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*** START OF THE PROJECT GUTENBERG EBOOK 74765 ***





Transcriber’s Notes:

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    in the original text.
  Equal signs “=” before and after a word or phrase indicate =bold=
    in the original text.
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                           A THEORY OF PURE DESIGN
                         _Harmony, Balance, Rhythm_

                       WITH ILLUSTRATIONS AND DIAGRAMS

                          BY DENMAN W. ROSS, PH. D.

                 LECTURER ON THE THEORY OF DESIGN IN HARVARD
                 UNIVERSITY, FELLOW OF THE AMERICAN ACADEMY
                            OF ARTS AND SCIENCES

                             BOSTON AND NEW YORK
                        HOUGHTON, MIFFLIN AND COMPANY
                                  MDCCCCVII

                      COPYRIGHT 1907 BY DENMAN W. ROSS

                             ALL RIGHTS RESERVED
                           _Published April, 1907_




PREFACE


My purpose in this book is to elucidate, so far as I can, the
principles which underlie the practice of drawing and painting as a
Fine Art. Art is generally regarded as the expression of feelings
and emotions which have no explanation except perhaps in such a word
as _inspiration_, which is expletive rather than explanatory. Art is
regarded as the one activity of man which has no scientific basis, and
the appreciation of Art is said to be a matter of taste in which no two
persons can be expected to agree. It is my purpose in this book to show
how, in the practice of Art, as in all other practices, we use certain
terms and follow certain principles. Being defined and explained, these
terms and principles may be known and understood by everybody. They
are, so to speak, _the form of the language_.

While an understanding of the terms and principles of Art will not,
in itself, enable any one to produce important works, such works
are not produced without it. It must be understood, however, that
the understanding of terms and principles is not, necessarily, an
understanding in words. It may lie in technical processes and in visual
images and may never rise, or shall I say fall, to any formulation in
words, either spoken or written. The terms and principles of Art have,
as a rule, been understood by the artist in the form of technical
processes and visual images, not in words. It is in words that they
will become generally understood. It is in words that I propose to
explain them in this book. I want to bring to definition what, until
now, has not been clearly defined or exactly measured. In a sense
this book is a contribution to Science rather than to Art. It is a
contribution to Science made by a painter, who has used his Art in
order to understand his Art, not to produce Works of Art. In a passage
of Plato (Philebus, ¶ 55) Socrates says: “If arithmetic, mensuration,
and weighing be taken out of any art, that which remains will not be
much.“ “Not much, certainly,” was the reply. The only thing which
remains in Art, beyond measurable quantities and qualities, is the
personality, the peculiar ability or genius of the artist himself.
That, I believe, admits of no explanation. The element of personality
is what we mean when we speak of the element of inspiration in a Work
of Art. Underlying this element of personality are the terms and
principles of the art. In them the artist has found the possibility of
expression; in them his inspiration is conveyed to his fellowmen. I
propose to explain, not the artist, but the mode of expression which
the artist uses. My purpose, in scientific language, is to define,
classify, and explain the phenomena of Design. In trying to do that, I
have often been at a loss for terms and have been obliged, in certain
instances, to use terms with new meanings, meanings which differ, more
or less, from those of common usage and from those of writers in other
branches of learning. In all such cases I have taken pains to define my
terms and to make my meanings perfectly clear. I do not expect any one
to read this book who is not willing to allow to my terms the meanings
I have given them. Those who are unwilling to accept my definitions
will certainly not follow me to my conclusions.

I am giving this book to the Public with great reluctance. Though I
have had it in mind for many years and have put no end of thought
and work into it, it seems to me inadequate and unsatisfactory. It
will hardly be published before I shall discover in it errors both
of omission and commission. The book presents a new definition of
principles, a new association of ideas. It is inconceivable that this,
my first published statement, should be either consistent or complete.
It will be a long time, I am sure, before it can be brought to a
satisfactory shape. It is simply the best statement that I can make at
this time. One reason, perhaps my best reason, for publishing this
Theory, before it is completely worked out, is to bring other students
into the investigation. I need their coöperation, their suggestions,
and their criticisms. Without assistance from others the book would not
be as good as it is. I am indebted to a number of persons for helpful
suggestions. I am particularly indebted to three men, who have been
associated with me in my teaching: William Luther Mowll, Henry Hunt
Clark, and Edgar Oscar Parker. Each of them has had a share in the
work. I am indebted to Professor Mowll for very important contributions
to the doctrine of Rhythm, as it is presented in this book, and he has
kindly helped me in the revision of the work for the press. My friend
Dean Briggs has kindly read my proof sheets, and I am indebted to him
for many suggestions.

                                           DENMAN W. ROSS.
   HARVARD UNIVERSITY,
      February 16, 1907.




CONTENTS


   INTRODUCTION                                       1
   POSITIONS IN HARMONY, BALANCE, AND RHYTHM          9
   LINES IN HARMONY, BALANCE, AND RHYTHM             37
   OUTLINES IN HARMONY, BALANCE, AND RHYTHM          96
   TONES AND TONE-RELATIONS                         131
   SEQUENCES OF VALUES AND COLORS                   143
   TONE-HARMONY                                     158
   TONE-BALANCE                                     172
   TONE-RHYTHM                                      182
   COMPOSITION, GENERAL RULES                       186
   THE STUDY OF ORDER IN NATURE AND IN WORKS OF ART 190
   CONCLUSION                                       192
   PARAGRAPH INDEX                                  195




INTRODUCTION


THE MEANING OF DESIGN

1. 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
expressed. By Order I mean, particularly, three things,—Harmony,
Balance, and Rhythm. These are the principal modes in which Order is
revealed in Nature and, through Design, in Works of Art.


THE ORDER OF HARMONY

2. Whenever two or more impressions or ideas have something in common
that is appreciable, they are in harmony, in the measure of what they
have in common. The harmony increases as the common element increases;
or the common elements. It diminishes in the measure of every
difference or contrast. By the Order of Harmony I mean some recurrence
or repetition, some correspondence or likeness. The likeness may be in
sounds or in sights, in muscular or other sense-impressions. It may lie
in sensations, in perceptions, in ideas, in systems of thought.


THE ORDER OF BALANCE

3. By the Order of Balance I mean some equal opposition and consequent
equilibrium, as it occurs at some moment of Time or at some point
of Space; an equilibrium which induces, for the moment and in its
place, a suspension of all change or movement, and causes a pause
or a rest. The equilibrium may be one of physical forces (forces of
weight or resistance) or forces of will. It may be an equilibrium
of sense-impressions or attractions, of interests, of alternative
propositions or ideas. It may be the equilibrium of a perfect
antithesis. Certain moments of Time, certain points of Space, are
distinguished from others by instances of equilibrium or balance. The
balance being lost, in any case, we have at once some movement. If this
movement is regular, and marked in its regularity, we get, instead of
Balance, Rhythm.


THE ORDER OF RHYTHM

4. By the Order of Rhythm I mean changes of sensation; changes in
muscular impressions as we feel them, in sounds as we hear them, in
sights as we see them; changes in objects, people, or things as we know
them and think of them, changes which induce the feeling or idea of
movement, either in the duration of Time or in the extension of Space;
provided that the changes take place at regular and marked intervals of
time or in regular and marked measures of space. By regular intervals
and measures I mean equal or lawfully varying intervals and measures. I
do not mean, by Rhythm, changes simply, inducing the sense or idea of
movement: I mean, by Rhythm, a regularity of changes in a regularity of
measures, with the effect of movement upon our minds.

Rhythms in Time differ from Rhythms in Space, inasmuch as the movement
in Time is in one direction, inevitably. It lies in the duration and
passing of time, from which nothing escapes. The movement in space,
on the contrary, may be in any one of many possible directions. A
movement in different directions, particularly in contrary directions,
amounts to a negation of movement. In any space-rhythm, therefore,
the direction in which the rhythm leads us, the direction in which we
follow it, must be unmistakable.

5. Of these three principles of Order, the first and foremost, the most
far-reaching and comprehensive, is the principle of Harmony. We have
Harmony in all balances, and we have it also in all rhythms. It is,
therefore, undesirable to think of the three principles as coördinate.
It will be better to think of the principle of Harmony first, and then
of two other principles, those of Balance and of Rhythm, as lying
within the range of Harmony but not coextensive with it. We might
express the idea in a logical diagram.

[Illustration: Fig. 1]

Within the field of Harmony we have two distinct modes of Order—Balance
and Rhythm; but we have Harmony beyond the range of Balance and beyond
the range of Rhythm.

In cases where rhythms, corresponding in character and in direction
of movement, are set side by side, one on the right, the other on the
left, of a vertical axis, so that they balance, one against the other,
and the vertical axis of the balance is the line of the movement,
we have the union of all three principles. This idea, also, may be
expressed in a logical diagram.

[Illustration: Fig. 2]

Examples of this union of the three principles of Order will be given
farther on.


BEAUTY A SUPREME INSTANCE OF ORDER

6. I refrain from any reference to Beauty as a principle of Design. It
is not a principle, but an experience. It is an experience which defies
analysis and has no explanation. We distinguish it from all other
experiences. It gives us pleasure, perhaps the highest pleasure that we
have. At the same time it is idle to talk about it, or to write about
it. The less said about it the better. “It is beautiful,” you say.
Then somebody asks, “Why is it beautiful?” There is no answer to that
question. You say it is beautiful because it gives you pleasure: but
other things give you pleasure which are not beautiful. Pleasure is,
therefore, no criterion of Beauty. What is the pleasure which Beauty
gives? It is the pleasure which you have in the sense of Beauty. That
is all you can say. You cannot explain either the experience or the
kind of pleasure which it gives you.

While I am quite unable to give any definition or explanation of
Beauty, I know where to look for it, where I am sure to find it. The
Beautiful is revealed, always, so far as I know, in the forms of Order,
in the modes of Harmony, of Balance, or of Rhythm. While there are many
instances of Harmony, Balance, and Rhythm which are not particularly
beautiful, there is, I believe, nothing really beautiful which is not
orderly in one or the other, in two, or in all three of these modes. In
seeking the Beautiful, therefore, we look for it in instances of Order,
in instances of Harmony, Balance, and Rhythm. We shall find it in what
may be called supreme instances. This is perhaps our nearest approach
to a definition of Beauty: that it is a supreme instance of Order,
intuitively felt, instinctively appreciated.


THE ARTS AS DIFFERENT MODES OF EXPRESSION

7. The Arts are different forms or modes of expression: modes of
feeling, modes of thought, modes of action. There are many Arts in
which different terms of expression, different materials, different
methods are used. The principal Arts are (1) Gymnastics, including
Dancing, (2) Music, (3) Speech, spoken and written, (4) Construction
with all kinds of materials, (5) Sculpture, including Modeling and
Carving, (6) Drawing and Painting. These are the principal Arts, but
there are many others, more or less connected with them. Design comes
into all of these Arts, bringing Order, in some cases Beauty.


THE ART OF DRAWING AND PAINTING

8. The Art which I have studied and practiced, the Art in which I am
giving instruction, is that of Drawing and Painting.

By the Art of Drawing and Painting I mean expression in pigment-tones
(values, colors, intensities of color) spread in different measures
or quantities and in different shapes: shapes being differences of
character given to a line by its straightness or curvature, to a spot
or area by its outline or contour. By Drawing and Painting I mean,
therefore, expression by lines and spots of paint.


TWO MODES OF DRAWING AND PAINTING

9. There are two modes of Drawing and Painting, the mode of Pure Design
and the mode of Representation.


PURE DESIGN

10. By Pure Design I mean simply Order, that is to say, Harmony,
Balance, and Rhythm, in lines and spots of paint, in tones, measures,
and shapes. Pure Design appeals to the eye just as absolute Music
appeals to the ear. The purpose in Pure Design is to achieve Order
in lines and spots of paint, if possible, the perfection of Order, a
supreme instance of it, the Beautiful: this with no other, no further,
no higher motive; just for the satisfaction, the pleasure, the delight
of it. In the practice of Pure Design we aim at Order and hope for
Beauty. Even the motive of giving pleasure to others lies beyond the
proper purpose of Pure Design, though it constantly happens that in
pleasing ourselves we give others pleasure.


APPLICATIONS OF DESIGN

11. The application of Design in the various Arts and Crafts is well
understood and appreciated. We have many instances and examples in the
Art of the Past. The possibility of Pure Design, pure Art, followed for
the sake of Order and Beauty, with no purpose of service or of utility,
is not at all understood or appreciated. I think of Pure Design as I
think of Music. Music is the arrangement and composition of sounds
for the sake of Order and Beauty, to give pleasure to the ear of the
composer. Pure Design is the arrangement and composition of lines and
spots of paint for the sake of Order and Beauty, to give pleasure to
the eye of the designer. I am prepared to admit, however, that as
Music, once created, being appropriate to the occasion when it is
performed and to the mood of the listeners, may give pleasure to many
persons, so Pure Design, once achieved, being appropriate to the time
and the place of exhibition and to the mood of the beholders, may give
pleasure to others besides the designer. In that sense, I am willing to
allow that Pure Design may be Applied Art,—Art applied in the service
of Humanity, its purpose being to bring pleasure into human experience.
The underlying motive of it, however, is found not in the service of
humanity, but in the ideal of the artist. He aims at Order and hopes
for Beauty, as the highest reward of his effort. John Sebastian Bach
said of Music: “It is for the glory of God and a pleasant recreation.”
That is what I mean. The designer, like the musician, seeks first of
all to achieve Order and Beauty for the sake of Order and Beauty. That
is his religion,—the worship of the Ideal. When the Ideal is realized,
the object which has been produced may serve a useful purpose in giving
pleasure, and perhaps inspiration, to others.

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 Crafts. In such applications, however, the
ideals of design are often obscured by the consideration of materials
and technical processes on the one hand, and of service or utility on
the other. It will be worth while, therefore, for those who wish to
bring Design into their work, whatever that is, to study Design in the
abstract, Pure Design, so that they may know, before they undertake to
use it, what Design is. It is the purpose of this book to explain what
it is.


REPRESENTATION

12. Order, which in Pure Design is an end, becomes in Representation
a means to an end; the end being the Truth of Representation. In
Representation we are no longer dealing, as in Pure Design, with
meaningless terms, or, if the terms have meanings, with no regard
for them. In Representation we are putting lines and spots of paint
together for the sake of their meanings. Design in Representation
means Order in the composition or arrangement of meanings. What we
aim at is the Truth of Representation in a form of expression which
will be simple, clear, reasonable, and consistent, as well as true.
The attention must be directed to what is important, away from what is
unimportant. Objects, people, and things represented must be brought
out and emphasized or suppressed and subordinated, according to the
Idea or Truth which the artist wishes to express. The irrelevant must
be eliminated. The inconsistent and the incongruous must be avoided.
That is what I mean by Design in Representation, the knowledge of
Nature and Life presented in a systematic, logical, and orderly way.


REPRESENTATION IN FORMS OF DESIGN

13. It sometimes happens that we have the Truth of Representation in a
form of Pure Design or Pure Design combined with Representation. In
Poetry we have the meaning of the words in the measures of the verse.
So in Representation it is sometimes possible to achieve the Truth in
forms of Harmony, Balance, and Rhythm. In such cases the appeal is
simultaneously to the love of Knowledge and to the sense of Order and
of Beauty, so that we have an æsthetic pleasure in the statement of the
Truth.

In this book I shall explain what I mean by Drawing and Painting
in Pure Design. Later, I hope to write another book on Design in
Representation.




DRAWING AND PAINTING IN PURE DESIGN




POSITIONS


DEFINITION OF POSITIONS

14. Take a pencil and a piece of paper. With the pencil, on the paper,
mark a dot or point.

[Illustration: Fig. 3]

By this dot (A) three ideas are expressed: an idea of Tone, the tone of
lead in the pencil; an idea of Measure, the extent of the space covered
by the dot; and an idea of Shape, the character given to the dot by its
outline or contour. The dot is so small that its tone, its measure,
and its shape will not be seriously considered. There is another idea,
however, which is expressed by the dot or point,—an idea of Position.
That is its proper meaning or signification. There is presumably a
reason for giving the dot one position rather than another.


POSITIONS DETERMINED BY DIRECTIONS AND DISTANCES

15. Put another dot (B) on your paper, not far from dot “A.”

[Illustration: Fig. 4]

We have now a relation of two positions,—the relation of position “A”
to position “B.” The relation is one of Directions and of Distances.
Proceeding from “A” in a certain direction to a certain distance we
reach “B.” Proceeding from “B” in a certain direction and to a certain
distance we reach “A.” Every position means two things; a direction
and a distance taken from some point which may be described as the
premise-point.


DIRECTIONS

16. Directions may be referred either to the Horizontal or to the
Vertical. Referring them to the horizontal, we say of a certain
direction, that it is up-to-the-left, or up-to-the-right, or
down-to-the-left, or down-to-the-right, a certain number of degrees.
It may be thirty (30°), it may be forty-five (45°), it may be sixty
(60°),—any number of degrees up to ninety (90°), in which case we say
simply that the direction is up or down. Directions on the horizontal
may be described by the terms, to the right or to the left.

[Illustration: Fig. 5]

The method of describing and defining different directions from any
point, as a center, is clearly explained by this diagram.


DISTANCES

17. The definition of Distances in any direction is well understood.
In defining position “B,” in Fig. 4, we say that it is, in a direction
from “A,” the premise-point, down-to-the-right forty-five degrees
(45°), that it is at a distance from “A” of one inch. Distances are
always taken from premise-points.


POSITIONS DETERMINED BY TRIANGULATIONS

18. If we mark a third dot, “C,” on our paper and wish to define its
position, we may give the direction and the distance from “A,” or from
“B,” or, if we prefer, we may follow the principle of Triangulation and
give two directions, one from “A” and the other from “B.” No distances
need be given in that case. The position of “C” will be found at the
intersection of the two directions.

[Illustration: Fig. 6]

The principle of Triangulation is illustrated in the above diagram.


INTERVALS

19. We shall have occasion to speak not only of Distances, but of
Intervals. They may be defined as intermediate spaces. The spaces
between the points “A” and “B,” “A” and “C,” “B” and “C,” in Fig. 6,
are Intervals.


SCALE IN RELATIONS OF POSITIONS

20. Given any relation of positions, the scale may be changed by
changing the intervals, provided we make no change of directions. That
is well understood.

Before proceeding to the considerations which follow, I must ask the
reader to refer to the definitions of Harmony, Balance, and Rhythm
which I have given in the Introduction.


THE ORDER OF HARMONY

IN POSITIONS: DIRECTIONS, DISTANCES, INTERVALS

21. All Positions lying in the same direction and at the same distance
from a given point, taken as a premise-point, are one. There is no such
thing, therefore, as a Harmony of Positions. Positions in Harmony are
identical positions. Two or more positions may, however, lie in the
same direction from or at the same distance from a given point taken
as a premise-point. In that case, the two or more positions, having a
direction or a distance in common, are, to that extent, in harmony.


22. What do we mean by Harmony of Directions?

[Illustration: Fig. 7]

This is an example of Direction-Harmony. All the points or positions
lie in one and the same direction from the premise-point “A.” The
distances from “A” vary. There is no Harmony of Intervals.

Directions being defined by angles of divergence, we may have a Harmony
of Directions in the repetition of similar angles of divergence: in
other words, when a certain change of direction is repeated.

[Illustration: Fig. 8]

In this case the angles of divergence are equal. There is a
Harmony, not only in the repetition of a certain angle, but in the
correspondence of the intervals.

[Illustration: Fig. 9]

This is an example of Harmony produced by the repetition of a certain
alternation of directions.

[Illustration: Fig. 10]

In this case we have Harmony in the repetition of a certain relation
of directions (angles of divergence). In these cases, Fig. 9 and Fig.
10, there is Harmony also, in the repetition of a certain relation of
intervals.

23. Two or more positions may lie at the same distance from a given
point taken as a premise-point. In that case the positions, having a
certain distance in common, are, to that extent, in Harmony.

[Illustration: Fig. 11]

This is an example of Distance-Harmony. All the points are equally
distant from the premise-point “A.” The directions vary.

We may have Distance-Harmony, also, in the repetition of a certain
relation of distances.

[Illustration: Fig. 12]

This is an illustration of what I have just described. The Harmony is
of a certain relation of distances repeated.

24. Intervals, that is to say intermediate spaces, are in Harmony when
they have the same measure.

[Illustration: Fig. 13]

In this case we have, not only a Harmony of Direction, as in Fig. 7,
but also a Harmony of Intervals.

[Illustration: Fig. 14]

In this case the points are in a group and we have, as in Fig. 11, a
Harmony of Distances from the premise-point “A.” We have also a Harmony
of Intervals, the distances between adjacent points being equal. We
have a Harmony of Intervals, not only when the intervals are equal, but
when a certain relation of intervals is repeated.

[Illustration: Fig. 15]

The repetition of the ratio one to three in these intervals is
distinctly appreciable. In the repetition we have Harmony, though we
have no Harmony in the terms of the ratio itself, that is to say, no
Harmony that is appreciable in the sense of vision. The fact that one
and three are both multiples of one means that one and three have
something in common, but inasmuch as the common divisor, one, cannot be
visually appreciated, as such (I feel sure that it cannot), it has no
interest or value in Pure Design.

[Illustration: Fig. 16]

The relation of intervals is, in this case, the relation of
three-one-five. We have Harmony in the repetition of this relation of
intervals though there is no Harmony in the relation itself, which is
repeated.

[Illustration: Fig. 17]

In this case, also, we have Interval-Harmony, but as the intervals in
the vertical and horizontal directions are shorter than the intervals
in the diagonal directions, the Harmony is that of a relation of
intervals repeated.

25. In moving from point to point in any series of points, it will be
found easier to follow the series when the intervals are short than
when they are long. In Fig. 17 it is easier to follow the vertical or
horizontal series than it is to follow a diagonal series, because in
the vertical and horizontal directions the intervals are shorter.

[Illustration: Fig. 18]

In this case it is easier to move up or down on the vertical than in
any other directions, because the short intervals lie on the vertical.
The horizontal intervals are longer, the diagonal intervals longer
still.

[Illustration: Fig. 19]

In this case the series which lies on the diagonal up-left-down-right
is the more easily followed. It is possible in this way, by means of
shorter intervals, to keep the eye on certain lines. The applications
of this principle are very interesting.

26. In each position, as indicated by a point in these arrangements,
may be placed a composition of dots, lines, outlines, or areas. The
dots indicate positions in which any of the possibilities of design
may be developed. They are points from which all things may emerge and
become visible.


THE ORDER OF BALANCE

IN POSITIONS: DIRECTIONS, DISTANCES, AND INTERVALS

27. Directions balance when they are opposite.

[Illustration: Fig. 20]

The opposite directions, right and left, balance on the point from
which they are taken.

28. Equal distances in opposite directions balance on the point from
which the directions are taken.

[Illustration: Fig. 21]

The equal distances AB and AC, taken in the directions AB and AC
respectively, balance on the point “A” from which the directions are
taken.

29. Two directions balance when, taken from any point, they diverge at
equal angles from any axis, vertical, horizontal, or diagonal.

