# A Color Notation/Chapter 3

All colors grasped in the hand.
(54) Let us recall the names and order of colors given in the last chapter, with their assemblage in a sphere by the three qualities of hue, value, and chroma. It will aid the memory to call the thumb of the left hand red, the forefinger yellow, the middle finger green, the ring finger blue, and the little finger purple (Fig. 6). When the finger tips are in a circle, they represent a circuit of hues, which has neither beginning nor end, for we can start with any finger and trace a sequence forward or backward. Now close the tips together for white, and imagine that the five strong hues have slipped down to the knuckles, where they stand for the equator of the color sphere. Still lower down at the wrist is black.
(55) The hand thus becomes a color holder, with white at the finger tips, black at the wrist, strong colors around the outside, and weaker colors within the hollow. Each finger is a scale of its own color, with white above and black below, while the graying of all the hues is traced by imaginary lines which meet in the middle of the hand. Thus a child’s hand may be his substitute for the color sphere, and also make him realize that it is filled with grayer degrees of the outside colors, all of which melt into gray in the centre.
Neighborly and opposite hues; and their mixture.
(56) Let this circle (Fig. 7) stand for the equator of the color sphere with the five principal hues (written by their initials R, Y,
G, B, and P) spaced evenly about it. Some colors are neighbors, as red and yellow, while others are opposites. As soon as a child experiments with paints, he will notice the different results obtained by mixing them.
First, the neighbors, that is, any pair which lie next one another, as red and yellow, will unite to make a hue which retains a suggestion of both. It is intermediate between red and yellow, and we call it yellow-red.
(57) Green and yellow unite to form green-yellow, blue and green make blue-green, and so on with each succeeding pair. These intermediates are to be written by their initials, and inserted in their proper place between the principal hues. It is as if an orange (paragraph 9) were split into ten sectors instead of five, with red, yellow, green, blue, and purple as alternate sectors, while half of each adjoining color pair were united to form the sector between them. The original order of five hues is in no wise disturbed, but linked together by five intermediate steps.
(58) Here is a table of the intermediates made by mixing each pair:—
* Red and yellow unite to form yellow-red (YR), popularly called orange.
* Yellow and green unite to form green-yellow (GY), popularly called grass green.
* Green and blue unite to form blue-green (BG), popularly called peacock blue.
* Blue and purple unite to form purple-blue (PB), popularly called violet.
* Purple and red unite to form red-purple (RP), popularly called plum.
​Using the left hand again to hold colors, the principal hues remain unchanged on the knuckles, but in the hollows between them are placed intermediate hues, so that the circle now reads: red, yellow-red, yellow, green-yellow, green, blue-green, blue, purple-blue, purple, and red-purple, back to the red with which we started. This circuit is easily memorized, so that the child may begin with any color point, and repeat the series clock wise (that is, from left to right) or in reverse order.
(59) Each principal hue has thus made two close neighbors by mixing with the nearest principal hue on either hand. The neighbors of red are a yellow-red on one side and a purple-red on the other. The neighbors of green are a green-yellow on one hand and a blue-green on the other. It is evident that a still closer neighbor could be made by again mixing each consecutive pair in this circle of ten hues; and, if the process were continued long enough, the color steps would become so fine that the eye could see only a circuit of hues melting imperceptibly one into another.
(60) But it is better for the child to gain a fixed idea of red, yellow, green, blue, and purple, with their intermediates, before attempting to mix pigments, and these ten steps are sufficient for primary education.
(61) Next comes the question of opposites in this circle. A line drawn from red, through the centre, finds its opposite, blue- green. If these colors are mixed, they unite to form gray. Indeed, the centre of the circle stands for a middle gray, not only because it is the centre of the neutral axis between black and white, but also because any pair of opposites will unite to form gray. ​(62) This is a table of five mixtures which make neutral gray:
| Opposites | Red | Blue-green | Each pair of which unites in neutral gray. |
| Opposites | Yellow | Purple-blue | Each pair of which unites in neutral gray. |
| Opposites | Green | Red-purple | Each pair of which unites in neutral gray. |
| Opposites | Blue | Yellow-red | Each pair of which unites in neutral gray. |
| Opposites | Purple | Green-yellow | Each pair of which unites in neutral gray. |
(63) But if, instead of mixing these opposite hues, we place them side by side, the eye is so stimulated by their difference that each seems to gain in strength; i.e., each enhances the other when separate, but destroys the other when mixed. This is a very interesting point to be more fully illustrated by the help of a color wheel in Chapter V., paragraph 106. What we need to remember is that the mixture of neighborly hues makes them less stimulating to the eye, because they resemble each other, while a mixture of opposite hues extinguishes both in a neutral gray.
