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

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

HLt

LLt

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.