[Illustration: Fig. 22]

The directions AB and AC balance on the vertical axis AD from which
they diverge equally, that is to say, at equal angles.

30. Equal distances balance in directions which diverge equally from a
given axis.

[Illustration: Fig. 23]

The equal distances AB and AC balance in the directions AB and AC which
diverge equally from the axis AD, making the equal angles CAD and DAB.
Both directions and distances balance on the vertical axis AD.

31. The positions B and C in Fig. 23, depending on balancing directions
and distances, balance on the same axis. We should feel this balance of
the positions A and B on the vertical axis even without any indication
of the axis. We have so definite an image of the vertical axis that
when it is not drawn we imagine it.

[Illustration: Fig. 24]

In this case the two positions C and B cannot be said to balance,
because there is no suggestion, no indication, and no visual image of
any axis. It is only the vertical axis which will be imagined when not
drawn.

32. Perfect verticality in relations of position suggests stability
and balance. The relation of positions C-B in Fig. 24 is one of
instability.

[Illustration: Fig. 25]

These two positions are felt to balance because they lie in a perfectly
vertical relation, which is a relation of stability. Horizontality in
relations, of position is also a relation of stability. See Fig. 28, p.
21.

33. All these considerations lead us to the definition of Symmetry.
By Symmetry I mean opposite directions or inclinations, opposite and
equal distances, opposite positions, and in those positions equal,
corresponding, and opposed attractions on a vertical axis. Briefly,
Symmetry is right and left balance on a vertical axis. This axis will
be imagined when not drawn. In Symmetry we have a balance which is
perfectly obvious and instinctively felt by everybody. All other forms
of Balance are comparatively obscure. Some of them may be described as
occult.

[Illustration: Fig. 26]

In this case we have a symmetry of positions which means opposite
directions, opposite and equal distances, and similar and opposite
attractions in those positions. The attractions are black dots
corresponding in tone, measure, and shape.

[Illustration: Fig. 27]

In this case we have a balance of positions (directions and distances)
and attractions in those positions, not only on the vertical axis
but on a center. That means Symmetry regarding the vertical axis,
Balance regarding the center. If we turn the figure, slightly, from
the vertical axis, we shall still have Balance upon a center and axial
Balance; but Symmetry, which depends upon the vertical axis, will be
lost.

34. The central vertical axis of the whole composition should
predominate in symmetrical balances.

[Illustration: Fig. 28]

In this case we do not feel the balance of attractions clearly or
satisfactorily, because the vertical axis of the whole arrangement
does not predominate sufficiently over the six axes of adjacent
attractions. It is necessary, in order that symmetrical balance shall
be instinctively felt, that the central vertical axis predominate.

[Illustration: Fig. 29]

The central vertical axis is clearly indicated in this case.

[Illustration: Fig. 30]

Here, also, the central vertical axis is clearly indicated.

35. All relations of position (directions, distances, intervals), as
indicated by dots or points, whether orderly or not, being inverted on
the vertical axis, give us an obvious symmetrical balance.

[Illustration: Fig. 31]

This is a relation of positions to be inverted.

[Illustration: Fig. 32]

Here the same relation is repeated, with its inversion to the right on
a vertical axis. The result is an obvious symmetrical balance. If this
inversion were made on any other than the vertical axis, the result
would be Balance but not Symmetry. The balance would still be axial,
but the axis, not being vertical, the balance would not be symmetrical.

36. In the case of any unsymmetrical arrangement of dots, the dots
become equal attractions in the field of vision, provided they are
near enough together to be seen together. To be satisfactorily seen
as a single composition or group they ought to lie, all of them,
within a visual angle of thirty degrees. We may, within these limits,
disregard the fact that visual attractions lose their force as
they are removed from the center of the field of vision. As equal
attractions in the field of vision, 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 equilibrium.
This is best done by means of a symmetrical inclosure or frame. In
ascertaining just where the center is, in any case, we depend upon
visual sensitiveness or visual feeling, guided by an understanding
of the principle of balance: that equal attractions, tensions or
pulls, balance at equal distances from a given center, that unequal
attractions balance at distances inversely proportional to them. Given
certain attractions, to find the center, we weigh the attractions
together in the field of vision and observe the position of the
center. In simple cases we may be able to prove or disprove our visual
feeling by calculations and reasoning. In cases, however, where the
attractions vary in their tones, measures, and shapes, and where there
are qualities as well as quantities to be considered, calculations and
reasoning become difficult if not impossible, and we have to depend
upon visual sensitiveness. All balances of positions, as indicated by
dots corresponding in tone, measure, and shape, are balances of equal
attractions, and the calculation to find the center is a very simple
one.

[Illustration: Fig. 33]

Here, for example, the several attractions, corresponding and equal,
lie well within the field of vision. The method followed to balance
them is that which I have just described. The center of equilibrium
was found and then indicated by a symmetrical framing. Move the frame
up or down, right or left, and the center of the frame and the center
of the attractions within it will no longer coincide, and the balance
will be lost. We might say of this arrangement that it is a Harmony
of Positions due to the coincidence of two centers, the center of the
attractions and the center of the framing.

37. 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 it.

[Illustration: Fig. 34]

In this case the dots and the inclosure are about equally attractive.

[Illustration: Fig. 35]

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 it.

There is another form of Balance, the Balance of Inclinations, but I
will defer its consideration until I can illustrate the idea by lines.


THE ORDER OF RHYTHM


IN POSITIONS: DIRECTIONS, DISTANCES, INTERVALS

38. In any unsymmetrical relation of positions (directions, distances,
intervals), in which the balance-center is not clearly and sufficiently
indicated, there is a suggestion of movement. The eye, not being held
by any balance, readily follows this suggestion.

[Illustration: Fig. 36]

In this case we feel that the group of dots is unbalanced in character
and unstable in its position or attitude. It is easy, inevitable
indeed, to imagine the group falling away to the right. This is due,
no doubt, to the visual habit of imagining a base-line when it is not
drawn. Our judgments are constantly made with reference to the imagined
standards of verticality and horizontality. We seem to be provided with
a plumb-line and a level without being conscious of the fact.

[Illustration: Fig. 37]

In this case there is a suggestion of falling down to the left due
to the feeling of instability. A symmetrical framing holding the eye
at the center of equilibrium would prevent the feeling of movement,
provided the framing were sufficiently strong in its attractions. In
the examples I have given (Fig. 36 and Fig. 37) we have movement, but
no Rhythm.

39. There is another type of movement which we must consider,—the
type of movement which is caused by a gradual crowding together of
attractions.

[Illustration: Fig. 38]

There is nothing in this series of dots but the harmony of
corresponding attractions and intervals repeated in a harmony of
direction. If, instead of the repetition of equal intervals, we had a
regular progression of intervals, either arithmetical or geometrical,
we should feel a movement in the direction of diminishing intervals.

[Illustration: Fig. 39]

In the above example the changes of interval are those of an
arithmetical progression.

[Illustration: Fig. 40]

In Fig. 40 the changes of interval are those of a geometrical
progression. The movement to the left through these sequences is, no
doubt, somewhat checked or prevented by the habit of reading to the
right.

[Illustration: Fig. 41]

The angle FAB is the angle of vision within which the sequence is
observed. At the end F of the sequence there is a greater number of
attractions in a given angle of vision than at the end B, so the eye
is drawn towards the left. The pull on the eye is greater at the end F
because of the greater number and the crowding together of attractions.
In the examples just given (Figs. 39, 40), we have not only movements
in certain directions, but movements in regular and marked measures.
The movements are, therefore, rhythmical, according to the definition I
have given of Rhythm.

40. It is evident that any relation of positions, balanced or
unbalanced, may be substituted for the single dots or points in the
figures just given. Such substitutions have the following possibilities.

41. First. When the points lie in a series, at equal intervals, the
substitution of a symmetrical group of positions at each point gives no
Rhythm, only Harmony.

[Illustration: Fig. 42]

There is no movement in this series of repetitions. There is
consequently no Rhythm. Disregarding the habit of reading to the right,
which induces the eye to move in that direction, it is as easy to move
toward the left as toward the right. It requires more than repetitions
at equal intervals to produce the feeling of Rhythm. There must be
movement, and the movement must have a definite direction.

42. Second. The substitution at each point of a symmetrical group at
equal intervals, as before, but with a progressive change of scale,
will give us Rhythm. The movement will be due to the gradual crowding
together of attractions at one end of the series.

[Illustration: Fig. 43]

In this case we have the repetition of a symmetrical relation of
positions at equal intervals with a gradation of scale in the
repetitions. The result is a Rhythm, in which the movement is from left
to right, owing to the greater crowding together of attractions at the
right end of the series. The feeling of Rhythm is no doubt somewhat
enhanced by our habit of reading to the right, which facilitates the
movement of the eye in that direction.

43. Third. The substitution of an unstable group at each point of the
sequence, the repetitions being at equal intervals, gives us a Rhythm,
due simply to the movement of the group itself, which is unstable.

[Illustration: Fig. 44]

Taking the relation of positions given in Fig. 36 and repeating it at
equal intervals, it will be observed that the falling-to-the-right
movement, which is the result of instability, is conveyed to the whole
series of repetitions. 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 repeated, I will ask the reader to compare it with
the repetition of a symmetrical group in Fig. 42. There is no movement
in that case, therefore no Rhythm.

44. Fourth. The movement in Fig. 44 may be increased by a diminution
of scale and consequent crowding together of the dots, provided
the movement of the groups and the crowding together have the same
direction.

[Illustration: Fig. 45]

In this case, as I have said, the movement of Fig. 44 is enforced by
the presence of another element of movement, that of a gradation of
scale and consequent crowding together in the groups. The two movements
have the same direction. The movement of the crowding is not so strong
as that which is caused by the instability of the group itself.

45. Fifth. A symmetrical relation of positions, being repeated in a
series with gradually diminishing intervals between the repeats, will
give us a feeling of rhythmic movement. It will be due to a gradual
increase in the number of attractions as the eye passes from one angle
of vision to another. See Fig. 41. The Rhythm will, no doubt, be
somewhat retarded by the sense of successive axes of symmetry.

[Illustration: Fig. 46]

In this case a symmetrical group is repeated in a progression of
measures. The movement is toward the greater number of attractions at
the right end of the series. This increase in the number of attractions
is due simply to diminishing intervals in that direction. The eye
moves through a series of angles toward the angle which contains the
greatest number of attractions. The reader can hardly fail to feel the
successive axes of symmetry as a retarding element in this Rhythm.

46. Sixth. Symmetrical relations of position may be repeated in
progressions of scale and of intervals. In that case we get two
movements, one caused by a gradual increase in the number of
attractions in successive angles of vision, the other being due to a
gradual crowding together and convergence of attractions in the same
series of angles.

[Illustration: Fig. 47]

Comparing this Rhythm with the Rhythm of Fig. 43, the reader will
appreciate the force of a diminution of scale in connection with a
diminution of intervals.

47. Seventh. Unstable groups may be repeated in progressions of
intervals, in which case the movement in the group is conveyed to the
whole series, in which there will be, also, the movement of a gradual
increase of attractions from one angle of vision to another. In all
such cases contrary motion should be avoided if the object is Rhythm.
The several movements should have a harmony of direction.

[Illustration: Fig. 48]

In this case the movement in the group is felt throughout the series,
and the force of the movement is enhanced by the force of a gradual
increase of attractions from one visual angle to another, in the same
direction, to the right. By reversing the direction of increasing
attractions and so getting the two movements into contrary motion, the
feeling of rhythm would be much diminished. Such contrary motions are
unsatisfactory unless Balance can be achieved. In that case all sense
of movement and of rhythm disappears.

48. Eighth. Unstable groups may be repeated, not only in a gradation
of intervals, but in a gradation of scale, in which case we have a
combination of three causes of movement: lack of stability in the
group repeated, a gradual increase in the number of attractions in
the sequence of visual angles, and a crowding or convergence of the
attractions. Rhythms of this type will not be satisfactory unless the
three movements have the same direction.

[Illustration: Fig. 49]

Here we have the repetition of an unstable group of attractions in a
progression of scale and also of intervals. The arrangement gives us
three elements of movement, all in the same direction.

49. Two or even more of such rhythms as I have described may be
combined in one compound rhythm, in which the eye will follow two
or more distinct movements at the same time. It is important in all
compound rhythms that there should be no opposition or conflict of
movements, unless of course the object is to achieve a balance of
contrary movements. Corresponding rhythms in contrary motion balance
one another. If one of the movements is to the right, the other to the
left, the balance will be symmetrical.


ATTITUDES


RELATIONS OF POSITION IN DIFFERENT ATTITUDES

50. Given any relation of positions (directions, distances, intervals),
it may be turned upon a center and so made to take an indefinite number
and variety of attitudes. It may be inverted and the inversion may be
turned upon a center, producing another series of attitudes. Except
in cases of axial balance, the attitudes of the second series will be
different from those of the first.

[Illustration: Fig. 50]

In this case the relation of positions being turned upon a center
changes its attitude, while the positions within the group remain
relatively unchanged. There is no change of shape.

[Illustration: Fig. 51]

In this case the same group has been inverted, and a second series of
attitudes is shown, differing from the first series.

[Illustration: Fig. 52]

In this case, however, which is a case of axial balance, the inversion
of the group and the turning of the inversion on a center gives no
additional attitudes.

51. Among all possible attitudes there are four which are principal or
fundamental, which we may distinguish as follows:—

[Illustration: Fig. 53]

These principal attitudes are: First, I, the original attitude,
whatever it is; second, II, the single inversion of that attitude, to
the right on a vertical axis; third, III, the double inversion of the
original attitude, first to the right then down; and, fourth, IV, the
single inversion of the original position, down across the horizontal
axis.


THE ORDER OF HARMONY IN ATTITUDES

52. The repetition of any relation of positions without change of
attitude gives us Harmony of Attitudes.

[Illustration: Fig. 54]

In this case we have not only a Harmony in the repetition of a certain
relation of positions and of intervals, but a Harmony of Attitudes. We
have, in the relation of positions repeated, a certain shape. In the
repetition of the shape we have Shape-Harmony. In the repetition of the
shape in a certain attitude we have a Harmony of Attitudes.

[Illustration: Fig. 55]

In this case we have lost the Harmony of Attitudes which we had in Fig.
54, but not the Harmony of a certain shape repeated.

53. The possibilities of Harmony in the repetition of any relation
of positions in the same attitude has been discussed. A Harmony of
Attitudes will occur, also, in the repetition of any relation of
attitudes.

[Illustration: Fig. 56]

Here we have Harmony in the repetition of a relation of two attitudes
of a certain group of positions. The combination of the two attitudes
gives us another group of positions and the Harmony lies in the
repetition of this group.


THE ORDER OF BALANCE IN ATTITUDES

54. It is to be observed that single inversions in any direction, for
example the relation of attitudes I and II, II and III, III and IV,
IV and I, in Fig. 53, shows an opposition and Balance of Attitudes
upon the axis of inversion. The relation of positions I and II and
III and IV, the relation of the two groups on the left to the two
groups on the right, illustrates the idea of Symmetry of Attitudes,
the axis of balance being vertical. By Symmetry I mean, in all cases,
right and left balance on a vertical axis. All double inversions,
the relation of positions I and III, and II and IV, in Fig. 53, are
Attitude-Balances, not on axes, but on centers. The balance of these
double inversions is not symmetrical in the sense in which I use the
word symmetry, nor is it axial. It is central.


THE ORDER OF RHYTHM IN ATTITUDES

55. When movement is suggested by any series of attitudes and the
movement is regulated by equal or regularly progressive intervals, we
have a Rhythm of Attitudes.

[Illustration: Fig. 57]

In this case the changes of attitude suggest a falling movement to
the right and down. In the regular progression of this movement
through marked intervals we have the effect of Rhythm, in spite of
the fact that the relation of positions repeated has axial balance.
The intervals in this case correspond, producing Interval-Harmony.
The force of this Rhythm might be increased if the relation of
positions repeated suggested a movement in the same direction. We
should have Rhythm, of course, in the repetition of any such unstable
attitude-rhythms at equal or lawfully varying intervals.




LINES


DEFINITION OF LINES

56. Taking any dot and drawing it out in any direction, or in a series
or sequence of directions, it becomes a line. The line may be drawn in
any tone, in any value, color or color-intensity. In order that the
line may be seen, the tone of it must differ from the ground-tone upon
which it is drawn. The line being distinctly visible, the question of
tone need not be raised at this point of our discussion. We will study
the line, first, as a line, not as an effect of light.

The line may be drawn long or short, broad or narrow. As the line
increases in breadth, however, it becomes an area. 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 it, and
to possible changes in its length.

We can draw the line in one direction from beginning to end, in which
case it will be straight. If, in drawing the line, we change its
direction, we can do this abruptly, in which case the line becomes
angular, or we can do it gradually, in which case it becomes curved.
Lines may be straight, angular, or curved. They may have two of these
characteristics or all three of them. The shapes of lines are of
infinite variety.


CHANGES OF DIRECTION IN LINES


_Angles_

57. Regarding the line which is drawn as a way or path upon which we
move and proceed, we must decide, if we change our direction, whether
we will turn to the right or to the left, and whether we will turn
abruptly or gradually. If we change our direction abruptly we must
decide how much of a change of direction we will make. Is it to be a
turn of 30° or 60° or 90° or 135°? How much of a turn shall it be?

[Illustration: Fig. 58]

The above illustrations are easy to understand and require no
explanation. An abrupt change of 180° means, of course, returning upon
the line just drawn.


_Curves_

58. In turning, not abruptly but gradually, changing the direction at
every point, that is to say in making a curve, the question is, how
much of a turn to make in a given distance, through how many degrees
of the circle to turn in one inch (1″), in half an inch (½″), in two
inches (2″). In estimating the relation of arcs, as distances, to
angles of curvature, the angles of the arcs, the reader will find it
convenient to refer to what I may call an Arc-Meter. The principle of
this meter is shown in the following diagram:—

[Illustration: Fig. 59]

If we wish to turn 30° in ½″, we take the angle of 30° and look within
it for an arc of ½″. The arc of the right length and the right angle
being found, it can be drawn free-hand or mechanically, by tracing
or by the dividers. Using this meter, we are able to draw any curve
or combination of curves, approximately; and we are able to describe
and define a line, in its curvatures, so accurately that it can be
produced according to the definition. Owing, however, to the difficulty
of measuring the length of circular arcs accurately, 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 drawn.

[Illustration: Fig. 60]

Here, for example, is a certain circular arc. It is perhaps best
defined and described as the arc of a half inch radius and an angle
of ninety degrees, or in writing, more briefly, rad. ½″ 90°. Regarding
every curved line either as a circular arc or made up of a series of
circular arcs, the curve may be defined and described by naming the arc
or arcs of which it is composed, in the order in which they are to be
drawn, and the attitude of the curve may be determined by starting from
a certain tangent drawn in a certain direction. The direction of the
tangent being given, the first arc takes the direction of the tangent,
turning to the right of it or to the left.

[Illustration: Fig. 61]

Here is a curve which is composed of four circular arcs to be drawn in
the following order:—

Tangent up-right 45°, arc right radius 1″ 60°, arc left radius ⅓″ 90°,
arc right radius ¾″ 180°.

Two arcs will often come together at an angle. The definition of the
angle must be given in that case. It is, of course, the angle made by
tangents of the arcs. Describing the first arc and the direction (right
or left so many degrees) which the tangent of the second arc takes
from the tangent of the first arc; then describing the second arc and
stating whether it turns from its tangent to the right or to the left,
we shall be able to describe, not only our curves, but any angles which
may occur in them.

[Illustration: Fig. 62]

Here is a curve which, so far as the arcs are concerned, of which it is
composed, resembles the curve of Fig. 61; but in this case the third
arc makes an angle with the second. That angle has to be defined.
Drawing the tangents, it appears to be a right angle. The definition of
the line given in Fig. 62 will read as follows:—

Tangent down right 45°, arc left radius 1″ 60°, arc right radius ⅓″
90°, tangent left 90°, arc left ¾″ 180°.

59. In this way, regarding all curves as circular arcs or composed of
circular arcs, we shall be able to define any line we see, or any line
which we wish to produce, so far as changes of direction are concerned.
For the purposes of this discussion, I shall consider all curves as
composed of circular arcs.

There are many curves, of course, which are not circular in character,
nor composed, strictly speaking, of circular arcs. The Spirals are in
no part circular. Elliptical curves are in no part circular. All curves
may, nevertheless, be approximately drawn as compositions of circular
arcs. The approximation to curves which are not circular may be easily
carried beyond any power of discrimination which we have in the sense
of vision. The method of curve-definition, which I have described,
though it may not be strictly mathematical, will be found satisfactory
for all purposes of Pure Design. It is very important that we should be
able to analyze our lines upon a single general principle; to discover
whether they are illustrations of Order. We must know whether any given
line, being orderly, is orderly in the sense of Harmony, Balance, or
Rhythm. It is equally important, if we wish to produce an orderly as
distinguished from a disorderly line, that we should have some general
principle to follow in doing it, that we should be able to produce
forms of Harmony or Balance or Rhythm in a line, if we wish to do so.


DIFFERENCES OF SCALE IN LINES

60. Having drawn a line of a certain shape, either straight or angular
or curved, or partly angular, partly curved, we may change the measure
of the line, in its length, without changing its shape. That is to
say, we may draw the line longer or shorter, keeping all changes of
direction, such as they are, in the same positions, relatively. In that
way the same shape may be drawn larger or smaller. That is what we mean
when we speak of a change of scale or of measure which is not a change
of shape.


DIFFERENCES OF ATTRACTION IN LINES

61. A line attracts attention in the measure of the tone-contrast which
it makes with the ground-tone upon which it is drawn. It attracts
attention, also, according to its length, which is an extension of the
tone-contrast. It attracts more attention the longer it is, provided it
lies, all of it, well within the field of vision. It attracts attention
also in the measure of its concentration.

[Illustration: Fig. 63]

Line “a” would attract less attention than it does if the
tone-contrast, black on a ground of white paper, were diminished,
if the line were gray, not black. In line “b” there is twice the
extension of tone-contrast there is in “a.” For that reason “b” is more
attractive. If, however, “a” were black and “b” were gray, “a” might be
more attractive than “b,” because of the greater tone-contrast.

[Illustration: Fig. 64]

In this illustration the curved line is more attractive than the
straight line because it is more concentrated, therefore more definite.
The extent of tone-contrast is the same, the lines being of the same
length.

[Illustration: Fig. 65]

In this line there is no doubt as to the greater attraction of the
twisted end, on account of the greater concentration it exhibits.
The extent of tone-contrast is the same at both ends. The force of
attraction in the twisted end of the line would be diminished if the
twisted end were made gray instead of black. The pull of concentration
at one end might, conceivably, be perfectly neutralized by the pull of
a greater tone-contrast at the other.

[Illustration: Fig. 66]

In “b” we have a greater extension of tone-contrast in a given space.
The space becomes more attractive in consequence.

This might not be the case, however, if the greater extension
of tone-contrast in one case were neutralized by an increase of
tone-contrast in the other.


THE ORDER OF HARMONY IN LINES

62. Harmony of Direction means no change of direction.

[Illustration: Fig. 67]

In this case we have a Harmony of Direction in the line, because it
does not change its direction.

