acb1 p4 #acg4  
,definition of the terms used to        
describe different                      
,colors4     #acc1 p4 #ach4             
,color-,intensities found in different  
values4     #acd1 p4 #aci4              
,value-,relation of different ,colors   
shown in the                  ,spectrum4
     #ace1 p4 #aci4 ,the ,spectrum a    
sequence not a circuit2 a circuit in    
pigments only4     #acf1 p4 #adj4 ,the  
,complementaries4     #acg1 p4 #adj4 ,a 
,general ,classification of ,tones as to
 ,value1 ,color1                        
,color-,intensity1 and                  
,color-,neutralization4     #ach1 p4    
#ada4 ,the distinction between          
,color-,intensities and                 

,color-,neutralizations4     #aci1 p4   
#ada4 ,definition of particular tones4  
#adj1 p4 #ada4 ,theoretical character of
 our classification of tones4     #ada1 
p4 #adb4 ,definition of particular      
tone-relations4     #adb1 p4 #adc4      
,sequences of ,values and ,colors4      
#adc1 p4 #adc4 ,the ,sequence of        
,neutral ,values4     #add1 p4 #add4    
,vertical ,sequences4     #ade1 p4 #add4
 ,horizontal ,sequences4     #adf1 p4   
#add4 ,diagonal ,sequences4     #adg1 p4
 #ade4 ,diagonal ,sequences of the      
,right and ,left ,modes4     #adh1 p4   
#adf4 ,different ,intervals in ,diagonal
 ,sequences4     #adi1 p4 #adf4         
,peculiar value of the ,diagonal        
,sequence of ,colors at the             
interval of the ,fifth4 ,the four       
,triads4     #aej1 p4 #adg4 ,sequences  
in which a certain relation of intervals
 is                  repeated4     #aea1
 p4 #adg4 ,the combination of two or    
more ,vertical ,sequences4     #aeb1 p4 
#adh4 ,the combination of two or more   

,horizontal ,sequences4     #aec1 p4    
#adi4 ,the ,combination of ,diagonal    
,sequences of the same and              
different modes4     #aed1 p4 #aea4     
,alternations in ,vertical ,sequences4  
#aee1 p4 #aea4 ,alternations in         
,horizontal ,sequences4     #aef1 p4    
#aea4 ,alternations of different        
value-intervals in                      
color-sequences of equal intervals4     
#aeg1 p4 #aec4 ,alternations of         
different color-intervals in            
value-sequences of equal intervals4     
,particular                  ,sequences 
recommended4     #aeh1 p4 #aec4         
,possibility of extending the           
classification of values                
and colors to a scale of seventeen      
values1 including                       
,black and ,white4     #aei1 p4 #aed4   
,the method of using the ,sequences     
described4 ,possible                    
extension of the sequence by mixtures4  
#afj1 p4 #afe4 ,the value of the        
sequences found in the more definite    

thinking which they make possible1 and  
in the ,harmony of                      
repetitions4     #afa1 p4 #aef4         
,considerations of position1 measure1   
and shape in                            
tone-relations4     #afb1 p4 #aeh4      
,tone-,harmony4     #afc1 p4 #aeh4      
,tones harmonized on the palette or by  
changes in the                  design4 
#afd1 p4 #aei4 ,value-,harmony4         
#afe1 p4 #afa4 ,color-,harmony4         
#aff1 p4 #afc4 ,harmony of proportional 
neutralizations4     #afg1 p4 #afd4     
,value-,harmony and the ,harmony of     
,proportional                           
,neutralizations combined4     #afh1 p4 
#afg4 ,harmony in the repetition of a   
certain relation of tones               
not in itself harmonious4     #afi1 p4  
#agj4 ,harmony of a predominant tone in 
the repetition of a                     
certain relation of tones4     #agj1 p4 
#agj4 ,the ,harmony of a grayness       
induced by the opposition of            
tones which neutralize one another in   

the sense of                  vision4   
#aga1 p4 #aga4 ,strong contrasts1       
inconsistent with ,harmony1 may be      
perfectly consistent with both ,balance 
and ,rhythm4     #agb1 p4 #agb4         
,tone-,balance in the abstract4         
#agc1 p4 #agc4 ,use of the ,diagram of  
,values and ,colors for the             
calculation of tone-balances4     #agd1 
p4 #agd4 ,element of ,color-,intensity  
in tone-balances4     #age1 p4 #agd4    
,tone-,balances always connected with   
,measure and                            
,shape-,balances4     #agf1 p4 #age4    
,tone and ,measure-,balance4     #agg1  
p4 #age4 ,tone-,relations in ,single and
 in ,double ,inversions4     #agh1 p4   
#agf4 ,occult ,tone1 ,measure and       
,shape-,balances4     #agi1 p4 #agh4    
,further considerations on the same     
subject4     #ahj1 p4 #agh4 ,further    
considerations on the same subject4     
#aha1 p4 #aha4 ,the effect of           
,representations in ,tone-,balances4    
#ahb1 p4 #ahb4 ,tone-,rhythm4     #ahc1 

p4 #ahd4 ,attitudes in ,tone-,rhythms4  
#ahd1 p4 #ahe4 ,inversions in           
,tone-,rhythms4     #ahe1 p4 #ahf4      
,composition of tones1 measures1 and    
shapes4 ,three                  general 
rules4     #ahf1 p4 #ahh4 ,design and   
8,decoration40     #ahg1 p4 #aij4 ,the  
study of ,order in ,nature and in ,works
 of ,art4     #ahh1 p4 #aij4 ,method of 
study by ,analysis with ,synthetic      
,performance4     #ahi1 p4 #aib4        
,conclusion4 ,the practice of ,pure     
,design4 ,its purpose and               
end4                             ,the   
,riverside ,press                       
,,cambridge  ,,massachusetts            
,u  ,s  ,a