63. Harmony of Angles. We may have Harmony in the repetition of a
certain relation of directions, as in an angle.

[Illustration: Fig. 68]

The angle up 45° and down 45° is here repeated seven times.

[Illustration: Fig. 69]

In this case we have a great many angles in the line, but they are all
right angles, so we have a Harmony of Angles.

[Illustration: Fig. 70]

In this case we have Harmony in the repetition of a certain relation
of angles, that is to say, in the repetition of a certain form of
angularity.

64. Equality of lengths or measures between the angles of a line means
a Harmony of Measures.

[Illustration: Fig. 71]

In this case, for example, we have no Harmony of Angles, but a Harmony
of Measures in the legs of the angles, as they are called.

65. We have a Harmony of Curvature in a line when it is composed wholly
of arcs of the same radius and the same angle.

[Illustration: Fig. 72]

This is a case of Harmony of Curvature. There is no change of direction
here, in the sequence of corresponding arcs.

[Illustration: Fig. 73]

Here, again, we have a Harmony of Curvature. In this case, however,
there is a regular alternation of directions in the sequence of
corresponding arcs. In this regular alternation, which is the
repetition of a certain relation of directions, there is a Harmony of
Directions.

[Illustration: Fig. 74]

In this case the changes of direction are abrupt (angular) as well
as gradual. There is no regular alternation, but the harmony of
corresponding arcs repeated will be appreciated, nevertheless.

66. Arcs produced by the same radius are in harmony to that extent,
having the radius in common.

[Illustration: Fig. 75]

This is an example of a harmony of arcs produced by radii of the same
length. The arcs vary in length.

67. Arcs of the same angle-measure produced by different radii are in
Harmony to the extent that they have an angle-measure in common.

[Illustration: Fig. 76]

This is an example.

Arcs having the same length but varying in both radius and angle may be
felt to be in Measure-Harmony. It is doubtful, however, whether lines
of the same length but of very different curvatures will be felt to
correspond. If the correspondence of lengths is not felt, visually, it
has no interest or value from the point of view of Pure Design.

68. Any line may be continued in a repetition or repetitions of
its shape, whatever the shape is, producing what I call a Linear
Progression. In the repetitions we have Shape-Harmony.

[Illustration: Fig. 77]

This is an example of Linear Progression. The character of the
progression is determined by the shape-motive which is repeated in it.

69. The repetition of a certain shape-motive in a line is not,
necessarily, a repetition in the same measure or scale. A repetition of
the same shape in the same measure means Measure and Shape-Harmony in
the progression. A repetition of the same shape in different measures
means Shape-Harmony without Measure-Harmony.

[Illustration: Fig. 78]

Here we have the repetition of a certain shape in a line, in a
progression of measures. That gives us Shape-Harmony and a Harmony of
Proportions, without Measure-Harmony.

70. In the repetition of a certain shape-motive in the line, the
line may change its direction abruptly or gradually, continuously or
alternately, producing a Linear Progression with changes of direction.

[Illustration: Fig. 79]

In Fig. 79 there is a certain change of direction as we pass from
one repetition to the next. In the repetition of the same change
of direction, of the same angle of divergence, we have Harmony. If
the angles of divergence varied we should have no such Harmony,
though we might have Harmony in the repetition of a certain relation
of divergences. Any repetition of a certain change or changes of
direction in a linear progression gives a Harmony of Directions in the
progression.

[Illustration: Fig. 80]

In this case there is a regular alternation of directions in the
repeats. The repeats are drawn first to the right, then up, and the
relation of these two directions is then repeated.

71. By inverting the motive of any progression, in single or in double
inversion, and repeating the motive together with its inversion, we are
able to vary the character of the progression indefinitely.

[Illustration: Fig. 81]

In this case we have a single inversion of the motive and a repetition
of the motive with its inversion. Compare this progression with the one
in Fig. 77, where the same motive is repeated without inversion.

[Illustration: Fig. 82]

Here we have the same motive with a double inversion, the motive
with its double inversion being repeated. The inversion gives us
Shape-Harmony without Harmony of Attitudes. We have Harmony, however,
in a repetition of the relation of two attitudes. These double
inversions are more interesting from the point of view of Balance than
of Harmony.


THE ORDER OF BALANCE IN LINES

72. We have Balance in a line when one half of it is the single or
double inversion of the other half; that is, when there is an equal
opposition and consequent equilibrium of attractions in the line. When
the axis of the inversion is vertical the balance is symmetrical.

[Illustration: Fig. 83]

There is Balance in this line because half of it is the single
inversion of the other half. The balance is symmetrical because the
axis is vertical. The balance, although symmetrical, is not likely
to be appreciated, however, 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 contrasts. The eye is not held at the center when
there is nothing to hold the eye on the center. Mark the center in any
way and the eye will go to it at once. A mark or accent may be put at
the center, or accents, corresponding and equal, may be put at equal
distances from the center in opposite directions. The eye will then be
held at the center by the force of equal and opposite attractions.

[Illustration: Fig. 84]

In this case the eye is held at the balance-center of the line by a
change of character at that point.

[Illustration: Fig. 85]

In this case the changes of character are at equal distances, in
opposite directions, from the center. The center is marked by a break.
The axis being vertical, the balance is a symmetrical one.

73. The appreciation of Balance in a line depends very much upon the
attitude in which it is drawn.

[Illustration: Fig. 86]

In this case the balance in the line itself is just as good as it is
in Fig. 85; but the axis of the balance being diagonal, the balance
is less distinctly felt. The balance is unsatisfactory because the
attitude of the line is one which suggests a falling down to the left.
It is the instability of the line which is felt, more than the balance
in it.

[Illustration: Fig. 87]

In this case of double inversion, also, we have balance. The balance
is more distinctly felt than it was in Fig. 86. The attitude is one of
stability. This balance is neither axial nor symmetrical, but central.

74. A line balances, in a sense, when its inclinations are balanced.

[Illustration: Fig. 88]

This line may be said to be in balance, as it has no inclinations,
either to the right or to the left, to suggest instability. The
verticals and the horizontals, being stable, look after themselves
perfectly well.

[Illustration: Fig. 89]

This line has two unbalanced inclinations to the left. It is,
therefore, less satisfactory than the line in Fig. 88, from the point
of view of Balance.

[Illustration: Fig. 90]

The two inclinations in this line counteract one another. One
inclination toward the left is balanced by a corresponding inclination
toward the right.

[Illustration: Fig. 91]

In this case, also, there is no inclination toward the left which is
not balanced by a corresponding inclination toward the right.

[Illustration: Fig. 92]

In this line, which is composed wholly of inclinations to the right
or left, every inclination is balanced, and the line is, therefore,
orderly in the sense of Balance; more so, certainly, than it would
be if the inclinations were not counteracted. This is the problem of
balancing the directions or inclinations of a line.

75. A line having no balance or symmetry in itself may become balanced.
The line may be regarded as if it were a series of dots close together.
The line is then a relation of positions indicated by dots. It is
a composition of attractions corresponding and equal. It is only
necessary, then, to find what I have called the center of equilibrium,
the balance-center of the attractions, and to indicate that center by a
symmetrical inclosure. The line will then become balanced.

[Illustration: Fig. 93]

Here is a line. To find the center of its attractions it may be
considered as if it were a line of dots, like this:—

[Illustration: Fig. 94]

The principle according to which we find the balance-center is stated
on page 23. The balance-center being found, it must be indicated
unmistakably. This may be done by means of any symmetrical inclosure
which will draw the eye to the center and hold it there.

[Illustration: Fig. 95]

In this case the balance-center is indicated by a rectangular
inclosure. This rectangle is not, however, in harmony of character with
the line inclosed by it, which is curved.

[Illustration: Fig. 96]

In this case the balance-center is indicated by a circle, which, being
a curve, is in harmony of character with the inclosed line, which is
also a curve. I shall call this Occult Balance to distinguish it from
the unmistakable Balance of Symmetry and other comparatively obvious
forms of Balance, including the balance of double inversions. As I
have said, on page 24, the symmetrical framing must be sufficiently
attractive to hold the eye steadily at the center, otherwise it does
not serve its purpose.


THE ORDER OF RHYTHM IN LINES

76. The eye, not being held on a vertical axis or on a balance-center,
readily follows any suggestion of movement.

[Illustration: Fig. 97]

In this case there is no intimation of any vertical axis or
balance-center. The figure is consequently unstable. There is a sense
of movement to the right. This is due, not only to the inclinations to
the right, but to the convergences in that direction.

[Illustration: Fig. 98]

In this case the movement is unmistakably to the left. In such cases we
have movement, but no Rhythm.

77. Rhythm requires, not only movement, but the order of regular and
marked intervals.

[Illustration: Fig. 99]

In Fig. 99 we have a line, a linear progression, which gives us the
feeling of movement, unmistakably. The movement, which in the motive
itself is not rhythmical, becomes rhythmical in its repetition at
regular, and in this case equal, intervals. The intervals are marked by
the repetitions.

78. It is a question of some interest to decide how many repetitions
are required in a Rhythm. In answer to this question I should say
three as a rule. A single repetition shows us only one interval, and
we do not know whether the succeeding intervals are to be equal or
progressive, arithmetically progressive or geometrically progressive.
The rhythm is not defined until this question is decided, as it will
be by two more repetitions. The measures of the rhythm might take the
form of a repeated relation of measures; a repetition, for example, of
the measures two, seven, four. 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 appreciated.

79. Any contrariety of movement in the motive is extended, of course,
to its repetitions.

[Illustration: Fig. 100]

In this case, for example, there are convergences and, consequently,
movements both up and down. This contrariety of movements is felt
through the whole series of repetitions. Other things being equal, I
believe the eye moves up more readily than down, so that convergences
downward have less effect upon us than corresponding convergences
upward.

[Illustration: Fig. 101]

In this case, by omitting the long vertical line I have diminished the
amount of convergence downward. In that way I have given predominance
to the upward movement. Instead of altogether omitting the long
vertical line, I might have changed its tone from black to gray. That
would cause an approximate instead of complete disappearance. It should
be remembered that in all these cases the habit of reading comes in to
facilitate the movements to the right. It is easier for the eye to move
to the right than in any other direction, other things being equal.
The movement back to the beginning of another line, which is of course
inevitable in reading, produces comparatively little impression upon
us, no more than the turning of the page. The habit of reading to the
right happens to be our habit. The habit is not universal.

80. Reading repetitions and alternations to the right, always, I, for
a long time, regarded such repetitions and alternations as rhythmical,
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 another. Why not read them to the left as well as to the right?
We at once decided that the movement in a Rhythm must be determined
by the character of the Rhythm itself, not by any habit of reading,
or any other habit, on our part. It was in that way that we came
to regard repetitions and alternations as illustrations of Harmony
rather than of Rhythm. 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 another, and when the movement is carried on from
repetition to repetition, from measure to measure.

81. The repetition of a motive at equal intervals, when there is no
movement in the motive, gives us no feeling of Rhythm.

[Illustration: Fig. 102]

In this case, for example, we have a repetition in the line of a
certain symmetrical shape. As there is no movement in the shape
repeated, there is no Rhythm in the repetition. There is nothing to
draw the eye in one direction rather than another. The attractions at
one end of the line correspond with the attractions at the other.

82. 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 place.

[Illustration: Fig. 103]

In this case the shape repeated is still symmetrical, but it is
repeated with a gradual diminution of scale and of intervals, by which
we are given a feeling of rhythmic movement. The change of scale and of
intervals, to induce a sense of rhythmic motion, must be regular. To
be regular the change must be in the terms of one or the other of the
regular progressions; the arithmetical progression, which proceeds by
a certain addition, or the geometrical, which proceeds by a certain
multiplication. The question may arise in this case (Fig. 103) whether
the movement of the Rhythm is to the right or to the left. I feel,
myself, that the movement is to the right. In diminishing the scale of
the motive and of the intervals we have, hardly at all, diminished the
extent of the tone-contrast in a given angle of vision. See Fig. 41,
p. 27, showing the increase of attractions from one visual angle to
another. At the same time we come at the right end of the progression
to two or more repetitions in the space of one. We have, therefore,
established the attraction of a crowding together at the right end
of the series. See the passage (p. 43) on the attractiveness of a
line. The force of the crowding together of attractions is, I feel,
sufficient to cause a movement to the right. It must be remembered,
however, 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 direction, so the movement of the Rhythm in that direction may not
be very strong after all. If the direction of any Rhythm is doubtful,
the Rhythm itself is doubtful.

83. The feeling of Rhythm may be induced, as I have said, by a gradual
increase of the number of attractions from measure to measure, an
increase of the extent of tone-contrast.

[Illustration: Fig. 104]

Increasing the extent of tone-contrast and the number of attractions in
the measures of the Rhythm in Fig. 103, we are able to force the eye to
follow the series in the direction contrary to the habit of reading,
that is to say from right to left.

A decrease in the forces of attraction in connection with a decrease
of scale is familiar to us all in the phenomena of perspective. The
gradual disappearance of objects in aerial perspective does away
with the attraction of a greater crowding together of objects in the
distance.

[Illustration: Fig. 105]

In this case the diminution of scale has been given up and there is
no longer any crowding together. There is no chance of this rhythm
being read from left to right except by an effort of the will. The
increase of attractions toward the left is much more than sufficient to
counteract the habit of reading.

84. The force of a gradual coming together of attractions, inducing
movement in the direction of such coming together, is noticeable in
spiral shapes.

[Illustration: Fig. 106]

In this case we have a series of straight lines with a constant and
equal change of direction to the right, combined with a regular
diminution of measures in the length of the lines, this in the terms
of an arithmetical progression. The movement is in the direction of
concentration and it is distinctly marked in its measures. The movement
is therefore rhythmical.

[Illustration: Fig. 107]

In this case we have a series of straight lines with a constant change
of direction to the right; but in this case the changes of measure in
the lines are in the terms of a geometrical progression. The direction
is the same, the pull of concentration perhaps stronger.

[Illustration: Fig. 108]

In this Rhythm there is an arithmetical gradation of measures
in the changes of direction, both in the length of the legs and
in the measure of the angles. The pull of concentration is, in
this case, very much increased. It is evident that the legs may
vary arithmetically and the angles geometrically; or the angles
arithmetically and the legs geometrically.

85. If, in the place of the straight lines, which form the legs, in
any of the examples given, are substituted lines which in themselves
induce movement, the feeling of Rhythm may be still further increased,
provided the directions of movement are consistent.

[Illustration: Fig. 109]

In this case the movement is in the direction of increasing
concentration and in the direction of the convergences.

If the movement of the convergences be contrary to the movement of
concentration, there will be in the figure a contrary motion which
may diminish or even entirely prevent the feeling of Rhythm. If the
movement in one direction or the other predominates, we may still
get the feeling of Rhythm, in spite of the drawback of the other and
contrary movement.

[Illustration: Fig. 110]

In this case the linear convergences substituted for the straight lines
are contrary to the direction of increasing concentration. The movement
is doubtful.

86. Corresponding rhythms, set in contrary motion, give us the feeling
of Balance rather than of Rhythm. The balance in such cases is a
balance of movements.

[Illustration: Fig. 111]

This is an example of corresponding and opposed rhythms producing the
feeling, not of Rhythm, but of Balance.


ATTITUDES


LINES IN DIFFERENT ATTITUDES

87. Any line or linear progression may be turned upon a center, and so
made to take an indefinite number and variety of attitudes. It may be
inverted upon an axis, and the inversion may be turned upon a center
producing another series of attitudes which, except in the case of
axial symmetry in the line, will be different from those of the first
series.

[Illustration: Fig. 112]

In this case the line changes its attitude.

[Illustration: Fig. 113]

In this case I have inverted the line, and turning the inversion upon a
center I get a different set of attitudes.

[Illustration: Fig. 114]

In this case, which is a case of axial symmetry in the line, the
inversion gives us no additional attitudes.


THE ORDER OF HARMONY IN THE ATTITUDES OF LINES

88. When any line or linear progression is repeated, without change of
attitude, we have a Harmony of Attitudes.

[Illustration: Fig. 115]

This is an illustration of Harmony of Attitudes. It is also an
illustration of Interval-Harmony.

89. We have a Harmony of Attitudes, also, in the repetition of any
relation of two or more attitudes, the relation of attitudes being
repeated without change of attitude.

[Illustration: Fig. 116]

We have here a Harmony of Attitudes due to the repetition of a certain
relation of attitudes, without change of attitude.


THE ORDER OF BALANCE IN THE ATTITUDES OF LINES

90. When a line or linear progression is inverted upon any axis or
center, and we see the original line and its inversion side by side, we
have a Balance of Attitudes.

[Illustration: Fig. 117]

The relation of attitudes I, II, of III, IV, and of I, II, III, IV,
is that of Symmetrical Balance on a vertical axis. The relation of
attitudes I, IV, and of II, III, is a relation of Balance but not
of Symmetrical Balance. This is true, also, of the relation of I,
III and of II, IV. Double inversions are never symmetrical, but they
are illustrations of Balance. The balance of double inversions is
central, not axial. These statements are all repetitions of statements
previously made about positions.


THE ORDER OF RHYTHM IN THE ATTITUDES OF LINES

91. It often happens that a line repeated in different attitudes
gives us the sense of movement. It does this when the grouping of the
repetitions suggests instability. The movement is rhythmical when it
exhibits a regularity of changes in the attitudes and in the intervals
of the changes.

[Illustration: Fig. 118]

In this case we have a movement to the right, but no Rhythm, the
intervals being irregular.

[Illustration: Fig. 119]

In this case the changes of attitude and the intervals of the changes
being regular, the movement becomes rhythmical. The direction of the
rhythm is clearly down-to-the-right.

92. In the repetition of any line we have a Harmony, due to the
repetition. If the line is repeated in the same attitude, we have a
Harmony of Attitudes. If it is repeated in the same intervals, we have
a Harmony of Intervals. We have Harmony, also, in the repetition of any
relation of attitudes or of intervals.

We have not yet considered the arrangement or composition of two or
more lines of different measures and of different shapes.


THE COMPOSITION OF LINES

93. By the Composition of Lines I mean putting two or more lines
together, in juxtaposition, in contact or interlacing. Our object in
the composition of lines, so far as Pure Design is concerned, is to
achieve Order, if possible Beauty, in the several modes of Harmony,
Balance, and Rhythm.


HARMONY IN THE COMPOSITION OF LINES

94. We have Harmony in line-compositions when the lines which are
put together correspond in all respects or in some respects, when
they correspond in attitudes, and when there is a correspondence of
distances or intervals.

[Illustration: Fig. 120]

In this case the lines of the composition correspond in tone, measure,
and shape, but not in attitude; and there is no correspondence in
distances or intervals.

[Illustration: Fig. 121]

In this case the attitudes correspond, as they did not in Fig. 120.
There is still no correspondence of intervals.

[Illustration: Fig. 122]

Here we have the correspondence of intervals which we did not have
either in Fig. 120 or in Fig. 121. There is not only a Harmony of
Attitudes and of Intervals, in this case, but the Harmony of a
repetition in one direction, Direction-Harmony. In all these cases we
have the repetition of a certain angle, a right angle, and of a certain
measure-relation between the legs of the angle, giving Measure and
Shape-Harmony.

95. The repetition in any composition of a certain relation of
measures, or of a certain proportion of measures, gives Measure-Harmony
to the composition. The repetition of the relation one to three in
the legs of the angle, in the illustrations just given, gives to the
compositions the Harmony of a Recurring Ratio. By a proportion I mean
an equality between ratios, when they are numerically different. The
relation of one to three is a ratio. The relation of one to three and
three to nine is a proportion. We may have in any composition the
Harmony of a Repeated Ratio, as in Figs. 120, 121, 122, or we may have
a Harmony of Proportions, as in the composition which follows.

[Illustration: Fig. 123]

96. To be in Harmony lines are not necessarily similar in all respects.
As I have just shown, lines may be in Shape-Harmony, without being
in any Measure-Harmony. Lines are approximately in harmony when they
correspond in certain particulars, though they differ in others. The
more points of resemblance between them, the greater the harmony. When
they correspond in all respects we have, of course, a perfect harmony.

[Illustration: Fig. 124]

This is a case of Shape-Harmony without Measure-Harmony and without
Harmony of Attitudes.

[Illustration: Fig. 125]

In this case we have a Harmony of Shapes and of Attitudes, without
Measure-Harmony or Harmony of Intervals. This is a good illustration of
a Harmony of Proportions.

Straight lines are in Harmony of Straightness because they are all
straight, however much they differ in tone or measure. They are in
Harmony of Measure when they have the same measure of length. The
measures of width, also, may agree or disagree. In every agreement we
have Harmony.

Angular lines are in Harmony when they have one or more angles in
common. The recurrence of a certain angle in different parts of a
composition brings Harmony into the composition. Designers are very apt
to use different angles when there is no good reason for doing so, when
the repetition of one would be more orderly.

[Illustration: Fig. 126]

The four lines in this composition have right angles in common. To
that extent the lines are in Harmony. There is also a Harmony in
the correspondence of tones and of width-measures in the lines.
Considerable Harmony of Attitudes occurs in the form of parallelisms.

[Illustration: Fig. 127]

These two lines have simply one angle in common, a right angle, and
the angle has the same attitude in both cases. They differ in other
respects.

[Illustration: Fig. 128]

In these three lines the only element making for Harmony, except the
same tone and the same width, is found in the presence in each line
of a certain small arc of a circle. Straightness occurs in two of the
lines but not in the third. There is a Harmony, therefore, between
two of the lines from which the third is excluded. There is, also, a
Harmony of Attitude in these two lines, in certain parallelisms.


BALANCE IN THE COMPOSITION OF LINES

97. Lines balance when in opposite attitudes. We get Balance in all
inversions, whether single or double.

[Illustration: Fig. 129]

Here similar lines are drawn in opposite attitudes and we get Measure
and Shape-Balance. In the above case the axis of balance is vertical.
The balance is, therefore, symmetrical. Symmetrical Balance is obtained
by the single inversion of any line or lines on a vertical axis. Double
inversion gives a Balance of Measures and Shapes on a center. We have
no Symmetry in double inversions. All this has been explained.

[Illustration: Fig. 130]

We have Measure and Shape-Balance on a center in this case. It is
a case of double inversion. It is interesting to turn these double
inversions on their centers, and to observe the very different effects
they produce in different attitudes.

98. Shapes in order to balance satisfactorily must be drawn in the same
measure, as in Fig. 131 which follows.

[Illustration: Fig. 131]

[Illustration: Fig. 132]

Here, in Fig. 132, we have Shape-Harmony without Measure-Harmony.
It might be argued that we have in this case an illustration of
Shape-Balance without Measure-Balance. Theoretically that is so, but
Shape-Balance without Measure-Balance is never satisfactory. If we
want the lines in Fig. 132 to balance we must find the balance-center
between them, and then indicate that center by a symmetrical inclosure.
We shall then have a Measure-Balance (occult) without Shape-Balance.

99. When measures correspond but shapes differ the balance-center may
be suggested by a symmetrical inclosure or framing. When that is done
the measures become balanced.

[Illustration: Fig. 133]

Here we have Measure-Harmony and a Measure-Balance without
Shape-Harmony or Shape-Balance. The two lines have different shapes but
the same measures, lengths and widths corresponding. The balance-center
is found for each line. See pp. 54, 55. Between the two centers is
found the center, upon which the two lines will balance. This center is
then suggested by a symmetrical inclosure. The balancing measures in
such cases may, of course, be turned upon their centers, and the axis
connecting their centers may be turned in any direction or attitude,
with no loss of equilibrium, so far as the measures are concerned.

[Illustration: Fig. 134]

The Balance of Measures here is just as good as it is in Fig.
133. The attitudes are changed but not the relation of the three
balance-centers. The change of shape in the inclosure makes no
difference.

100. Measure-Balance without Shape-Harmony or Shape-Balance is
satisfactory only when the balance-center is unmistakably indicated or
suggested, as in the examples which I have given.

101. There is another form of Balance which is to be inferred from what
I have said, on page 18, of the Balance of Directions, but it needs to
be particularly considered and more fully illustrated. I mean a Balance
in which directions or inclinations to the right are counteracted by
corresponding or equivalent directions or inclinations to the left. The
idea in its simplest and most obvious form is illustrated in Fig. 22,
on page 18. In that case the lines of inclination correspond. They do
not necessarily correspond except in the extent of contrast, which may
be distributed in various ways.

[Illustration: Fig. 135]

The balance of inclinations in this case is just as good as the balance
in Fig. 22. There is no symmetry as in Fig. 22. Three lines balance
against one. The three lines, however, show the same extent of contrast
as the one. So far as the inclinations are concerned they will balance
in any arrangement which lies well within the field of vision. 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 left.

[Illustration: Fig. 136]

This arrangement of the inclining lines is just as good as the
arrangement in Fig. 135. The inclinations may be distributed in any
way, provided they counteract one another properly.

[Illustration: Fig. 137]

In this case I have again changed the composition, and having
suggested the balance-center of the lines, as attractions, by a
symmetrical inclosure, I have added Measure-Balance (occult) to
Inclination-Balance. The Order in Fig. 137 is greater than the Order in
Figs. 135 and 136. In Fig. 137 two forms of Balance are illustrated,
in the other cases only one. The value of any composition lies in the
number of orderly connections which it shows.

[Illustration: Fig. 138]

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
inclinations. The horizontal part of the long line is stable, so it
needs no counteraction, but the other parts incline in various degrees,
to the left or to the right. Each inclining part requires, therefore,
either a corresponding line in a balancing direction, or two or more
lines of equivalent extension in that direction. In one case I have set
three lines to balance one, but they equal the one in length, that is
to say, in the extent of contrast. We have in Fig. 138 an illustration
of occult Measure-Balance and the Balance of Inclinations. I have
illustrated the idea of Inclination-Balance by very simple examples.
I have not considered the inclinations of curves, nor have I gone,
at all, into the more difficult problem of balancing averages of
inclination, when the average of two or more different inclinations of
different extents of contrast has to be counteracted. In Tone-Relations
the inclinations are of tone-contrasts, and a short inclination with a
strong contrast may balance a long inclination with a slight one, or
several inclinations of slight contrasts may serve to balance one of a
strong contrast. The force of any inclining line may be increased by
increasing the tone-contrast with the ground-tone. In tone-relations
the problem becomes complicated and difficult. The whole subject of
Inclination-Balance is one of great interest and worthy of a separate
treatise.


RHYTHM IN THE COMPOSITION OF LINES

102. We will first consider the Measure-Rhythms which result from a
gradual increase of scale, an increase in the extent of the contrasts.
The intervals must, in such Rhythms, be regular and marked. They may be
equal; they may alternate, or they may be regularly progressive.

[Illustration: Fig. 139]

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 lines, in that direction.

[Illustration: Fig. 140]

In this case I have, by means of regularly diminishing intervals, added
the force of a crowding together of contrasting edges to the force
of a gradual extension of them. The movement is still more strongly
up-to-the-right.

[Illustration: Fig. 141]

In this case a greater extension of contrasts pulls one way and a
greater crowding of contrasts the other. I think that crowding has
the best of it. The movement, though much retarded, is, I feel,
down-to-the-left rather than up-to-the-right, in spite of the fact that
the greater facility of reading to the right is added to the force of
extended contrasts.

103. Substituting unstable for stable attitudes in the examples just
given, we are able to add the movement suggested by instability of
attitude to the movement caused by a gradual extension of contrasts.

[Illustration: Fig. 142]

The movement up-to-the-right in Fig. 139 is here connected with an
inclination of all the lines down-to-the-right.

[Illustration: Fig. 143]

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 direction. A crowding together of the lines,
due to the diminution of intervals toward the left, adds force to the
movement in that direction.

[Illustration: Fig. 144]

In this case a movement up is caused by convergences, a movement down
by crowding. The convergences are all up, the crowding down. I think
that the convergences have it. I think the movement is, on the whole,
up. The intervals of the crowding down diminish arithmetically.

[Illustration: Fig. 145]

The convergences and the crowding of attractions are, here, both
up-to-the-right. The Rhythm is much stronger than it was in Fig. 144.
The intervals are those of an arithmetical progression.

[Illustration: Fig. 146]

The movement here is up-to-the-right, because of convergences in that
direction and an extension of contrasts in that direction.

[Illustration: Fig. 147]

In this case the two movements part company. One leads the eye
up-to-the-left, the other leads it up-to-the-right. The movement as
a whole is approximately up. As the direction of the intervals is
horizontal, not vertical, this is a case of movement without Rhythm.
The movement will become rhythmic only in a vertical repetition. That
is to say, the direction or directions of the movement in any Rhythm
and the direction or directions of its repetitions must coincide.
In Fig. 139, the movement is up-to-the-right, and the intervals may
be taken in the same direction, but in Fig. 147 the movement is up.
The intervals cannot be taken in that direction. It is, therefore,
impossible to get any feeling of Rhythm from the composition. We shall
get the feeling of Rhythm only when we repeat the movement in the
direction of the movement, which is up.

[Illustration: Fig. 148]

Here we have a vertical repetition of the composition given in Fig.
147. The result is an upward movement in regular and marked intervals,
answering to our understanding of Rhythm.

[Illustration: Fig. 149]

In this case we have a curved movement. The lines being spaced at
regular intervals, the movement is in regular and marked measures.
Its direction is due to an increase in the number of attractions, to
crowding, and to convergences. The movement is, accordingly, rhythmical.

[Illustration: Fig. 150]

The movement of Fig. 149 is here partly destroyed by an inversion and
opposition of attitudes and directions. The movement is, on the whole,
up, but it can hardly be described as rhythmical, because it has no
repetition upwards, as it has in the next illustration, Fig. 151.
Before proceeding, however, to the consideration of Fig. 151, I want to
call the attention of the reader to the fact that we have in Fig. 150 a
type of Balance to which I have not particularly referred. It is a case
of unsymmetrical balance on a vertical axis. The balancing shapes and
movements correspond. They incline in opposite directions. They diverge
equally from the vertical axis. The inclinations balance. At the same
time the composition does not answer to our understanding of Symmetry.
It is not a case of right and left balance on the vertical axis. The
shapes and movements are not right and left and opposite. One of the
shapes is set higher than the other. The balance is on the vertical. It
is obvious, but it is not symmetrical. It is a form of Balance which
has many and very interesting possibilities.

[Illustration: Fig. 151]

The repetition, in this case, of somewhat contrary movements, a
repetition at equal intervals on a vertical axis, gives us more Balance
than Rhythm. We feel, however, a general upward movement through the
repetitions and, as this movement is regular, it must be described as
rhythmical.

The feeling of upward movement in Fig. 151 is, no doubt, partly due
to the suggestion of upward growth in certain forms of vegetation.
The suggestion is inevitable. So far as the movement is caused by
this association of ideas it is a matter, not of sensation, but of
perception. The consideration of such associations of ideas does
not belong, properly, to Pure Design, where we are dealing with
sense-impressions, exclusively.

104. Rhythm is not inconsistent with Balance. 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 principles.

[Illustration: Fig. 152]

Here we have a Rhythm, of somewhat contrary movements, with
Balance,—Balance on a diagonal axis. The Balance is not satisfactory.
The Balance of Inclinations is felt more than the Balance of Shapes.

[Illustration: Fig. 153]

In this case we have the combination of a Rhythm of somewhat contrary,
but on the whole upward, movements with Symmetry.

If the diverging movements of Fig. 153 should be made still more
diverging, so that they become approximately contrary and opposite,
the feeling of a general upward movement will disappear. The three
movements to the right will balance the three movements to the left,
and we shall have an illustration of Symmetrical Balance, with no
Rhythm in the composition as a whole. It is doubtful whether the
balance of contrary and opposite movements is satisfactory. Our eyes
are drawn in opposite directions, away from the axis of balance,
instead of being drawn toward it. Our appreciation of the balance must,
therefore, be diminished. Contrary and opposite movements neutralize
one another, so we have neither rest nor movement in the balance of
contrary motions.

By bringing the divergences of movement together, gradually, we shall
be able to increase, considerably, the upward movement shown in Fig.
153. At the same time, the suggestion of an upward growth of vegetation
becomes stronger. The increase of movement will be partly explained by
this association of ideas.

[Illustration: Fig. 154]

Here all the movements are pulled together into one direction. The
Rhythm is easier and more rapid. The Balance is just as good. The
movement in this case is no doubt facilitated by the suggestion of
upward growth. It is impossible to estimate the force which is added by
such suggestions and associations.

[Illustration: Fig. 155]

Here the movements come together in another way.

The number and variety of these illustrations might, of course, be
indefinitely increased. Those which I have given will, I think, serve
to define the principal modes of line-composition, when the lines are
such as we choose to draw.


THE COMPOSITION OF VARIOUS LINES

105. In most of the examples I have given I have used repetitions of
the same line or similar lines. When the lines which are put together
are not in harmony, when they are drawn, as they may be, without any
regard to the exigencies of orderly composition, the problem becomes
one of doing the best we can with our terms. We try for the greatest
possible number of orderly connections, connections making for Harmony,
Balance, and Rhythm. We arrange the lines, so far as possible, in
the same directions, giving them similar attitudes, getting, in
details, as much Harmony of Direction and of Attitudes as possible,
and establishing as much Harmony of Intervals as possible between the
lines. 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 Rhythm. A suggestion
of Symmetry is sometimes possible. Occult Balance is possible in
all cases, as it depends, not upon the terms balanced, but upon the
indication of a center of attractions by a symmetrical framing of them.

Let us take seven lines, with a variety of shape-character, with as
little Shape-Harmony as possible, and let us try to put these lines
together in an orderly way.

[Illustration: Fig. 156]

With these lines, which show little or no harmony of character, which
agree only in tone and in width-measure, lines which would not be
selected certainly as suitable material for orderly compositions, I
will make three compositions, getting as much Order into each one as I
can, just to illustrate what I mean. I shall not be able to achieve a
great deal of Order, but enough, probably, to satisfy the reader that
the effort has been worth while.

[Illustration: Fig. 157]

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-Harmony.

[Illustration: Fig. 158]

In this case, also, I have achieved a suggestion of Order, if not
Order itself. Consider the comparative disorder in Fig. 156, where no
arrangement has been attempted.

[Illustration: Fig. 159]

Here is another arrangement of the same terms. Fortunately, in all of
these cases, the lines agree in tone and in width-measure. That means
considerable order to begin with.

This problem of taking any terms and making the best possible
arrangement of them is a most interesting problem, and the ability
to solve it has a practical value. We have the problem to solve in
every-day life; when we have to arrange, as well as we can, in the
best possible order, all the useful and indispensable articles we
have in our houses. To achieve a consistency and unity of effect
with a great number and variety of objects is never easy. It is
often very difficult. It is particularly difficult when we have no
two objects alike, no correspondence, no likeness, to make Harmony.
With the possibility of repetitions and inversions the problem
becomes comparatively easy. With repetitions and inversions we have
the possibility, not only of Harmony, but of Balance and Rhythm.
With inversions we have the possibility, not only of Balance, but of
Symmetrical Balance, 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 not. We feel the Order of Symmetry and we are satisfied.

[Illustration: Fig. 160]

In this design I repeat an inversion of the arrangement in Fig. 158.
The result is a symmetry, and no one is likely to ask whether the
elements of which it is composed are harmonious or not. By inversions,
single and double, it is possible to achieve the Order of Balance, in
all cases.

[Illustration: Fig. 161]

For this design I have made another arrangement of my seven lines. The
arrangement suggests movement. In repeating the arrangement at regular
and equal intervals, without change of attitude, I produce the effect
of Rhythm. Without resorting to inversion, it is difficult to make
even an approximation to Symmetry with such terms (see Fig. 157),
but there is little or no difficulty in making a consistent or fairly
consistent movement out of them, which, being repeated at regular
intervals, without change of attitude, or with a gradual change of
attitude, will produce the effect of Rhythm.

Up to this point I have spoken of the composition of lines in
juxtaposition, that is to say, the lines have been placed near together
so as to be seen together. I have not spoken of the possibilities of
Contact and Interlacing. The lines in any composition may touch one
another or cross one another. The result will be a composition of
connected lines. In certain cases the lines will become the outlines of
areas. I will defer the illustration of contacts and interlacings until
I come to consider the composition of outlines.




OUTLINES


DEFINITION OF OUTLINES

106. Outlines are lines which, returning to themselves, make inclosures
and describe areas of different measures and shapes. What has been
said of lines may be said, also, of outlines. It will be worth
while, however, to give a separate consideration to outlines, as a
particularly interesting and important class of lines.

As in the case of dots and lines, I shall disregard the fact that the
outlines may be drawn in different tones, making different contrasts of
value, color, or color-intensity with the ground-tone upon which they
are drawn. I shall, also, disregard possible differences of width in
the lines which make the outlines. I shall confine my attention, here,
to the measures and shapes of the outlines and to the possibilities of
Harmony, Balance, and Rhythm in those measures and shapes.


HARMONY, BALANCE, AND RHYTHM IN OUTLINES

107. What is Harmony or Balance or Rhythm in a line is Harmony,
Balance, or Rhythm in an Outline.

[Illustration: Fig. 162]

In this outline we have Measure-Harmony in the angles, Measure-Harmony
of lengths in the legs of the angles, Measure and Shape-Balance on a
center and Symmetry on the vertical axis. The same statement will be
true of all polygons which are both equiangular and equilateral, when
they are balanced on a vertical axis.

[Illustration: Fig. 163]

In this case we have Measure-Harmony of angles but no Measure-Harmony
of lengths in the legs of the angles. We have lost Measure and
Shape-Balance on a center which we had in the previous example.

[Illustration: Fig. 164]

In this case the angles are not all in a Harmony of Measure; but we
have Measure-Harmony of lengths in the legs of the angles, and we have
Measure and Shape-Balance on a center. There is a certain Harmony in
the repetition of a relation of two angles.

[Illustration: Fig. 165]

In this case we have Measure-Harmony in the angles, which are equal,
and a Harmony due to the repetition of a certain measure-relation in
the legs of the angles. As in Fig. 162, we have here a Measure and
Shape-Balance on a center and Symmetry on the vertical axis. This
polygon is not equilateral, but its sides are symmetrically disposed.
Many interesting and beautiful figures may be drawn in these terms.

[Illustration: Fig. 166]

We have in the circle the most harmonious of all outlines. The Harmony
of the circle is due to the fact that all sections of it have the same
radius and equal sections of it have, also, the same angle-measure.
The circle is, of course, a perfect illustration of Measure and
Shape-Balance on a center. The balance is also symmetrical. We have a
Harmony of Directions in the repetition of the same change of direction
at every point of the outline, and we have a Harmony of Distances in
the fact that all points of the outline are equally distant from the
balance-center, which is unmistakably felt.

[Illustration: Fig. 167]

The Ellipse is another example of Measure and Shape-Balance on a
center. In this attitude it is also an illustration of Symmetry.

[Illustration: Fig. 168]

In this case we still have balance but no symmetry. The attitude
suggests movement. We cannot help feeling that the figure is falling
down to the left. A repetition at equal intervals would give us Rhythm.

[Illustration: Fig. 169]

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 measures. That gives Shape-Harmony without
Measure-Harmony. This is a case of Symmetrical Balance. It is also
a case of rhythmic movement upward. The movement is mainly due to
convergences.

[Illustration: Fig. 170]

In this case, also, the shapes repeated on the right side and on the
left side of the outline show movements which become in repetitions
almost rhythmical. The movement is up in spite of the fact that each
part of the movement is, in its ending, down. We have in these examples
symmetrical balance on a vertical axis combined with rhythm on the same
axis. It may be desirable to find the balance-center of an outline
when only the axis is indicated by the character of the outline. The
principle which we follow is the one already described. In Fig. 169 we
have a symmetrical balance on a vertical axis, but there is nothing to
indicate the balance-center. It lies on the axis somewhere, but there
is nothing to show us where it is. Regarding the outline as a line
of attractions, the eye is presumably held at their balance-center,
wherever it is. Exactly where it is is a matter of visual feeling. The
balance-center being ascertained, it may be indicated by a symmetrical
outline or inclosure, the center of which cannot be doubtful.

[Illustration: Fig. 171]

The balance-center, as determined by visual feeling, is here clearly
indicated. In this case besides the balance on a center we have also
the Symmetry which we had in Fig. 169.

[Illustration: Fig. 172]

The sense of Balance is, in this case, much diminished by the change of
attitude in the balanced outline. We have our balance upon a center,
all the same; but the balance on the vertical axis being lost, we have
no longer any Symmetry. It will be observed that balance on a center is
not inconsistent with movement. If this figure were repeated at equal
intervals without change of attitude, or with a gradual change, we
should have the Rhythm of a repeated movement.

In some outlines only certain parts of the outlines are orderly, while
other parts are disorderly.

[Illustration: Fig. 173]

In the above outline we have two sections corresponding in measure and
shape-character and in attitude. We have, therefore, certain elements
of the outline in harmony. We feel movement but not rhythm in the
relation of the two curves. There is no balance of any kind.

We ought to be able to recognize elements of order as they occur in any
outline, even when the outline, as a whole, is disorderly.

[Illustration: Fig. 174]

In order to balance the somewhat irregular outline given in Fig. 173,
we follow the procedure already described. The effect, however, is
unsatisfactory. The composition lacks stability.

[Illustration: Fig. 175]

The attitude of the figure is here made to conform, as far as possible,
to the shape and attitude of the symmetrical framing: this for the sake
of Shape and Attitude-Harmony. The change of attitude gives greater
stability.


INTERIOR DIMENSIONS OF AN OUTLINE

108. A distinction must be drawn between the measures of the outline,
as an outline, and the measures of the space or area lying within the
outline: what may be called the interior dimensions of the outline.

[Illustration: Fig. 176]

In this case we must distinguish between the measures of the outline
and the dimensions of the space inclosed within it. When we consider
the measures—not of the outline, but of the space or area inside of the
outline—we may look in these measures, also, for Harmony, for Balance,
or for Rhythm, and for combinations of these principles.


HARMONY IN THE INTERIOR DIMENSIONS OF AN OUTLINE

109. We have Harmony in the interior dimensions of an outline when
the dimensions correspond or when a certain relation of dimensions is
repeated.

[Illustration: Fig. 177]

In this case we have an outline which shows a Harmony in the
correspondence of two dimensions.

[Illustration: Fig. 178]

In this case we have Harmony in the correspondence of all vertical
dimensions, Harmony in the correspondence of all horizontal dimensions,
but no relation of Harmony between the two. It might be argued, from
the fact that the interval in one direction is twice that in the other,
that the dimensions have something in common, namely, a common divisor.
It is very doubtful, however, whether this fact is appreciable in the
sense of vision. The recurrence of any relation of two dimensions
would, no doubt, be appreciated. We should have, in that case,
Shape-Harmony.

[Illustration: Fig. 179]

In this circle we have a Measure-Harmony of diameters.

[Illustration: Fig. 180]

In this case we have a Harmony due to the repetition of a certain ratio
of vertical intervals: 1:3, 1:3, 1:3.

110. 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 contact. The more rapid the
convergence the more rapid the movement.

[Illustration: Fig. 181]

In this case we have not only symmetrical balance on a vertical axis
but movement, in the upward and rapid convergence of the sides BA and
CA toward the angle A. The question may be raised whether the movement,
in this case, is up from the side BC to the angle A or down from the
angle A toward the side BC. I think that the reader will agree that
the movement is from the side BC into the angle A. In this direction
the eye is more definitely guided. The opposite movement from A toward
BC is a movement in diverging directions which the eye cannot follow
to any distance. As the distance from BC toward A decreases, the
convergence of the sides BA and CA is more and more helpful to the eye
and produces the feeling of movement. The eye finds itself in a smaller
and smaller space, with a more and more definite impulse toward A.
It is a question whether the movement from BC toward A is rhythmical
or not. The movement is not connected with any marked regularity of
measures. I am inclined to think, however, that the gradual and even
change of measures produces the feeling of equal changes in equal
measures. If so, the movement is rhythmical.

When the movement of the eye in any convergence is a movement in
regular and marked measures, as in the example which follows, the
movement is rhythmical, without doubt.

[Illustration: Fig. 182]

The upward movement in this outline, being regulated by measures which
are marked and equal, the movement is certainly rhythmical, according
to our understanding and definition of Rhythm. Comparing Fig. 181 with
Fig. 182, the question arises, whether the movement in Fig. 182 is felt
to be any more rhythmical than the movement in Fig. 181. The measures
of the movement in Fig 181 are not marked, but I cannot persuade myself
that they are not felt in the evenness of the gradation. The movement
in Fig. 181 is easier than it is in Fig. 182, when the marking of the
measures interferes with the movement.

[Illustration: Fig. 183]

In this case we have another illustration like Fig. 182, only the
measures of the rhythm are differently marked. The force of the
convergence is greatest in Fig. 181. It is somewhat diminished by the
measure-marks in Fig. 182. It is still further diminished, in Fig. 183,
by the angles that break the measures.

[Illustration: Fig. 184]

In this case the movement is more rapid again, the measures being
measures of an arithmetical progression. There is a crowding together
of attractions in the direction of the convergence, and the movement
is easier than it is in Fig. 183, in spite of the fact that the lines
of convergence are more broken in Fig. 184. There is an arithmetical
diminution of horizontal as well as of vertical lines in Fig. 184.

[Illustration: Fig. 185]

In this case the measures of the rhythm are in the terms of a
geometrical progression. The crowding together of attractions is still
more rapid in this case and the distance to be traversed by the eye is
shorter. The convergence, however, is less compelling, the lines of the
convergence being so much broken—unnecessarily.

The movement will be very much retarded, if not prevented, by having
the movement of the crowding and the movement of the convergence
opposed.

[Illustration: Fig. 186]

There is no doubt that in this example, which is to be compared with
that of Fig. 184, the upward movement is almost prevented. There are
here two opposed movements: that of the convergence upward and that
of a crowding together of attractions downward. The convergence is
stronger, I think, though it must be remembered that it is probably
easier for the eye to move up than down, other things being equal.

111. The movements in all of these cases may be enhanced by
substituting for the straight lines shapes which are in themselves
shapes of movement.

[Illustration: Fig. 187]

Here, for example, the movement of Fig. 184 is facilitated and
increased by a change of shape in the lines, lines with movement being
substituted for lines which have no movement, beyond the movement of
the convergence.

[Illustration: Fig. 188]

In Fig. 188 all the shapes have a downward movement which contradicts
the upward movement of convergence. The movement down almost prevents
the movement up.

112. The movement of any convergence may be straight, angular, or
curved.

[Illustration: Fig. 189]

In this case the movement of the convergence is angular. It should
be observed that the movement is distributed in the measures of an
arithmetical progression, so that we have, not only movement, but
rhythm.

[Illustration: Fig. 190]

In this case the movement of convergence is in a curve. The stages of
the movement, not being marked, the movement is not rhythmical, unless
we feel that equal changes are taking place in equal measures. I am
inclined to think that we do feel that. The question, however, is one
which I would rather ask than answer, definitely.

[Illustration: Fig. 191]

In this case the movement is, unquestionably, rhythmical, because
the measures are clearly marked. The measures are in an arithmetical
progression. They diminish gradually in the direction of the
convergence, causing a gradual crowding together of attractions in that
direction.

Substituting, in the measures, shapes which have movement, the movement
of the rhythm may be considerably increased, as is shown in the example
which follows.

[Illustration: Fig. 192]

This is a case in which the movement is, no doubt, facilitated by an
association of ideas, the suggestion of a growth.

113. The more obvious the suggestion of growth, the more inevitable is
the movement in the direction of it, whatever that direction is. It
must be understood, however, that the movement in such cases is due to
an association of ideas, not to the pull of attractions in the sense of
vision. The pull of an association of ideas may or may not be in the
direction of the pull of attractions.

[Illustration: Fig. 193]

In Fig. 193 we have an illustration of a rhythmic movement upward. The
upward movement is due quite as much to an association of ideas, the
thought of a growth of vegetation, as it is to mere visual attractions.
It happens that the figure is also an illustration of Symmetrical
Balance. As we have Harmony in the similarity of the opposite sides,
the figure is an illustration of combined Harmony, Balance, and Rhythm.

There is another point which is illustrated in Fig. 193. It is this:
that we may have rhythmic movement in an outline, or, indeed, in any
composition of lines, which shows a gradual and regular change from
one shape to another; which shows a gradual and regular evolution or
development of shape-character; provided the changes are distributed
in regular and marked measures and the direction of the changes, the
evolution, the development, is unmistakable; as it is in Fig. 193. The
changes of shape in the above outline are changes which are gradual and
regular and suggest an upward movement unmistakably. The movement,
however, involves a comparison of shape with shape, so it is as much
a matter of perception as of sensation. Evolutions and developments
in Space, in the field of vision, are as interesting as evolutions
and developments in the duration of Time. When the changes in such
movements are regular, when they take place in regular and marked
measures, when we must take them in a certain order, the movements are
rhythmical, whether in Time or in Space.


THE ATTITUDES OF OUTLINES

114. Any outline, no matter what dimensions or shape it has, may be
turned upon a center and in that way made to take a great number and
variety of attitudes. Not only may it be turned upon a center but
inverted upon an axis. Being inverted, the inversion may be turned upon
a center and made to take another series of attitudes, and this second
series of attitudes will be different from the first series, except
in cases of axial symmetry in the outline or area. It must be clearly
understood that a change of attitude in any outline or area is not a
change of shape.

115. What has been said of Harmony, Balance, and Rhythm in the
attitudes of a line applies equally well to outlines and to the spaces
defined by them.


THE ARRANGEMENT AND COMPOSITION OF OUTLINES

116. By the composition of outlines I mean putting two or more
outlines in juxtaposition, in contact or interlacing. In all cases of
interlacing, of course, the shape-character of the interlacing outlines
is lost. The outlines become the outlines of other areas and of a
larger number of them. Our object in putting outlines together is, in
Pure Design, to illustrate the orders of Harmony, Balance, and Rhythm,
to achieve Order, as much as we can, if possible Beauty.

I will now give a series of examples with a brief analysis or
explanation of each one.

[Illustration: Fig. 194]

In this case we have Shape-Harmony in the outlines and also a Harmony
of Attitudes.

[Illustration: Fig. 195]

Here we have another illustration of the Harmony of Shapes and of
Attitudes, with a Harmony of Intervals, which we did not have in Fig.
194.

[Illustration: Fig. 196]

In this case we have a Harmony of Attitudes and of Intervals (the
Harmony of a repeated Relation of Intervals) in what may be called an
All-Over Repetition.

[Illustration: Fig. 197]

In this case we have a Harmony of Attitudes in the repetition of
a relation of two opposite attitudes; this with Shape-Harmony and
Interval-Harmony.

[Illustration: Fig. 198]

In this case we have a Symmetry of Attitudes, with Shape-Harmony and
Interval-Harmony. Turning the composition off the vertical axis we
should have Balance but no Symmetry. The balance-center will be felt in
all possible attitudes of this composition.

[Illustration: Fig. 199]

In this case I have repeated a certain outline, which gives me the
Harmony of a repetition,—this in connection with a progression in
scale, so that the Harmony is Shape-Harmony, not Measure-Harmony. We
have in the attitude of this repetition a Symmetrical Balance. The
movement is rhythmical and the direction of the rhythm is up.

The movement in Fig. 199 might be indefinitely increased by the
introduction into it of a gradation of attractions, increasing in
number. That means that the extent of contrasting edges is increased
from measure to measure.

[Illustration: Fig. 200]

The addition of details, increasing in number from measure to measure
upward, increases the movement of the rhythm in that direction.

[Illustration: Fig. 201]

Taking the arrangement of Fig. 199 and repeating it six times at
diverging angles of sixty degrees, we get what may be called a radial
balance upon the basis of a hexagon.

Outlines may be drawn one inside of the other or several inside of one.

[Illustration: Fig. 202]

This is a case of outlines-within-outlines and of Shape-Harmony without
Measure-Harmony. There is, also, a Harmony of Attitudes, but no Harmony
of Intervals.

Interesting results may be produced by drawing a series of outlines
similar in shape, the second inside of the first, the third inside of
the second, and so on.

[Illustration: Fig. 203]

In this case, for example, we have the outlines drawn one inside of the
other. The outlines have all the same shape, but different measures.
It is a case of Shape-Harmony and Harmony of Attitudes, without
Measure-Harmony, and without any Harmony of Intervals. This is a very
interesting and important form of Design which has many applications.

[Illustration: Fig. 204]

In this case, also, we have Shape-Harmony without Measure-Harmony. We
have a Harmony of Attitudes and also of Intervals, the spaces between
the outlines corresponding.

[Illustration: Fig. 205]

Here we have the Harmony of an alternation of Attitudes repeated, with
Shape-Harmony, without Measure-Harmony.

In all forms of design in which we have the concentric repetition
of a certain outline we have, in connection with the feeling of a
central balance, the feeling of a movement or movements toward the
center. These movements are due to convergences. Movements carrying
the eye away from the center, in opposite directions, interfere with
the feeling of balance. The feeling is enhanced, however, when the
movements converge and come together.

We may have not only an alternation of attitudes in these cases, but an
alternation of shape-character.

[Illustration: Fig. 206]

The repetition of outlines-within-outlines may be concentric or
eccentric. The repetition is concentric in Fig. 204. It is eccentric in
the example which follows.

[Illustration: Fig. 207]

In all eccentric repetitions like this we have a lack of balance and
the suggestion of movement. The direction of the movement is determined
by the direction of convergences and of the crowding together of
attractions. The movement in Fig. 207 is up-to-the-left, unmistakably.
Repeating the composition of Fig. 207, at regular intervals and without
change of attitude, the movement up-to-the-left would be extended to
the repetitions and the movement would be rhythmical. The movement is
rhythmical in the composition itself, as shown in Fig. 207, because the
movement in the composition is regular in character, regular in its
measures, and unmistakable in direction.

[Illustration: Fig. 208]

This is another example of eccentric repetition in
outlines-within-outlines. As in Fig. 207, we have movement, and the
movement is rhythmical.

In the examples I have given there have been no contacts and no
interlacings. Contacts and interlacings are possible.

[Illustration: Fig. 209]

Here, for an example, is an instance of contact, with Harmony of
Attitudes and a Symmetrical Balance on a vertical axis.

[Illustration: Fig. 210]

In this case we have contacts, with no Harmony of Attitudes. The
balance which is central as well as axial is in this attitude of the
figure symmetrical.

[Illustration: Fig. 211]

Here we have a similar composition with interlacings.

When the outlines have different shapes as well as different measures,
particularly when the outlines are irregular and the shapes to be put
together are, in themselves, disorderly, the problem of composition
becomes more difficult. The best plan is to arrange the outlines in
a group, making as many orderly connections as possible. Taking any
composition of outlines and repeating it in the different ways which
I have described, it is generally possible to achieve orderly if not
beautiful results.

[Illustration: Fig. 212]

Here are five outlines, very different in shape-character. Let us see
what can be done with them. A lot of experiments have to be tried,
to find out what connections, what arrangements, what effects are
possible. The possibilities cannot be predicted. Using tracing-paper, a
great many experiments can be tried in a short time, though it may take
a long time to reach the best possible results.

[Illustration: Fig. 213]

In this example I have tried to make a good composition with my five
outlines. The problem is difficult. The outlines to be combined
have so little Harmony. The only Harmony we can achieve will be the
Harmony of the same arrangement of shapes repeated, which amounts to
Shape-Harmony. Inversions will give us the satisfaction of Balance.
Inversions on a vertical axis will give us the satisfaction of
Symmetry. In the design above given I have achieved simply the Harmony
of a relation of shapes repeated, with Rhythm. The Rhythm is due to
the repetition of a decidedly unbalanced group of elements with a
predominance of convergences in one direction. The movement is on
the whole up, in spite of certain downward convergences. The upward
convergences predominate. There are more inclinations to the right
than to the left, but the composition which is repeated is unstable in
its attitude and suggests a falling away to the left. The resultant of
these slight divergences of movement is a general upward movement.

[Illustration: Fig. 214]

In this case I have less difficulty than in Fig. 213, having left out
one of my five outlines, the one most difficult to use with the others.
There is a great gain of Harmony. There is a Harmony of Intervals and
a Harmony in the repetition of the same grouping of outlines. In the
outlines themselves we have a Harmony of curved character, and the
curves fit one another very well, owing to a correspondence of measure
and shape-character in certain parts. In such cases we are able to
get considerable Harmony of Attitudes into the composition. There is
a Harmony of Attitudes in the repeats, as well as in certain details.
Comparing Fig. 214 with Fig. 213, I am sure the reader will agree that
we have in Fig. 214 the larger measure of Harmony.

[Illustration: Fig. 215]

In Fig. 215 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 outlines. Whatever merit the composition
has is due solely to the art of composition, to the presence of
Attitude-Harmony, Interval-Harmony, and to the inversions and
repetitions; inversions giving Balance, repetitions giving Harmony.

While it is important to recognize the limitation of the terms in this
problem, it is important to yield to any definite impulse which you may
feel, though it carries you beyond your terms. The value of a rule is
often found in breaking it for a good and sufficient reason; and there
is no better reason than that which allows you, in Design, to follow
any impulse you may have, provided that it is consistent with the
principles of Order.

[Illustration: Fig. 216]

In this case an effort has been made to modify the terms already used
so as to produce a more rapid and consistent movement. Advantage has
been taken of the fact that the eye is drawn into all convergences, so
all pointing down has been, so far as possible, avoided. The movement
is distinctly rhythmical.

In the previous examples I have avoided contacts and interlacing. It
was not necessary to avoid them.

[Illustration: Fig. 217]

117. What is done, in every case, depends upon the designer who does
it. He follows the suggestions of his imagination, not, however, with
perfect license. The imagination acts within definite limitations,
limitations of terms and of principles, limitations of certain modes in
which terms and principles are united. In spite of these limitations,
however, if we give the same terms, the same principles, and the same
modes to different people, they will produce very different results.
Individuality expresses itself in spite of the limitation of terms and
modes, and the work of one man will be very different from the work of
another, inevitably. We may have Order, Harmony, Balance, or Rhythm
in all cases, Beauty only in one case, perhaps in no case. It must be
remembered how, in the practice of Pure Design, we aim at Order and
hope for Beauty. Beauty is found only in supreme instances of Order,
intuitively felt, instinctively appreciated. The end of the practice of
Pure Design is found in the love of the Beautiful, rather than in the
production of beautiful things. Beautiful things are produced, not by
the practice of Pure Design, but out of the love of the Beautiful which
may be developed by the practice.


AREAS

118. I have already considered the measures of areas, in discussing
the interior dimensions of outlines, and in discussing the outlines
themselves I have considered the shapes of areas. 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
positions, measures, and shapes.


LINEAR AREAS

119. Before proceeding, however, to the subject of tones and
tone-relations, I must speak of a peculiar type of area which is
produced by increasing or diminishing the width of a line. I have
postponed the discussion of measures of width in lines until now.

A line may change its width in certain parts or passages. It may
become wider or narrower as the case may be. The wider it is the more
it is like an area. If it is sufficiently wide, the line ceases to be
a line, and becomes an area. The line may change its width abruptly
or gradually. The effect of the line is by these changes indefinitely
varied. The line of Design is not the line of Geometry.

120. Considerable interest may be given to what I have called Linear
Progressions by changing the width of the line at certain points, in
certain passages, and more or less abruptly. The changes will be like
accents in the line, giving variety and, possibly, an added interest.

[Illustration: Fig. 218]

Let us take this line as the motive of a linear progression. We can
give it a different character, perhaps a more interesting character, by
widening all the vertical passages, as follows:—

[Illustration: Fig. 219]

This is what we get for a motive by widening all the vertical passages.

[Illustration: Fig. 220]

This is what we get for a motive by widening all the horizontal
passages.

[Illustration: Fig. 221]

Compare this Progression, in which I have used the motive of Fig.
219, with that of Fig. 77, p. 47. The accents, which in Fig. 221
occur in every repetition of the motive, might occur only in certain
repetitions, at certain intervals.

[Illustration: Fig. 222]

It is not necessary that the changes in the width of the line be
abrupt, as in the examples just given. The width of the line may
increase or diminish gradually, in which case we may have, not only
accents in the line, but movements due to gradations of dimension,
to convergences, or to an increase or gradual crowding together of
attractions in a series of visual angles.

[Illustration: Fig. 223]

In this case we have a gradual increase followed by a diminution of
the width of the line in certain parts, and these changes occur at
equal intervals. A certain amount of rhythmic movement is given to
the progression by such accents, provided the direction of movement
is unmistakable, which it is not in this case. It is not at all clear
whether the movement is down-to-the-right or up-to-the-left. It seems
to me about as easy to move in one direction as in the other.

[Illustration: Fig. 224]

In this case there is less doubt about the movement. It seems to
be down-to-the-right. The eye is pulled through an increase of
width-measures toward a greater extension and crowding together of
contrasting edges.

[Illustration: Fig. 225]

Substituting outlines for areas in the previous illustration, we are
surprised, perhaps, to find that the movement is reversed. We go
up-to-the-left in this case, not down-to-the-right. The pull of a
greater extension of tone-contrast in a given area was, in Fig. 224,
sufficient to overcome the pull of a less evident convergence in the
other direction.

By increasing or diminishing the width of lines, doing it gradually
or abruptly, we are able to control the movement of the eye to an
indefinite extent. This is one of the important resources of the
designer’s art. Its use is not limited to forms of Linear Progression,
but may be extended to all forms of Design in which lines are used.

[Illustration: Fig. 226]

In this case, for example, the eye follows the direction of
convergences, but we can easily force it to turn and move in the
opposite direction, by widening the lines in that direction, thus
increasing the extent of contrasting edge until it more than
outbalances the convergences; as in the following illustration:—

[Illustration: Fig. 227]


THE ARRANGEMENT AND COMPOSITION OF AREAS

121. What has been said about the composition of Lines and Outlines
applies equally well to the composition of Areas, so far as they
are distinguished and defined by outlines. We will now proceed to
consider areas as distinguished and defined, not by outlines, but by
tone-contrasts. The composition of lines and outlines is one thing,
the composition of tones in different positions, measures, and shapes
is another. In putting lines and outlines together we draw. The point
of view is that of drawing. In putting tones in different positions,
measures, and shapes we paint. The point of view is that of the
painting.




TONES AND TONE-RELATIONS


122. Up to this point I have avoided the consideration of Tones and
Tone-Relations. I have spoken of possible changes of tone in dots and
in lines; changes of value, of color, of color-intensity; but it is not
in dots nor in lines that these changes call for particular attention.
Our interest has been in the positions, measures, shapes, and
attitudes of dots and lines, and in the possibilities of arrangement
and composition. When it comes to the consideration of areas and
area-systems, however, the subject of tone-relations becomes one of the
greatest interest, because areas are defined and distinguished, not
only by their outlines, but quite as much by differences of tone; that
is to say, by tone-contrasts.


THE PROCESS OF PAINTING AS DISTINGUISHED FROM DRAWING

123. The first thing to consider is the tone of the surface upon
which you are going to paint. You then take a tone differing from the
ground-tone, in value, in color, or in color-intensity, you put it in a
certain position, and you spread it over a certain extent of space. In
so doing you give to the space a certain shape. This is the process of
Painting, as distinguished from the process of Drawing. In Drawing we
think of lines and outlines first. In Painting we think of Tones first,
of positions, measures, and shapes afterwards.


DEFINITION OF THE WORD TONE

124. In producing tones we use, necessarily, certain pigment-materials
and mixtures of these materials. The effect of light produced by any
particular material or mixture we call its tone. Though I have been
using the word _Tone_ I have not yet defined its meaning. I will now do
that.


TONE-ANALYSIS,—VALUE, COLOR, INTENSITY, NEUTRALITY

125. In every tone we have to distinguish two elements, the quantity
of light in it—what we call its value—and the quality of the light
in it—its color; and the color, whatever it is,—Red, Orange, Yellow,
Green, Blue, or Violet,—may be intense or neutral. By intensity I
mean the quality of a color in its highest or in a very high degree.
By the intensity of Red I mean Red when it is as red as possible. The
mixture of Vermilion and Rose Madder, for example, gives us a Red of
great intensity. That is about the strongest Red which we are able to
produce with the pigment-materials which we use. Intensity must not be
confounded with value nor value with intensity. By value I mean more or
less light. By intensity I mean a great purity and brilliancy of color.
Intensity stands in opposition to neutrality, in which no color can be
distinguished. The more color we have in any tone the more intensity we
have. The less the intensity the less color, and the absence of color
means neutrality or grayness. Neutrality or grayness, though it is the
negation of color, the zero of color, so to speak, must be classed
as a color because upon analysis it proves to be a result of color
combination or mixture. When I speak, as I shall from time to time, of
the neutral as a color, it will be understood that I am speaking of a
combination or mixture of colors in which no particular color can be
distinguished. I speak of the neutral as a color just as I speak of
zero as a number. We use zero as a number though it is no number, and
counts for nothing.


STUDY OF TONES AND TONE-RELATIONS

126. The study of tones and tone-relations means the study of
pigment-materials and their effects, to find out what quantities
of light we can produce, what qualities of color, what intensities
of color, what neutralizations. That is the problem of tones and
tone-relations. We cannot know much about tones and tone-relations
until we have had experience in the use of pigment-materials. We must
be able to distinguish tones, however slight the differences of value
or of color or of color-intensity, and we must be able to produce tones
according to our discriminations: this with exact precision. In order
to think in tone-relations we must have definite ideas of tone and of
tone-relations, in the form of visual images. In order to express our
ideas we must be able to paint. We must have practice in painting and
a great deal of it. I propose to describe this practice in tones and
tone-relations: what it ought to be, what forms it should take.


PIGMENT-MATERIALS

127. Of pigments I use these: Blue Black, Madder Lake (Deep), Rose
Madder, Indian Red, Venetian Red, Vermilion, Burnt Sienna, Cadmium
Orange, Yellow Ochre, Pale Cadmium, Aureolin, Cremnitz White,
“Emeraude” Green (Green Oxide of Chromium, transparent), Cobalt Blue,
French Ultramarine Blue. These are the pigments which I suggest for
oil-painting. In water-color painting I should substitute Charcoal
Gray for Blue Black. “Emeraude Green” is often called Viridian in the
form in which it is used in water-color. For Cremnitz White I should
substitute, in water-color painting, Chinese White. These are the
pigment-materials which I use myself and recommend to others. There
are, of course, many other pigments which may be used, but these will,
I think, be found sufficient for all purposes. Provided with these
pigments, with a palette upon which to put them, with brushes and other
materials necessary for painting, we are prepared to take up the study
of tones and tone-relations.


THE SCALE OF VALUES

128. It is evident that we have in black paint the least quantity of
light which we can produce. Black is the lowest of all values. It is
equally evident that in white paint we have the greatest possible
quantity of light. White is the highest of all values. Mixing Black
and White in different proportions we can produce an indefinite number
of intermediates. We do not want, however, to be indefinite in our
terms; on the contrary we want to be as definite as possible. Let us,
therefore, establish, between Black and White, a Middle Value (M);
between Black and Middle Value an intermediate Dark (D); between Middle
Value and White an intermediate Light (Lt), and between these five
values the intermediates, Low Dark (LD), High Dark (HD), Low Light
(LLt), and High Light (HLt). Further intermediates (eight) may be
established, but to these we need not give any particular names. 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 names.
We can speak, for example, of the intermediate between Middle and High
Dark, and it may be described in writing by the formula M-HD. With this
terminology we shall be able to describe the principal quantities or
values of light both in speech and in writing.

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-intensity. To do that we produce our
Scale of Values in terms of perfect neutrality, in which no color can
be distinguished. When we use the names of different values it is
understood that they are values of Neutrality. The term M, for example,
stands for Neutral Middle, D for Neutral Dark, Lt for Neutral Light.


CONTRASTS OF THE SCALE OF VALUES

129. Having produced a scale of nine neutral values, including White
and Black, the question arises as to the number of contrasts which it
affords, and it is easy to see that the number is thirty-six.

The vertical lines in the following diagram indicate the possible
contrasts of value in the Scale of Values. Counting the lines, we see
that the number of contrasts is thirty-six. Producing these contrasts,
we shall see what each one amounts to.

[Illustration: Diagram 1]


DEFINITION OF VALUE-RELATIONS

130. The best method of describing and distinguishing these
value-contrasts will be to use the value-names in a form of fractions.
For example, Lt/D would mean a contrast of Dark on Light, D/Lt would
mean a contrast of Light on Dark, Wt/Blk would mean a contrast of Black
on White. That is to say, White is subdivided or crossed by Black. When
we wish to describe several contrasts in combination, we set the value
of the ground-tone above the line, always, the value of the tone or
tones put upon it below, thus:—

       Lt
   -----------
   Wt      Blk

This formula means, spots of White and Black on a ground of Light.

         Lt
   --------------
    Wt       Blk
   ---
    M

This formula means spots of White and Black on a ground-tone of Light,
with a spot of Middle on the White, the Middle being altogether
separated from the Light by the White.

There is no definite thinking except in definite terms, and without
some such terminology as I have devised and described, it will be
impossible to enter upon an experimental practice in value-relations
with the hope of definite results. With definite terms, however, we can
take up the practice in value-relations with a good chance of learning,
in the course of time, all that there is to be learned.


SCALES OF COLORS IN DIFFERENT VALUES

131. We must now proceed to the consideration of the qualities of
light beyond the Scale of Neutral Values, in the region of colors and
color-intensities,—a region of tones which we have not yet explored.

It is evident that no color can exist either in the value of Black or
in the value of White, but in every other value we have the possibility
of all colors. That is to say, we may have Red (R) or Orange (O) or
Yellow (Y) or Green (G) or Blue (B) or Violet (V) or any of the colors
lying intermediate between them,—Red Orange (RO), Orange Yellow (OY),
Yellow Green (YG), Green Blue (GB), Blue Violet (BV), or Violet Red
(VR): all these, in any value of the Scale of Values, except in the
value of Black and in the value of White. The possibilities of value
and color, in tones, are exhibited in the following diagram:—


DIAGRAM OF VALUES AND COLORS

   Wt                                             Wt

   HLt  R  RO  O  OY  Y  YG  G  GB  B  BV  V  VR  HLt

   Lt   R  RO  O  OY  Y  YG  G  GB  B  BV  V  VR  Lt

   LLt  R  RO  O  OY  Y  YG  G  GB  B  BV  V  VR  LLt

   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 2


DEFINITION OF THE COLOR-TERMS

132. It is important that the words which we use for the different
colors should be well understood, that in using them we use them with
the same meanings. By Red I mean the only positive color which shows
no element either of Yellow or of Blue. It is the color which we often
describe by the word crimson, and we produce it by the mixture of
Rose Madder and Vermilion. By Yellow I mean the only positive color
which shows no element either of Red or Blue. It is the color of the
primrose which may be produced by the pigment Aureolin. By Blue I mean
the only positive color which shows no element either of Yellow or of
Red. Blue is seen in a clear sky after rain and in the pigment Cobalt.
By Orange I mean a positive color showing equal elements of Red and
of Yellow. By Green I mean a positive color showing equal elements of
Yellow and of Blue. By Violet I mean a positive color showing equal
elements of Blue and Red. The character of the intermediates is clearly
indicated by their several names. In each one we see the adjacents in
equal measures. This definition of the colors is only approximate.
It does not pretend to be scientific, but it may help to bring us to
a common understanding. To carry these definitions farther, I should
have to produce examples. This I can do in my class-room, producing
each color according to my idea, exactly. I might reach the same result
approximately by color-printing, but the result would not, probably,
be permanent. The samples produced by hand, for use in the class-room,
can be reproduced from time to time when they no longer answer to the
ideas which they are intended to express. In this treatise I shall
use a terminology instead of colored illustrations which would not be
satisfactory, or, if satisfactory, not so permanently.


COLOR-INTENSITIES IN DIFFERENT VALUES

133. If we proceed to carry out the idea of Diagram 2, producing all
the twelve colors in all of the seven values intermediate between
the extremes of Black and White, making the colors, in every case,
as strong, as intense, as is possible with the pigment-materials we
have chosen to use, we shall discover that the twelve colors reach
their greatest intensities in different values; that is to say, in
different quantities of light. Red reaches its greatest intensity in
the value High Dark, Orange in Low Light, Yellow in High Light, Green
in Low Light, Blue in High Dark, Violet in Low Dark, approximately;
and the intermediate colors reach their greatest intensities in the
intermediate values, approximately. In order to indicate this fact
in our diagram, we will mark the positions of greatest intensity by
putting the color signs in larger type.

DIAGRAM OF VALUES, COLORS, AND COLOR-INTENSITIES

   Wt                                             Wt

   HLt  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

   LLt  R  RO =O= OY  Y  YG =G= GB  B  BV  V  VR  LLt

   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 3


TONES OF THE SPECTRUM AND OF PIGMENTS

134. It is probable that we have in the Spectrum an indication of
the natural value-relations of the different colors when in their
highest intensities. Owing to the limitations of pigment-material,
however, it is impossible to reproduce the intensities of the Spectrum
satisfactorily. An approximation is all that we can achieve in painting.


THE SPECTRUM SEQUENCE AND THE CIRCUIT OF THE COLORS

135. Having produced the scale of twelve colors in the values of
their greatest intensities, and as intense as possible, we get an
approximation to the Spectrum with this difference, that the color
Violet-Red (Purple) which we get in pigments and mixtures of pigments
does not occur in the Spectrum and, so far as we know, does not belong
in the Spectrum. We have in the Spectrum a sequence which begins
with Red and ends with Violet. It is a sequence, not a circuit. In
pigment-mixtures, however, we have a circuit, clearly enough, and
Violet-Red is a connecting link between Violet and Red.


THE COMPLEMENTARIES

136. Considering the circuit of the colors which we are able to produce
with our pigment-materials, the question arises, What contrasts of
color are the strongest? what interval in the Scale of Colors gives
us the strongest possible color-contrast? Producing the twelve colors
in the values of their greatest intensities, and as intense as
possible, and setting the tones in a circuit and in their natural and
inevitable order, you will observe that the greatest color-contrast
is the contrast between colors at the interval of the seventh: for
example, the contrasts of Red and Green, or Orange and Blue, or Yellow
and Violet. The colors at the interval of the sixth are less strong
in contrast. The contrast diminishes gradually as we pass from the
interval of the seventh to the interval of the second. The contrast of
colors at the interval of the seventh, the greatest possible contrast,
is called the contrast of the complementaries. In estimating intervals
we count the colors between which the intervals occur.


A GENERAL CLASSIFICATION OF TONES

137. Taking each color in the value of its greatest intensity (as
shown in the Spectrum), and as intense as possible, the color may be
neutralized in the direction of Black (neutral darkness) or White
(neutral light) or in the direction of any value of neutrality
intermediate between Black and White, including the value of the
color in its greatest intensity. If we think of five degrees of
neutralization, including the extremes of Intensity and Neutrality,
we shall get as definite a terminology for color-intensities and
color-neutralizations as we have for colors and for values. The
choice of five degrees is arbitrary. It is a question how far the
classification shall go, what it shall include. We are dealing with
infinity, and our limitations are necessarily arbitrary.

In Diagram 3 we have a general classification of tones as to value,
color, color-intensity, and color-neutralization. Of values we have
nine. Of colors we have twelve. Of degrees of intensity and of
neutralization we have five.


COLOR-INTENSITIES AND COLOR-NEUTRALIZATIONS

138. It is important to distinguish between degrees of intensity and
degrees of neutralization. The degrees of color-intensity and of
color-neutralization, in any value, are described by fractions. The
formula D-R¾ means, value Dark, color Red, intensity three quarters.
The formula D-R, ¾N means, value Dark, color Red, three quarters
neutralized. The formula M-O½ means, value Middle, color Orange,
intensity one half. The formula M-O, ½N means, value Middle, color
Orange, half neutralized. M-O, ½N is a tone somewhat less intense
in color than M-O½, as may be seen on the diagram. The degree of
neutralization has reference, in all cases, to the maximum intensity
for the given value. What that is, theoretically, may be seen by
referring to the triangle of the color, in which the possibilities of
intensity, in different values, are clearly indicated.


THE DEFINITION OF PARTICULAR TONES

139. To define any tone, in this classification, we must name its
value, its color, and the degree of color-intensity or neutralization.


THE CLASSIFICATION OF TONES NECESSARILY THEORETICAL

140. The general classification of tones in which is shown
all the possibilities of value, color, color-intensity, and
color-neutralization, in reflecting pigments, is necessarily
theoretical, or rather ideal, because the degrees of intensity
obtainable in any value depend upon the pigment-materials we have to
use, or choose to use. No very great intensity of Yellow, even in the
value of High Light, can be obtained if we choose to use a mixture of
Yellow Ochre with Ultramarine Blue and White to produce it. It is only
when we use the most brilliant pigments—the Madders, Vermilion, the
Cadmiums, Aureolin, and Cobalt Blue—that we can approximate toward the
highest intensities, as indicated in our diagram and exhibited in the
Spectrum.


THE DEFINITION OF PARTICULAR TONE-RELATIONS

141. The number of tone-contrasts—contrasts of value, of color, and of
color-intensity or neutralization—is, evidently, beyond calculation.

The method of describing any particular contrast or contrasts is easy
to understand. We have only to define the tones and to indicate how
they cross one another.

   RO, ½N
   ---------
      VR

This formula means that a spot of Violet-Red (Dark, full intensity) is
put on a ground-tone of Middle Red-Orange, half neutralized.

     RO½
   ----------
   VR      Wt
   --
   YG

This formula means that spots of Low Dark Violet-Red (full
intensity) and White are put on a ground-tone of Middle Red-Orange,
half intensity, and that on the spot of Low Dark Violet-Red (full
intensity), as a ground-tone, is put a spot of Light Yellow-Green
(full intensity). It is not necessary to name the value when the
color occurs in the value of its greatest intensity, and it is not
necessary to describe the intensity, in any value, when the greatest
intensity possible to that value is meant. In the first case the value
is understood, in the second case the intensity—the greatest for the
value—is understood.




SEQUENCES OF VALUES AND COLORS


142. When, in view of all possible tones, as indicated in the
general classification of tones, according to value, color, and
color-intensity, or color-neutralization (Diagram of the Triangles),
we try to think what tones we shall use, what contrasts of tone we
shall produce, we are sure to be very much “at sea,” because of the
great number and variety of possibilities. Even when we disregard
differences of intensity and consider simply the possibilities of
value and of color, as shown in the general classification of tones
according to value and color (Diagram of Values and Colors, p. 137),
we have still too many possibilities to consider, and our choice of
tones is determined by accident or habit rather than by clear vision or
deliberate preference. We shall find it worth while to limit our range
in each experiment to some particular sequence of values and colors, or
to some particular combination of sequences. Instead of trying to think
in the range of all values, all colors, we ought to limit our thinking,
in each case, to the range of a few values and a few colors,—a few
definite tones with which we can become perfectly familiar and of which
we can have definite visual images. It is only when we can imagine
tones vividly that we can think satisfactorily in tone-relations. We
shall achieve this power of thinking in tones and tone-relations best
through self-imposed limitations.

143. We ought to begin our study of Tones and Tone-Relations with the
Scale of Neutral Values (see p. 135). We ought to work with the nine
tones of this scale or sequence until we know them well, until we can
visualize them clearly, and until we can produce them accurately; until
we can readily produce any single tone of the scale and any of the
thirty-six possible contrasts which the scale affords.

Besides the Scale of Neutral Values there are three types of Value and
Color Sequence which we may use.

144. First. We have the sequences which may be described as those of
the Vertical; sequences which may be indicated by vertical lines drawn
across the Diagram of Values and Colors. In each of these sequences,
twelve in number, we have one color in all the values of the Scale of
Values, except Black and White. These sequences of the Vertical, as I
shall call them, are of very little use in Pure Design. They give us
value-contrasts and contrasts of color-intensity (intensities of one
color), but no color-contrasts, no differences of color. The tones in
these sequences are monotonous in color.

145. Second. We have the sequences which may be described as those of
the Horizontal; sequences which may be indicated by horizontal lines
drawn across the Diagram of Values and Colors. In these sequences we
have differences of color and color-intensity, but all in one value.
These sequences give us color-contrasts (different colors in different
degrees of intensity), but no value-contrasts. The tones in these
sequences are monotonous in value. The sequences of one horizontal are
of very little use.

146. Third. We have the sequences which may be described as those
of the Diagonal; sequences which may be indicated by lines drawn
diagonally across the Diagram of Values and Colors. In drawing these
sequences the reader must not forget that the Scale of Colors is a
circuit, so when he reaches the end of the diagram he returns and
continues from the other end. The diagram might, for convenience in
drawing these sequences, be extended to several repetitions of the
Scale of Colors. In the sequences of the Diagonal we have contrasts
both of value and of color. The color in these sequences changes from
value to value through the Scale of Values. Each sequence gives us
certain colors in certain values, and in no case have we two colors
in the same value. To these sequences of the Diagonal we must give
our particular attention. They are the sequences which we shall use
constantly, in Representation as well as in the practice of Pure Design.

147. The sequences of the Diagonal fall into two divisions. First,
there are the sequences which we draw through the Diagram of Values
and Colors from Black up-to-the-right to White. I shall call these the
Sequences of the Right Mode (Sign ⍁). Second, there are the sequences
which we draw from Black up-to-the-left to White. I shall call these
the Sequences of the Left Mode (Sign ⍂).

Taking the lowest color in the sequence as the keynote, we have for the
Right Mode, in the Scale of Twelve Colors, twelve distinct sequences of
which this which follows is an example.

   Seq. LD-BV, ⍁ 2ds

        Wt
   HLt  -  OY
   Lt   -  O
   LLt  -  RO
   M    -  R
   HD   -  VR
   D    -  V
   LD   -  BV
       Blk

In this sequence the colors are taken at the interval of the second.
That is what is meant by the abbreviation 2ds.

Taking the lowest color of the sequence as its keynote, as before, we
have for the Left Mode twelve distinct sequences, of which that which
follows is an example.

   Seq. LD-OY, ⍂ 2ds

       Wt
   HLt  -  BV
   Lt   -  V
   LLt  -  VR
   M    -  R
   HD   -  RO
   D    -  O
   LD   -  OY
       Blk

In this sequence, as in the one previously given, the colors are taken
at the interval of the second.

148. The colors in these diagonal sequences may be taken not only at
intervals of the second, but at intervals of the third, the fourth, the
fifth, the sixth, and the seventh. Taking the colors at these different
intervals we have, for each interval, twenty-four distinct sequences;
twelve for the Right Mode, twelve for the Left Mode; in all one hundred
and forty-four different sequences.

149. Among the sequences of the Diagonal those in which the colors are
taken at the interval of the fifth are particularly interesting. The
colors taken at the interval of the fifth fall into four triads,—the
first, R-Y-B, the second, RO-YG-BV, the third, O-G-V, the fourth,
OY-GB-VR. Taking the colors in any of these triads in the two modes,
the Right and the Left, we get six sequences of different colors in
different values for each triad. Of these Triad-Sequences I will give
one as an example.

   Seq. LD-R, ⍂ 5ths

        Wt
   HLt  -  R
   Lt   -  Y
   LLt  -  B
   M    -  R
   HD   -  Y
   D    -  B
   LD   -  R
       Blk

The Triad-Scales, whether in the Right Mode or in the Left Mode,
are of great interest both in Pure Design and in Representation. In
Representation, however, the number of tones between the limits of
Black and White would, as a rule, be increased, as in the extended
diagram given farther on.

150. Instead of taking the colors at a certain interval in one mode or
the other, it is possible to take the colors in a certain relation of
intervals repeated; this in either mode. The relation of a third to a
fifth, for instance, being repeated, in one mode or the other, gives us
some very interesting sequences. The one which follows is an example.

   LD-V, ⍁ 5th-3d

       Wt
   HLt  -  Y
             3d
   Lt   -  O
             5th
   LLt  -  V
             3d
   M    -  B
             5th
   HD   -  Y
             3d
   D    -  O
             5th
   LD   -  V
       Blk

The relation of a seventh followed by two fifths, when repeated, in
either mode, gives a large number of sequences of very great interest,
particularly for Representation.

151. Any two of the sequences which I have described as those of the
Vertical, or more than two, may be combined and used together. In
that case we have two or more colors to a value. The monotony which
is inevitable in any single vertical sequence is avoided in the
combination of two or more such sequences.

   Seq. R and Seq. Y

          Wt
     R   HLt   Y
     R    Lt   Y
     R   LLt   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 Yellow. I have not found
the sequences of this type very interesting. In using them in
Representation I have found it desirable to have the intensities
increase gradually toward white, or, what amounts to the same thing,
to have each color neutralized as it loses light. That happens,
constantly, in Nature.

152. Any two of the sequences which I have described as of the
Horizontal, or even more than two, may be combined and used together.

       Seq. Lt and D, 3ds

   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-contrast. The colors are taken at the interval of the third. They
might be taken at any interval up to that of the seventh, in which
case we should have a contrast of complementary colors in two values,
each color occurring in each value. The monotony of value which is
inevitable in any single horizontal sequence is in the combination of
two or more such sequences avoided. I have used the Red-Yellow-Blue
triad in three and in five values with satisfaction. Each value
represents a plane of light in which certain differences of color are
observed.

153. Any two of the sequences which I have described as of the Diagonal
may be combined, in two ways. First, two sequences of the same mode may
be combined. Second, two sequences of different modes, one of the Right
Mode and one of the Left Mode, may be combined.

   LD-GB ⍂ 3ds with LD-RO ⍂ 3ds

           Wt
       GB  HLt  RO
       BV  Lt   OY
       VR  LLt  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 third.
Changing the mode of these two sequences we get them inverted, thus:—

   LD-GB ⍁ LD-RO ⍁ 3ds

         Wt
     GB  HLt  RO
     YG  Lt   VR
     OY  LLt  BV
     RO   M   GB
     VR  HD   YG
     BV   D   OY
     GB  LD   RO
         Blk

Here the mode is changed and the combined sequences inverted. The
combined sequences may be both in the same mode or in different modes.
When the modes are different the sequences come into contact, and in
some cases cross one another.

   LD-V ⍁ 2ds with LD-V ⍂ 2ds

            Wt
            Y
         OY   YG
          O    G
         RO   GB
          R    B
         VR   BV
            V
           Blk

In this case we have a combination of two diagonal sequences. One of
the sequences is in the Right, the other is in the Left Mode. The
colors are in the values of their greatest intensities.

   Seq. LD-GB ⍁ 3ds with LD-GB ⍂ 3ds

                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-RO. The combined sequences have three tones in common. It may happen
that the sequences combined will have no tones in common. This is shown
in the sequence which follows:—

   LD-O ⍂ 5ths with LD-B ⍁ 5ths

                Wt
            O  HLt   B
            G   Lt   Y
            V  LLt   R
            O   M    B
            G   HD   Y
            V   D    R
            O   LD   B
               Blk

154. Instead of having two colors to a value in the combination of two
vertical sequences, we may have an alternation of colors in the values,
giving one color to a value, thus:—

       Wt
   R  HLt
       Lt   Y
   R  LLt
       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 value.

155. Instead of having each color in two values in the combination
of two horizontal sequences, we may have the colors, taken at equal
intervals, occurring alternately first in one value and then in the
other.

   Lt  R  .  Y  .  B  .
   D   .  O  .  G  .  V

156. These alternating sequences may proceed, not only vertically and
horizontally, but diagonally across the diagram. 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-intervals.

    Wt
   HLt                          VR
    Lt                    BV
   LLt               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 Colors. The movement being, as a whole,
up-to-the-right, is in the Right Mode. I have not used any of the
sequences, of this type, in which the value-intervals alternate, first
in one mode then in the other, with a constant color-interval, but I
have used, frequently, the alternation of two different color-intervals
in a series of equal value-intervals. The sequences produced in this
way are among the most interesting of all the many I have used. I will
give several examples.

       Wt
   HLt  Y
           7th
   Lt   V
           5th
   LLt  O
           7th
    M   B
           5th
   HD   R
           7th
    D   G
           5th
   LD   V
       Blk

In this case the alternation is from the keynote, Low Dark Violet, up
first in the Left Mode a fifth, then up in the Right Mode a seventh,
then in the Left Mode a fifth, and so on up to White. This particular
alternation might be described as the relation of a fifth and a seventh
repeated, in the Left Mode.

        Wt
   HLt  Y
           7th
   Lt   V
           5th
   LLt  G
           7th
    M   R
           5th
   HD   B
           7th
    D   O
           5th
   LD   V
       Blk

In the sequence just given the alternation is, from the keynote Low
Dark Violet, first in the Right Mode a fifth, then in the Left Mode a
seventh: this through the Scale of Values up to White. The order of the
previous sequence is inverted. This particular alternation might be
described as the relation of a fifth and seventh repeated in the Right
Mode.

The alternation of intervals of the fifth with intervals of the third
gives some interesting sequences, in which the alternation of intervals
is, necessarily, an alternation of modes.

        Wt
   HLt  Y
           3d
   Lt   G
           5th
   LLt  O
           3d
    M   Y
           5th
   HD   R
           3d
    D   O
           5th
   LD   V
       Blk

157. I have by no means exhausted the possibilities of value and color
combination, but I have indicated a sufficient number to serve the
purposes of experimental practice in tone-relations, for a long time
to come. The sequences which I have found most interesting, in my own
experiments, have been the diagonal sequences of the two modes, using
intervals of the fifth, and the diagonal sequences in which with equal
value-intervals there is an alternation of certain color-intervals,—the
seventh and the fifth, and the seventh and two fifths. 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 easily.

158. For the purposes of Pure Design the Scale of Nine Values,
including Black and White, will be found sufficient; but when it comes
to the combination of Design with Representation, and particularly
to Representation in Full Relief, it will be necessary to introduce
intermediates into the Scale of Values. With this purpose in view
I give one more diagram in which intermediates of value have been
introduced. 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 Red. This diagram (5) is simply an extension of the
Diagram of Values and Colors given on p. 137.

159. We may use the various sequences I have described without mixing
the tones, using the tones one at a time as they may be required; but
if we choose we may mix adjacents or thirds or even threes. In that
way the tone-possibilities of each sequence may be very much extended.
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 described.

   Seq. LD-R ⍂ 5ths

         Wt
        HLt   R
         Lt   Y
        LLt   B
         M    R
        HD    Y
         D    B
        LD    R
        Blk

This is the sequence in which we decide to mix adjacents, thirds, and
threes.


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

   HLt  R RO O OY Y YG G GB B BV V VR R RO O OY Y YG G GB B BV V VR  HLt

        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

   LLt  R RO O OY Y YG G GB B BV V VR R RO O OY Y YG G GB B BV V VR  LLt

        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 5


              2ds  3ds  3s
   Wt

   HLt   R
              O
   Lt    Y         V    N
              G
   LLt   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 seconds, thirds, and threes.
It is evident that in mixing the tones of any sequence in this way
we go beyond the strict limitations of the sequence, particularly in
mixing thirds and threes. The results obtained are fairly definite,
however, and the tones obtainable are still within the range of
definite thinking. If we should go farther, to the mixture of tones
beyond the interval of the third, we should get into the region of
indefinite possibilities.

160. 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 extent. When
we limit our thinking in any case to a few tones,—certain colors in
certain values,—we come to know those tones so well that we can imagine
any one of them vividly, without seeing it. 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 tones.

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 sequence, whatever it is. That gives the painter certain
colors in certain values. That is to say, he has a certain number
of tones to consider and to use. He takes one of the tones into his
brush and gives it a position, a measure, and a shape. That done, he
takes another tone and gives to that a position, measure, and shape.
Proceeding in this way he creates a certain relationship of tones,
positions, measures, and shapes, the terms of which relationship are
perfectly definite. He repeats what he finds satisfactory. He avoids
what he finds unsatisfactory. Experimenting in this way, in such
definite terms, he ought to make a sure and steady progress toward the
discovery of what is orderly and beautiful. The use of any particular
sequence of values and colors is like the use, by the musician, of a
well-tuned instrument. It is at once a definition of terms and a source
of suggestion and of inspiration.

There is nothing occult or sacred about these sequences and
combinations of sequences. In using them we are in no way safeguarded
against error. Using these sequences, we can produce bad effects of
light and of color as well as good ones. Whether the results of using
these sequences are good or bad depends upon the user—what his thinking
amounts to. It will be a grave mistake to regard any of these sequences
as recipes for righteousness, when they are simply modes of thought.
They are nothing more than the sections or divisions of a general
classification of tones. In using any particular sequence we observe
that the same value and color-relations recur repeatedly. That is
always desirable from the point of view of Design. It means Harmony.

161. The beauty of any scheme of values and colors depends, not only
upon the pigment-materials used, upon the sequence of values and colors
chosen and upon the particular tones produced, but quite as much
upon the relative positions and juxtapositions given to the tones,
the quantities or measures in which they are used, and, lastly, the
way in which the paint is handled. To find out what tones to use as
ground-tones, what tones to put upon these ground-tones, and in what
quantities or measures, is a matter of experimental practice and of
visual and imaginative discrimination.

Having defined the word tone and its elements, value, color, and
color-intensity, and having established a general classification of
tones to show the possibilities of tone, I must go on to describe what
will be orderly in tone-relations. Order and Beauty in tone-relations
will be found in Tone-Harmonies, Tone-Balances, and Tone-Rhythms.




TONE-HARMONY


162. By Tone-Harmony I mean a relation of likeness in tones. Tones
are in Harmony when they resemble one another in all or in certain
respects. To be in Harmony two or more tones must have at least
something in common, either value or color. If they have the same
color they may be in the same degree of intensity, giving a Harmony
of Intensities. Tone-Harmony resolves itself into Value-Harmony,
Color-Harmony, and the Harmony of Intensities. The Harmony of
Intensities lies between tones of the same color, when they are
equally neutralized or neutralized in approximately the same degree.
When different colors are neutralized we have the Harmony of a common
neutrality or grayness of color.

163. Tones may be harmonized on the palette before they are used, that
is to say, before any positions, measures, and shapes are given to
them on paper or canvas, or they may be harmonized after positions,
measures, and shapes have been given to them. To harmonize tones on
the palette, as to value, we must bring them approximately to the same
value, with as little change of color as possible. To harmonize tones
on the palette as to color we must bring them approximately to the same
color, with as little change of value as possible. 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 intensity. 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 Triangles.

As the tone-effect which we produce depends very largely upon the
positions, measures, and shapes which we give to our tones, we may not
be satisfied with an effect which has been produced with previously
prepared and harmonized tones. We may wish to change the effect,
to achieve a still greater Harmony. Given a certain arrangement or
composition of tones, certain tones in certain positions, measures, and
shapes, and given the problem to harmonize those tones, what do we do?

164. Suppose it is Value-Harmony which we want; what is our procedure?

       Wt
   HLt  -  B
    Lt  -  V
   LLt  -  Y
    M   -  RO
   HD   -  G
    D   -  O
   LD   -  VR
       Blk

Here, let us say, are the tones of a design, certain colors in
certain values. What shall we do with these tones to bring them into
Value-Harmony?

[Illustration:

       Wt
   HLt  -  B
    Lt  -  V
   LLt  -  Y
    M   -  RO
   HD   -  G
    D   -  O
   LD   -  VR
       Blk

Diagram 6]

For Value-Harmony we must diminish the range of values toward one
value. In the above diagram I have shown a diminution of the range of
values toward High Light: this in several degrees.

[Illustration:

       Wt
   HLt  -  B
    Lt  -  V
   LLt  -  Y
    M   -  RO
   HD   -  G
    D   -  O
   LD   -  VR
       Blk

Diagram 7]

Following the indications of this diagram, we pull the colors together
toward Light in one case (B), toward Middle in another (A), toward
Dark in a third (C). As we do this we increase the Value-Harmony. In
reproducing the tones in a diminished range of values, raising the
colors in value or lowering them, we are not obliged to change the
colors except in cases where they become, possibly, confounded with
Black or with White. It will often happen, however, that the intensity
of a color has to be diminished when the value is changed. For example,
if Red Orange, in the illustration given, is in its greatest intensity,
the color may remain unchanged in System “A,” but its intensity will
be, necessarily, diminished in System “B,” or System “C.” See Diagram
of the Triangles.

For the sake of Value-Harmony we diminish the range of values, making
as little changes of color as possible, and only those changes
of color-intensity which are inevitable. A complete and perfect
Value-Harmony is, as a rule, undesirable because it means that all
the colors are reduced to one value which gives a monotony of value.
Approximate Harmony of Values is generally sufficient. The range of
values is narrowed, the contrasts are diminished, and an even tonality
is secured. That is all we require, in most cases, an approximation to
one value.

165. Suppose it is Color-Harmony which we want to achieve: what
procedure shall we follow?

   Wt
   B
   V
   Y
   R
   G
   O
   Blk

Here are certain tones, certain colors in certain values. What shall we
do with these tones to get Color-Harmony? We must diminish the range
of color-contrasts by giving predominance to one color, either to one
of the colors to be harmonized or to some other. That may be done by
mixing one color into all our tones.

    Wt                                          Wt
     B                                           V
     V                                          VR
     Y    Giving predominance to Red, we get:    O
     R                                           R
     G                                           N
     O                                          RO
   Blk                                          Blk
                    Diagram 8

The range of color-contrast is in this way diminished to the intervals
between Violet, Orange, and Neutral. The process, so far as color is
concerned, disregarding value-relations, is fully explained in the
following diagram:—

[Illustration: Diagram 9]

Suppose, instead of giving predominance to Red, as in the example
above, we give predominance to Blue, taking the same range of colors.

    Wt                                          Wt
     B                                           B
     V                                          BV
     Y    Giving predominance to Blue we get:    G
     R                                           V
     G                                          GB
     O                                           N
   Blk                                         Blk

    Diagram 10

The range of color-contrast is in this way diminished to the intervals
between Green, Violet, and Neutral. The process, so far as color is
concerned, is fully explained in the following diagram:—

[Illustration: Diagram 11]

In the diagrams which I have given the predominance is in the
measure of one half. That is to say, the mixtures are half and
half, theoretically speaking. The theoretical result is a range of
intermediate colors. The predominance is not necessarily in the measure
of one half. It may be in any measure. 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 difficulty.

166. Suppose it is the harmony of grayness, a Harmony of
Neutralization, which we want. What is the procedure to follow?

[Illustration: Diagram 12]

The procedure is shown in this diagram. We see here what is meant by a
Harmony of Neutralization, without changes of value. The neutralization
is in the measure of one half in each case. Red Orange and Green
are the only colors which exist in their maximum intensities. Their
intensities are diminished to the half-point, without change of
value,—from RO to RO½ in one case, and from G to G½ in the other. The
other colors are reduced in their intensities proportionally. The value
in each case remains unchanged.

167. Having considered the methods of getting Value-Harmony and
Color-Harmony separately, I must now describe the method of getting the
combination of Value-Harmony with the Harmony of Neutralization. To do
this we must set the colors in positions regarding the Scale of Neutral
Values, which will indicate their several values, and in each case
the degree of intensity. We must then decide whether to neutralize
the several tones toward Black or White, or toward some neutral value
between these extremes.

[Illustration: Diagram 13]

This illustrates the method of a neutralization toward Black in the
measures of one quarter, one half, and three quarters.

[Illustration: Diagram 14]

This illustrates the method of a neutralization toward White in the
measures of one third and two thirds.

[Illustration: Diagram 15]

This illustrates the method of a neutralization toward the Middle
Neutral, between Black and White, a neutralization in the measures of
one quarter, one half, and three quarters.

In bringing tones into harmony, by one or another or all of these
various methods, we must remember that when we have diminished the
contrast of value and of color beyond a certain point the result is
monotony, a monotony which may be undesirable. It is easy to get into a
state of mind in which we dislike all contrasts. In this state of mind
we find no æsthetic satisfaction except in monotony. Such a state of
mind should be avoided. Monotony is the Nirvana of æstheticism.

168. We may have a Harmony in the repetition and recurrence of two or
more contrasting, even strongly contrasting, tones. We may have Harmony
in the repetition and recurrence of a contrast in which there is
perhaps no Harmony.

For example: I may repeat the contrast Orange-Blue any number of times
in a certain composition. There is no Harmony of Value or of Color in
the contrast, but in repeating the contrast I have the Harmony of a
Repetition, just as I have a Harmony in the repetition of a certain
line or outline in which there is no order of any kind. The Harmony
lies solely in the repetition or recurrence. In this way I may repeat,
at equal intervals all over a certain space, the various contrasts
indicated by the following diagram:—

[Illustration: Diagram 16]

There is no Harmony in the relation of tones here indicated, but we
shall get Harmony in the repetition of this relation.

[Illustration: Diagram 17]

The Harmony here indicated will lie in the repetition of certain
contrasts in which there is no Harmony.

The Harmony of a repeated contrast, or contrasts, is a very important
form of Tone-Harmony. It means that a certain effect of light due to
the juxtaposition or association of certain tones recurs repeatedly,
let us say at equal or approximately equal intervals, all over a
certain space. The result is sure to be harmonious, no matter how
strong the tone-contrasts are in the group or series, provided that the
repetitions are well within the range of vision so that they may be
compared, and the recurrence of the same effect of light appreciated.
We must not be too near to the arrangement, for in that case the
contrasts of the repeated group will be more noticeable than the even
tonality of the all-over repetition. Every even, all-over effect of
light, no matter what the contrasts are which produce it, gives us the
feeling of Harmony.

169. In such compositions as the one indicated in Diagram 17
predominance may be given to one tone by having it recur in larger
spots in each group or in a greater number of spots, two or more in
each group. In this way, in a composition of many colors in different
values, predominance may be given to Middle Blue or Light Orange or
Dark Blue-Violet, or any other particular tone. Predominance may be
given to neutral gray of a certain value, by having it recur in larger
spots or in numerous small spots.

170. Neutral gray may be made to predominate in another way; by so
composing the tones, in the group to be repeated, that they neutralize
one another at a certain distance,—the point of view of the observer.

   +---+---+---+---+---+---+
   | 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 18

In this case Yellow and Violet will neutralize one another and Red will
neutralize Green. The effect of the repetition of these complementary
oppositions ought to be, at a certain distance, a very lively neutral.

It has been the idea of certain painters of our time to subject every
tone-impression to analysis, and to produce the effect of the tone by
an arrangement or composition of its elements. Many interesting and
some beautiful results have been produced in this way.

[Illustration: Diagram 19]

In this case we have a repetition of the triad Red-Yellow-Blue, which,
at a certain distance, ought to produce the effect of a middle neutral.
The principle of these arrangements is one of the most important in
tone-composition.

171. There is another consideration which ought to keep us from any
morbid interest in harmonious monotonies, which ought to reconcile
us to contrasts, even strong contrasts, and to a great variety in
tones. Harmony is only one principle of composition in Design; we
have two others which are equally important,—the principle of Balance
and the principle of Rhythm. The principles of Balance and Rhythm
are consistent with the greatest possible contrasts of tone. The
tone-contrasts in forms of Balance and Rhythm may be strong, even
harsh, and the appreciation and enjoyment of the Balance or of the
Rhythm in no degree diminished.

We will now proceed to the consideration of Tone-Balance and
Tone-Rhythm.




TONE-BALANCE


172. Tones, simply as tones, disregarding the positions, measures, and
shapes which may be given to them, balance, when the contrasts which
they make with the ground-tone upon which they are placed are equal. We
have an indication of such a balance of tones, simply as tones, in the
following formula:—

          LD - V
   --------------------
   HLt - Y      HLt - Y

Two spots of High Light Yellow occur on a ground-tone of Low Dark
Violet. The two spots of Yellow make equal contrasts with the
ground-tone, and for that reason balance as tones, no matter what
positions, measures, and shapes are given to them. The value-contrast
is that of the interval of the seventh in the Scale of Values; the
color-contrast is that of the interval of the seventh in the Scale of
Colors. We must assume that the intensities are so adjusted as not to
disturb the balance.

          M - V
   -----------------
   Lt - O      D - O

In this case the values making the contrasts differ. The contrasts
are, nevertheless, equal because the value-intervals are equivalent
intervals. The value difference between Light and Middle is equivalent
to the value difference between Dark and Middle. Though the contrasting
elements differ, the contrasts are equal. In this case the contrasting
colors are the same and the color-contrasts correspond. We must assume
that the intensities are so adjusted as not to disturb the balance.

          LD - V
   --------------------
   LLt - O      LLt - G

In this case the contrasting colors differ, but the contrasts are
equal because the color-interval between Orange and Violet is the
same as the color-interval between Green and Violet. In this case the
value-contrasts correspond. We must assume here, as before, that there
is no difference of color-intensity to disturb the balance.

          D - R
   ------------------
   HD - O      LD - V

In this case the two tones which balance on the ground-tone differ both
in value and in color. They balance, nevertheless, because both the
value and the color-contrasts are of the interval of the third. Again
we must assume that there is no disparity of intensities to disturb the
balance.

173. The reader will find the Diagram of Values and Colors (No.
5) very useful in making calculations for tone-balances, so far
as value-contrasts and color-contrasts are concerned, leaving out
considerations of color-intensity.

Taking any tone indicated on the Diagram as a ground-tone, any tones
at equal distances in balancing directions will balance on that
ground-tone.

[Illustration: Diagram 20]

The various types of tone-balance are shown in the above diagram. The
tones which balance, one against the other, on the ground-tone of
Blue-Violet, are the tones marked by the same number.

The value and color-balances being achieved, the intensities may be
adjusted, increased or diminished, until the balance is perfect.

174. As you increase the color-intensity in any tone it attracts more
attention, and unless you increase the intensity in the opposite tones
there will be a disparity which will disturb your balance. When the
intensity in any tone is too great, you can increase the color-contrast
or the value-contrast of the opposite tones until the balance is
achieved.

175. Up to this point I have been speaking of Tone-Balance in the
abstract, of Tone-Balance as such. I have spoken of Tone-Balance as
something apart from Position, Measure, and Shape-Balance, as if
tones could balance without having any positions, measures, or shapes
assigned to them. The fact is that a tone does not exist until you give
it a position, a measure, and a shape. It follows that Tone-Balance is,
in all cases, more or less complicated by considerations of position,
measure, and shape.

176. The principle of balance being that equal attractions balance
at equal distances and unequal attractions at distances inversely
proportional to them, it follows, that if the attraction of a tone
is increased by quantity, the attraction of quantity may be balanced
against the attraction of contrast. The calculation of such balances
may be made on the Diagram of Values and Colors.

[Illustration: Diagram 21]

In this case, for example, 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 Violet, the difference of contrast in one case making up for
a difference of quantity and of contrasting edge in the other.

177. So far as Tone-Balance depends upon positions, measures,
and shapes, the problem is the problem of Position, Measure, and
Shape-Balance, which we have already considered.

Given certain tones in certain measures and shapes, the inversion of
the measures and shapes involves an inversion of the tones, so we have
a Tone-Balance as well as a Measure and Shape-Balance. The inversion in
any case may be single or double.

[Illustration: Diagram 22]

In this case we have an instance of single inversion, which gives us a
Symmetrical Balance, of tones, as well as of measures and shapes.

[Illustration: Diagram 23]

In this case we have an instance of double inversion of tones, as well
as of measures and shapes.

178. The tones and tone-contrasts on one side of a center or axis
are not necessarily the same as those on the other side. We may have
a Tone-Balance in which very different tones and tone-contrasts are
opposed to one another. This brings us to the consideration of Occult
Balance in Tones, Measures, and Shapes.

A balance of any tones and of any tone-contrasts, in any measures and
in any shapes, is obtained when the center of tone-attractions is
unmistakably indicated, either by the symmetrical character of the
balance or by a symmetrical inclosure which will indicate the center.
Given any combination of tones, measures, and shapes, and the problem
to find the balance-center, how shall we solve the problem? It cannot
very well be done by reasoning. It must be done by visual feeling. The
principle of Balance being clearly understood, 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 tone, and
who make the greatest effort to feel the centers and to indicate them
accurately. Experience and practice are necessary in all cases.

[Illustration: Fig. 228]

Here, within this circle, are the attractions to be balanced. The
problem is to find the balance-center, and to indicate that center
by a symmetrical inclosure which will bring the tones, measures, and
shapes into a Balance. The center is here indicated by the circle.
Whether it is correctly indicated is a matter of judgment in which
there may be a difference of opinion. There is a center somewhere upon
which the attractions are balancing. The question is, where is it? The
illustration which I have given is in the terms of the Scale of Neutral
Values. Differences of color and color-intensity would complicate the
problem, but would not in any way affect the principle involved. I
know of no more interesting problem or exercise than this: to achieve
Tone-Balance where there is no Tone-Symmetry.

179. It will sometimes happen, that a gradation of tones or measures
will draw the eye in a certain direction, toward the greater contrast,
while a larger mass or measure of tone, on the other side, will be
holding it back. In such a case we may have a mass balancing a motion.

[Illustration: Fig. 229]

In this case the eye is drawn along, by a gradation of values, to the
right, toward the edge of greater contrast, away from a large dark
mass of tone in which there is no movement. The tendency of the dark
mass is to hold the eye at its center. The problem is to find the
balance-center between the motion and the mass. I have done this, and
the balance-center is indicated by the symmetrical outline of the
diagram.

180. Some shapes hold the eye with peculiar force, 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 balance. Symmetrical shapes have
a tendency to hold the eye at centers and on axes. Given certain
attractions on the other side, we must be sure that they are sufficient
to balance the force of the symmetry in addition to the force of its
tone-contrasts, whatever they are.

[Illustration: Fig. 230]

In this case we have an approximate balance in which the force of a
symmetry, with contrasting edges, on one side, is balanced by contrasts
and certain movements on the other. If I should turn down the upper
spot on the right, we would feel a loss of balance due to the turning
of two movements, which combine to make one movement to the right, into
two movements down to the right. If I should increase the force of the
symmetry, by filling in the center with black, it would be necessary
either to move the symmetry nearer to the center or to move the
opposite attractions away from it. An unstable attitude in the symmetry
would have to be counteracted, in some way, on the other side.

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-contrasts.

[Illustration: Fig. 231]

In this case the shape on the right requires a pretty strong dark spot
to balance its contrasts and its intricacy.

The problem is further complicated when there are, also, inclinations,
to the right or to the left, to be balanced.

[Illustration: Fig. 232]

In this case I have tried to balance, on the center of a symmetrical
inclosure, various extensions and inclinations of tone-contrast, the
movement of a convergence, and the force of a somewhat intricate and
unstable symmetry.

These occult forms of Balance are not yet well understood, and I feel
considerable hesitation in speaking of them. We have certainly a great
deal to learn about them. They are far better understood by the Chinese
and by the Japanese than by us.

181. When any line or spot has a meaning, when there is any symbolism
or representation in it, it may gain an indefinite force of attraction.
This, however, is a force of attraction for the mind rather than
for the eye. It affects different persons in different measures.
The consideration of such attractions, suggestions, meanings, or
significations does not belong to Pure Design but to Symbolism or to
Representation.




TONE-RHYTHM


182. The idea of Tone-Rhythm is expressed in every regular and perfect
gradation of Tones; of values, of colors or of color-intensities,
provided the eye is drawn through the gradation in one direction or
in a series or sequence of directions. This happens when there is a
greater tone-contrast at one end of the gradation than at the other.
When the terminal contrasts are equal there is no reason why the
eye should move through the gradation in any particular direction.
According to our definition of Rhythm, the gradation should be
marked in its stages or measures, and the stages or measures should
be regular. That is certainly true, but in all regular and perfect
gradations I feel that corresponding changes are taking place in
corresponding measures, and I get the same feeling from such a
gradation that I get from it when it is marked off in equal sections.
Though the measures in regular and perfect gradations are not marked,
they are, it seems to me, felt. They seem sufficiently marked by
the regularity and perfection of the gradation, any irregularity
or imperfection being appreciable as a break in the measure. I am
inclined, therefore, to say of any regular and perfect gradation that
it is rhythmical provided the direction of movement is unmistakable.
The direction, as I have said, depends upon the relation of terminal
contrasts. The eye is drawn toward the greater contrast, whatever that
is and wherever it is. A few examples will make this clear.

                   M
   -----------------------------------
   Blk  LD  D  HD  M  LLt  Lt  HLt  Wt

In this case we have the gradation of the Scale of Values set on a
ground-tone of the middle value. Here there are two opposed gradations
with equal contrasts at the opposite ends. The result is Balance, not
Rhythm.

                   Wt
   -----------------------------------
   Blk  LD  D  HD  M  LLt  Lt  HLt  Wt

In this case we have a gradation of values beginning with White on
White, no contrast at all, and reaching ultimately the contrast of
Black and White. The eye is drawn through the tones of this gradation
in the direction of this contrast, that is to say, from right to left.
It is a clear case of Rhythm. If, instead of white, we had black, as
a ground-tone, the movement of the rhythm would be in the opposite
direction,—from left to right.

   Wt  HLt  Lt  LLt  M  HD   D   LD  Blk
   -------------------------------------
   Blk  LD  D   HD   M  LLt  Lt  HLt  Wt

In this case, as in the first, we have equally great contrasts at the
ends and no contrast at the middle. The result is Balance, not Rhythm.

            V
   -------------------
   Y  YG  G  GB  B  BV

In this case, disregarding possible differences of value and
color-intensities, there will be a color-rhythm proceeding from
right to left. The contrast to which the eye will be drawn is the
color-contrast of Yellow and Violet.

                   LD-V
   -------------------------------------
   D-Y  HD-YG  M-G  LLt-GB  Lt-B  HLt-BV

In this case, disregarding possible differences of intensity, there
will be a rhythm of color moving from right to left and a rhythm
of values moving from left to right. Assuming that we are equally
attracted by corresponding value and color-contrasts, these two
rhythms, when produced, will neutralize one another and we shall
have an illustration of Tone-Balance rather than Tone-Rhythm. If
corresponding color and value-contrasts are not equally attractive we
shall have an unequal tug-of-war between the two rhythms.

                    LD-V
   -------------------------------------
   HLt-Y  Lt-YG  LLt-G  M-GB  HD-B  D-BV

In this case we have two rhythms, one of values and one of colors, in a
Harmony of Direction. The direction of movement will be from right to
left.

                          HLt-Y⅛
   -------------------------------------------------------
   HLt-Y  HLt-Y⅞  HLt-Y⁶/₈  HLt-Y⅝  HLt-Y⁴/⁸  HLt-Y⅜

In this case we have no change of color and no change of value, but a
rhythm of the intensities of one color, in one value. The movement will
be from right to left. The ground-tone might be Neutral High Light, the
zero-intensity of Yellow. That would not change the direction of the
movement.

                         LD-Y⅛
   -------------------------------------------------
   HLt-Y  Lt-Y⅞  LLt-Y⁶/₈  M-Y⅝  HD-Y⁴/⁸  D-Y⅜

In this case I have indicated a combined movement of values and
color-intensities. The direction of the movement will be from right to
left.

The tone-rhythms which I have described are based upon the repetition
at regular intervals of a certain change of value, of color or of
color-intensity. We have Harmony, of course, in the repetition of equal
changes, though the changes are not the same changes. The change of
value from Middle to Low Light is equal to the change from Low Light to
Light, though these changes are not the same changes. The Harmony is,
therefore, the Harmony of equivalent contrasts which are not the same
contrasts.

183. We have more or less movement in every composition of tones
which is unbalanced, in which the eye is not held between equivalent
attractions, either upon a vertical axis or upon a center. In all such
cases, of tones unbalanced, the movement is in the direction of the
greatest contrast. Unless the movement is regular and marked in its
measures, as I think it is in all regular and perfect gradations, the
movement is not rhythmical. We get Rhythm, however, in the repetition
of the movement, whatever it is, in equal or lawfully varying measures,
provided the direction of the movement remains the same or changes
regularly or gradually. 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 intervals, without changes of direction; but
we should have Rhythm, also, if the direction of the movement, in its
repetitions, were changed, regularly or gradually; if, for example,
the direction were changed first from up-right forty-five degrees to
up-right forty degrees, then to up-right thirty-five degrees, then
to up-right thirty degrees, this at equal or at lawfully varying
intervals. In this way the movement of the composition repeated may
be carried on and gradually developed in the movement of the series.
A reference to Fig. 161, p. 94, and to Fig. 119, p. 68, will help the
reader to understand these statements.

184. When any unbalanced composition of tones is singly inverted upon
a vertical axis and the movement of the composition follows the axis,
either up or down, and this movement, up or down, is repeated, up or
down, we get forms of Tone-Rhythm which are also forms of Symmetrical
Balance. In the inversions and repetitions of the tone-composition
we have Tone-Harmony. As the tones in the repeated composition have
certain positions, measures, and shapes, the Harmony, the Balance, and
the Rhythm are of Positions, Measures, and Shapes as well as of Tones;
so we get the combination of all the terms of Design in all the three
modes of Design.




COMPOSITION

THREE GENERAL RULES


185. It is quite impossible for me, in this discussion of terms
and principles, to indicate, in any measure, the possibilities of
composition, in lines and spots of paint, in tones, measures, and
shapes. This is in no sense a Book of Designs. All I have undertaken to
do is to give a few very simple examples and to indicate the kind of
reasoning to be followed, recommending the same kind of reasoning in
all cases. There are three general rules, however, which I must state.

First. Given a certain outline and certain tones, measures, and shapes
to be put into it, it is the Problem of Pure Design to do the best we
can, getting as many connections making unity as possible. The process
is one of experimenting, observing, comparing, judging, arranging and
rearranging, taking no end of time and pains to achieve Order, the
utmost possible Order, if possible the Beautiful.

Second. When only an outline is given and we can put into it lines and
spots of paint,—tones, measures, and shapes,—_ad libitum_, 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 started,
when it had nothing in it. As we proceed to add features we must be
sure that we are not diminishing the order of the composition as a
whole. If the composition as a whole is orderly, we do not want to make
it less so by cutting it up and introducing additional attractions
which may be disorderly and confusing. It may be harder to achieve
Order with a greater number and variety of terms. We may deserve credit
for overcoming this difficulty, but it is a difficulty which confronts
us only when the terms are given and we have to make the best of them.
When no terms are given, only a perfectly orderly outline, we should
hesitate before we put anything into it. If we add anything we must be
sure that it does not diminish, in the slightest degree, the order we
had before, when we had nothing but the outline. The order of the whole
must never be diminished.

Third. When we have an outline with certain tones, measures, and shapes
in it, the question is: whether we can increase the order by adding
other tones, other measures, or other shapes.

[Illustration: Fig. 233]

Arrangement “a” is less orderly than arrangement “b,” so I have acted
wisely in adding the other outlines.

[Illustration: Fig. 234]

In this case, however, I have added features without achieving any
increase of Order in the composition. The order is less than it was
before. The additions have no interest from the point of view of Pure
Design. I may add features for the sake of variety or novelty, to
give a change of feeling, a new sensation, but such motives are not
the motives of Pure Design. In Pure Design our motive is, always, to
achieve Order, in the hope that in so doing we may achieve a supreme
instance of it which will be beautiful.

[Illustration: Fig. 235]

Consider these illustrations. Arrangement “b” is more orderly than
arrangement “a,” so I am justified in making the additions. The
additions have brought occult balance into the composition with
Direction and Interval-Harmony. Arrangement “c” is less orderly than
“b,” less orderly than “a.” It has, therefore, no value for us. There
is no merit in the multiplication of features which it exhibits.
The surface is “enriched” at the expense of Direction-Harmony,
Interval-Harmony, and Shape-Harmony. There may be an approximation
to an occult balance in arrangement “c,” but you cannot feel it
unmistakably as you do in “b.” Its value is, therefore, less.

186. I object to the word “decoration,” as commonly used by designers,
because it implies that additions are likely to be improvements, that
to multiply features, to enrich surfaces, is worth while or desirable.
The fact is, that additions are, as a rule, to be avoided. There is no
merit in the mere multiplication of features. It is a mistake. The rule
of Pure Design, and it is the rule for all Design, is simplification
rather than complication. As designers we ought to avoid additions, if
possible.

We ought to make them only when in so doing we are able to increase the
order of the whole. We make additions, indeed, to achieve the greater
simplicity of Order, and for no other reason. Our object in all cases
is to achieve Order, if possible a supreme instance of Order which will
be beautiful. We aim at Order and hope for Beauty.




THE STUDY OF ORDER IN NATURE AND IN WORKS OF ART


187. In connection with the practice of Pure Design, as I have
described it,—the composition and arrangement of lines and spots of
paint; of tones, measures, and shapes: this in the modes of Harmony,
Balance, and Rhythm, for the sake of Order and in the hope of
Beauty,—the student should take up the study of Order in its three
modes, as revealed in Nature and achieved in Works of Art.

188. The method of study should be a combination of analysis with
synthetic reproduction. Taking any instance of Order, whether in
Nature or in some work of Art, the first thing to do is to consider
its terms,—its positions, its lines, its areas, its measure and
space-relations, its tones and tone-relations,—bringing every element
to separate and exact definition. The next thing to do is to note
every occurrence of Harmony, of Balance, of Rhythm,—every connection
making for consistency, unity, Order. In that way we shall get an exact
knowledge of the case. We shall know all the facts, so far as the
terms and the principles of Design are concerned. That is what I mean
by analysis. By a synthetic reproduction I mean a reproduction of the
effect or design, whatever it is, following the images which we have
in mind as the result of our analysis. The reproduction should be made
without reference to the effect or design which has been analyzed.
There should be no direct imitation, no copying. We must not depend
so much upon the memory as upon the imagination. Having reproduced
the effect or design in this way, following the suggestions of the
imagination, the reproduction should be brought into comparison with
the effect or design reproduced and the differences noted. Differences
should be carefully observed and the previous analysis should be
reviewed and reconsidered. When this is done another attempt at
reproduction should be made. This process should be repeated until the
effect or design is thoroughly understood and imaginatively grasped.
The evidence of understanding and comprehension will be seen in the
reproduction which is made, which ought to have an essential but not
a literal correspondence with the original. Analysis should precede;
synthesis should follow.

I hope, in another book or books, to be published later, to give some
examples of Order in natural objects or effects, also examples of
Order in Works of Art, with a careful analysis of each one, showing
how the points, lines, and areas, the measure and the space-relations,
the tones and tone-relations come together in the forms of Harmony,
Balance, and Rhythm, in the modes of Order, in instances of Beauty.
In the mean time, as the methods of analytic study and of synthetic
practice are clearly indicated in the preceding pages, the student who
has taken pains to understand what he has read will find himself well
prepared for the work. He can take up the study of Order in Nature and
of Design in Works of Art without further assistance.




CONCLUSION


189. It does not follow, even when our minds, in consequence of the
study and the practice which I have described, are richly stored with
the terms and the motives of Design, that we shall produce anything
important or remarkable. Important work comes only from important
people. What we accomplish, at best, is merely the measure and
expression of our own personalities. Nevertheless, though we may not
be able to produce anything important, it is something to appreciate
and enjoy what is achieved by others. If our studies and our work bring
us to the point of visual discrimination, to æsthetic appreciation
and enjoyment, and no farther, we are distinguished among men. The
rarest thing in the world is creative genius, the faculty which creates
great works. Next to that comes the faculty of appreciation. That,
too, is rare. We must not believe that appreciation is easy. It is
true that the recognition of Order is instinctive and spontaneous, but
untrained people recognize it only in a few simple and obvious forms.
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 people. It is only as we are
trained, exercised, and practiced in the use of terms and in following
principles that we rise to the appreciation of great achievements. The
sense of order, which we all have, in a measure, needs to be exercised
and developed. The spontaneity of undeveloped faculty does not count
for much. It carries us only a little way. Let no one believe that
without study and practice in Design he can recognize and appreciate
what is best in Design.

Appreciation and enjoyment are the rewards of hard thinking with
hard work. 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 followed. We know the terms only when we have ourselves
used them, and the principles when we have tried to follow them. 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 write,
constantly, and try, so many of us, to speak and write well. 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 understood, as they should be, in the light of
personal experience and effort. It is for this reason that I am anxious
to see the teaching and practice of Design introduced into the schools,
public and private, everywhere, and into our colleges as well as our
schools. I have no idea that many able designers will be produced,
but what I expect, as a result of this teaching, is a more general
understanding of Design, more interest in it, and more appreciation and
enjoyment of its achievements. Among the many who will appreciate and
enjoy will be found the few who will create and produce.

The purpose of what is called art-teaching should be the production,
not of objects, but of faculties,—the faculties which being exercised
will produce objects of Art, naturally, inevitably. Instead of trying
to teach people to produce Art, which is absurd and impossible, we
must give them a training which will induce visual sensitiveness with
æsthetic discrimination, an interest in the tones, measures, and
shapes of things, the perception and appreciation of Order, the sense
of Beauty. In these faculties we have the causes of Art. Inducing
the causes, Art will follow as a matter of course. In exercising and
developing the faculties which I have named, which naturally and
inevitably produce Art, we are doing all that can be done by teaching.
There is no better training for the visual and æsthetic faculties
than is found in the practice of Pure Design, inducing, as it does,
discrimination in tones, measures, and shapes, and the appreciation
of what is orderly and beautiful. The result of the practice will be
a wide spread of visual and æsthetic faculty which will have, as its
natural and inevitable result, the appreciation and the production of
Works of Art.

Our object, then, in the study and practice of Pure Design is, not so
much the production of Works of Art, as it is to induce in ourselves
the art-loving and art-producing faculties. With these faculties we
shall be able to discover Order and Beauty everywhere, and life will
be happier and better worth living, whether we produce Works of Art,
ourselves, or not. We shall have an impulse which will lead us to
produce Works of Art if we can. At the same time we shall have the
judgment which will tell us whether what we have done is or is not
beautiful.




PARAGRAPH INDEX


     1, p.   1. The Meaning of Design.
     2, p.   1. The Order of Harmony.
     3, p.   1. The Order of Balance.
     4, p.   2. The Order of Rhythm.
     5, p.   2. Relations of Harmony, Balance, and Rhythm.
     6, p.   4. Beauty a supreme instance of Order.
     7, p.   4. The Arts as different modes of Expression.
     8, p.   5. Drawing and Painting.
     9, p.   5. Two modes of Drawing and Painting.
    10, p.   5. Pure Design.
    11, p.   6. Applied Design.
    12, p.   7. Representation.
    13, p.   7. Representation in Forms of Design.
    14, p.   9. The Definition of Positions.
    15, p.   9. The Relation of Directions and Distances.
    16, p.  10. Directions defined.
    17, p.  11. Distances defined.
    18, p.  11. Positions determined by Triangulations.
    19, p.  11. Intervals.
    20, p.  12. Scale in Relations of Position.
    21, p.  12. Harmony of Positions.
    22, p.  12. Harmony of Directions.
    23, p.  13. Harmony of Distances.
    24, p.  14. Harmony of Intervals.
    25, p.  16. Intervals in any series of Positions.
    26, p.  17. Positions and their possibilities.
    27, p.  17. Balance of opposite Directions.
    28, p.  17. Balance of Distances in opposite Directions.
    29, p.  18. Balance of Directions not opposite.
    30, p.  18. Balance of Distances in Directions not opposite.
    31, p.  19. Positions in Balance.
    32, p.  19. Stable equilibrium of vertical and horizontal
                directions.
    33, p.  20. Symmetry defined.
    34, p.  21. The central axis should predominate in symmetrical
                Balances.
    35, p.  22. Balance in Relations of Position, when inverted.
    36, p.  22. Finding the center of equilibrium in unbalanced
                relations of position. Indication of centers by
                symmetrical inclosures.
    37, p.  24. Tendency of symmetrical inclosures, when sufficiently
                attractive, to prevent movement.
    38, p.  25. How unstable equilibrium suggests movement.
    39, p.  26. Rhythmic movement in a gradual increase in the number of
                attractions through a series of visual angles.
    40, p.  27. The possibilities of rhythmic movement in relations of
                position.
    41, p.  27. Balanced attractions at equal intervals give no
                movement, consequently no Rhythm.
    42, p.  28. The gradual increase of attractions in a series of
                visual angles, as produced by gradual changes of scale,
                causes rhythmic movement.
    43, p.  28. How unbalanced groups of positions being repeated at
                equal intervals produce rhythmic movement.
    44, p.  29. Rhythmic movements produced by the repetition of
                unbalanced relations of position and by a gradual
                diminution of scale.
    45, p.  30. Rhythmic movements produced by the repetition of a
                balanced relation of positions with a gradual diminution
                of intervals, causing a gradual increase of attractions
                through a series of visual angles.
    46, p.  30. Rhythmic movements produced by the repetition of a
                balanced relation of positions with diminution of
                intervals and of scale.
    47, p.  31. Rhythmic movements produced by the repetition of an
                unbalanced relation of positions with a crowding due
                to gradual diminution of intervals.
    48, p.  31. 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 groups.
                The combination of two or more rhythms.
    49, p.  32. The combination of two or more rhythms.
    50, p.  32. Relations of position in different attitudes.
    51, p.  33. Principal Attitudes.
    52, p.  34. Harmony in Attitudes.
    53, p.  35. Harmony in the repetition of any relation of attitudes.
    54, p.  35. Balance in Attitudes.
    55, p.  36. Rhythm in Attitudes.
    56, p.  37. The Line.
    57, p.  37. Changes of Direction in a line. Angles.
    58, p.  38. Gradual changes of Direction in a line. Curves.
    59, p.  41. Curves regarded as compositions of circular arcs.
    60, p.  42. Differences of scale in lines.
    61, p.  42. Differences of attractive force in lines.
    62, p.  44. Harmony of Direction in lines.
    63, p.  44. Harmony of Angles in lines.
    64, p.  45. Harmony in Legs of Angles.
    65, p.  45. Harmony in Curvatures.
    66, p.  46. Harmony in Arcs when they have the same radius.
    67, p.  46. Harmony in Arcs when they have the same angle.
    68, p.  47. Linear Progressions.
    69, p.  47. Variations of scale in Linear Progressions.
    70, p.  48. Changes of Direction in Linear Progressions.
    71, p.  49. Inversions in Linear Progressions.
    72, p.  50. Balance in a Line.
    73, p.  51. Appreciation of Balance in a line depends very much on
                its attitude.
    74, p.  52. Balance of Inclinations in a line.
    75, p.  54. Finding the center of equilibrium of a line and
                indicating that center by a symmetrical inclosure.
    76, p.  56. Rhythm in a Line.
    77, p.  56. Rhythm requires more than movement. The movement must be
                in regular and marked measures.
    78, p.  57. The number of repetitions required in a Rhythm.
    79, p.  57. Contrary movements in Rhythms.
    80, p.  58. Regular alternations in space not necessarily
                rhythmical. That depends upon the character of the
                motive.
    81, p.  59. Repetition and alternation without Rhythm.
    82, p.  59. Rhythm due to gradation of scale.
    83, p.  60. Rhythm due to the gradual increase in the number of
                attractions from measure to measure.
    84, p.  61. Rhythm in Spiral Concentrations.
    85, p.  63. Direct and Contrary Motion in Spiral lines.
    86, p.  64. The Balance of corresponding but opposed Rhythms.
    87, p.  64. Lines in different Attitudes.
    88, p.  65. Harmony in Attitudes of lines.
    89, p.  66. Harmony in the repetition of any relation of attitudes.
    90, p.  66. Balance in Attitudes of Lines.
    91, p.  67. Rhythm in Attitudes of Lines.
    92, p.  68. Recapitulation.
    93, p.  68. The Composition of Lines.
    94, p.  69. Harmony in the Composition of Lines.
    95, p.  70. Measure-Harmony of ratios and of proportions.
    96, p.  70. Elements making for Harmony in dissimilar lines.
    97, p.  73. Balance in the Composition of Lines.
    98, p.  74. Shape-Harmony without Measure-Harmony.
    99, p.  74. Measure-Balance without Shape-Balance.
   100, p.  76. The centers of equilibrium in mere measure-balances
                should be indicated by symmetrical inclosures.
   101, p.  76. Balance of Inclinations.
   102, p.  79. Measure-Rhythm in the Composition of Lines.
   103, p.  80. The combination of various types of rhythmic movement.
   104, p.  86. Rhythm not necessarily inconsistent with Balance.
   105, p.  89. The Composition of various lines.
   106, p.  96. Outlines.
   107, p.  96. Harmony, Balance, and Rhythm in Outlines.
   108, p. 102. Interior Dimensions of an Outline.
   109, p. 102. Harmony of Interior Dimensions.
   110, p. 104. Convergence as a cause of movement.
   111, p. 108. Rhythm of Convergence. Contrary Motion in Convergences.
   112, p. 109. Changes of Direction in Convergences.
   113, p. 110. Ideas of association in rhythmic movements. Rhythm in
                changes of shape.
   114, p. 112. Outlines in different Attitudes.
   115, p. 112. Harmony, Balance, and Rhythm in the Attitudes of
                Outlines.
   116, p. 112. The Composition of Outlines.
   117, p. 124. The purpose of designing to induce the sense of Beauty
                which is the cause of all that is fine in Design.
   118, p. 125. Areas.
   119, p. 125. Linear Areas.
   120, p. 125. Changes of width-measure in Linear Progressions.
   121, p. 129. Areas defined by outlines, and also by tone-contrasts.
   122, p. 131. The Composition of Areas as defined by tone-contrasts.
   123, p. 131. Difference between drawing and painting, if there
                is any.
   124, p. 131. Definition of the word Tone.
   125, p. 132. Tone-Analysis.
   126, p. 132. The study of Tones and Tone-Relations.
   127, p. 133. Pigment-Materials.
   128, p. 133. The Scale of Neutral Values.
   129, p. 134. Contrasts of the Scale of Values.
   130, p. 135. Definition of Value-Relations.
   131, p. 136. Scales of Colors in Different Values.
   132, p. 137. Definition of the terms used to describe different
                Colors.
   133, p. 138. Color-Intensities found in different values.
   134, p. 139. Value-Relation of different Colors shown in the
                Spectrum.
   135, p. 139. The Spectrum a sequence not a circuit; a circuit in
                pigments only.
   136, p. 140. The Complementaries.
   137, p. 140. A General Classification of Tones as to Value, Color,
                Color-Intensity, and Color-Neutralization.
   138, p. 141. The distinction between Color-Intensities and
                Color-Neutralizations.
   139, p. 141. Definition of particular tones.
   140, p. 141. Theoretical character of our classification of tones.
   141, p. 142. Definition of particular tone-relations.
   142, p. 143. Sequences of Values and Colors.
   143, p. 143. The Sequence of Neutral Values.
   144, p. 144. Vertical Sequences.
   145, p. 144. Horizontal Sequences.
   146, p. 144. Diagonal Sequences.
   147, p. 145. Diagonal Sequences of the Right and Left Modes.
   148, p. 146. Different Intervals in Diagonal Sequences.
   149, p. 146. Peculiar value of the Diagonal Sequence of Colors at the
                interval of the Fifth. The four Triads.
   150, p. 147. Sequences in which a certain relation of intervals is
                repeated.
   151, p. 147. The combination of two or more Vertical Sequences.
   152, p. 148. The combination of two or more Horizontal Sequences.
   153, p. 149. The Combination of Diagonal Sequences of the same and
                different modes.
   154, p. 151. Alternations in Vertical Sequences.
   155, p. 151. Alternations in Horizontal Sequences.
   156, p. 151. Alternations of different value-intervals in
                color-sequences of equal intervals.
   157, p. 153. Alternations of different color-intervals in
                value-sequences of equal intervals. Particular
                Sequences recommended.
   158, p. 153. Possibility of extending the classification of values
                and colors to a scale of seventeen values, including
                Black and White.
   159, p. 154. The method of using the Sequences described. Possible
                extension of the sequence by mixtures.
   160, p. 165. The value of the sequences found in the more definite
                thinking which they make possible, and in the Harmony of
                repetitions.
   161, p. 156. Considerations of position, measure, and shape in
                tone-relations.
   162, p. 158. Tone-Harmony.
   163, p. 158. Tones harmonized on the palette or by changes in the
                design.
   164, p. 159. Value-Harmony.
   165, p. 161. Color-Harmony.
   166, p. 163. Harmony of proportional neutralizations.
   167, p. 164. Value-Harmony and the Harmony of Proportional
                Neutralizations combined.
   168, p. 167. Harmony in the repetition of a certain relation of tones
                not in itself harmonious.
   169, p. 170. Harmony of a predominant tone in the repetition of a
                certain relation of tones.
   170, p. 170. The Harmony of a grayness induced by the opposition of
                tones which neutralize one another in the sense of
                vision.
   171, p. 171. Strong contrasts, inconsistent with Harmony, may be
                perfectly consistent with both Balance and Rhythm.
   172, p. 172. Tone-Balance in the abstract.
   173, p. 173. Use of the Diagram of Values and Colors for the
                calculation of tone-balances.
   174, p. 174. Element of Color-Intensity in tone-balances.
   175, p. 174. Tone-Balances always connected with Measure and
                Shape-Balances.
   176, p. 175. Tone and Measure-Balance.
   177, p. 175. Tone-Relations in Single and in Double Inversions.
   178, p. 176. Occult Tone, Measure and Shape-Balances.
   179, p. 178. Further considerations on the same subject.
   180, p. 178. Further considerations on the same subject.
   181, p. 181. The effect of Representations in Tone-Balances.
   182, p. 182. Tone-Rhythm.
   183, p. 184. Attitudes in Tone-Rhythms.
   184, p. 185. Inversions in Tone-Rhythms.
   185, p. 186. Composition of tones, measures, and shapes. Three
                general rules.
   186, p. 188. Design and “Decoration.”
   187, p. 190. The study of Order in Nature and in Works of Art.
   188, p. 190. Method of study by Analysis with Synthetic Performance.
   189, p. 192. Conclusion. The practice of Pure Design. Its purpose and
                end.

                         _The Riverside Press_
                       CAMBRIDGE · MASSACHUSETTS
                               U · S · A



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