Hues once removed, and their mixture.
(64) There remains the question, What will happen if we mix, not two neighbors, nor two opposites, but a pair of hues once
removed in the circle, such as red and green? A line joining this pair does not pass through the neutral centre, but to one side nearer yellow, and blue shows that this mixture falls between neutral gray and yellow, partaking somewhat of each. In the same way a line joining yellow and blue shows that their mixture contains both green and gray. Indeed, a line joining any two colors in the circuit may be said to describe their union. A radius crossing this line passes to some hue on the circumference, and describes by its intersection with the first line ​the chroma of the color made by a mixture of the two original colors.
| Red | Green | Yellow-gray | Each pair unites in a colored gray, which is an intermediate hue of weak chroma. |
| Yellow | Blue | Green-gray | Each pair unites in a colored gray, which is an intermediate hue of weak chroma. |
| Green | Purple | Blue-gray | Each pair unites in a colored gray, which is an intermediate hue of weak chroma. |
| Blue | Red | Purple-gray | Each pair unites in a colored gray, which is an intermediate hue of weak chroma. |
| Purple | Yellow | Red-gray | Each pair unites in a colored gray, which is an intermediate hue of weak chroma. |
Mixture of white and black: a scale of grays.
(65) So far we have thought only of the plane of the equator, with its circle of middle hues in ten steps, and studied their mixture
by drawing lines to join them. Now let us start at the neutral centre, and think upward to white and downward to black (Fig. 9.)
This vertical line is the neutral axis joining the poles of white and black, which represent the opposites of light and darkness. Middle 4) pray is half-way between. If black is called 0, and white is 10, then the middle point is 5, with 6, 7, 8, and 9 above, while 4, 3, 2, and 1 are below, thus making a vertical scale of grays from black to white (Chapter II., paragraph 25).
If left to personal preference, an estimate of middle value will vary with each individual who attempts to make it. This appears in the neutral scales already published for schools, and students who depend upon them, discover a variation of over 10 per cent. in the selection of middle gray. Since this value scale underlies all color work, it needs accurate adjustment by scientific means, as in scales of sound, of length, of weight, or of temperature.
A Photometer (photo, light, and meter, a measure) is shown ​on the next page. It measures the relative amount of light which the eye receives from any source, and so enables us to make a scale with any number of regular steps. The principle on which it acts is very simple.
A rectangular box, divided by a central partition into halves, has symmetrical openings in the front walls, which permit the light to reach two white fields placed upon the back walls. If one looks in through the observation tube, both halves are seen to be exactly alike, and the white fields equally illuminated. A valve is then fitted to one of the front openings, so that the light in that half of the photometer may be gradually diminished. Its white field is thus darkened by measured degrees, and becomes black when all light is excluded by the closed valve. While this darkening process goes on in one-half of the instrument, the white field in the other half does not change, and, looking into the eye-piece, the observer sees each step contrasted with the original white. One-half is thus said to be variable because of its valve, and the other side is said to be fixed. A dial connected with the valve has a hand moving over it to show how much light is admitted to the field in the variable half.
Let us now test one of these personal decisions about middle value. A sample replaces the white field in the fixed half, and by means of the valve, the white field in the variable half is alternately darkened and lightened, until it matches the sample and the eye sees no difference in the two. The dial then discloses the fact that this supposedly middle value reflects only 42 per cent. of the light; that is to say, it is nearly a whole step too low in a decimal scale. Other samples err nearly as far on the light side of middle value, and further tests prove not only the varying color sensitiveness of individuals, but detect a difference between the left and right eye of the same person.
PHOTOMETER.
The vagaries of color estimate thus disclosed, lead some to seek shelter in “feeling and inspiration”; but feeling and inspiration are temperamental, and have nothing to do with the simple facts of vision. A measured and unchanging scale is as necessary and valuable in the training of the eye as the musical scale in the discipline of the ear.
It will soon be necessary to talk of the values in each color. We may distinguish the values on the neutral axis from color values by writing them N$^1$, N$^2$, N$^3$, N$^4$, N$^5$, N$^6$, N$^7$, N$^8$, N$^9$, N$^{10}$. Such a scale makes it easy to foresee the result of mixing light values with dark ones. Any two gray values in varying proportions unite to form a gray midway between them. Thus N$^4$ and N$^6$ being equally above and below the centre, unite to form ​
PARTS.
C, Cabinet, with sample-holder (H) and mirror (M), which may be removed and stored to left of dial (D) when instrument is closed for transportation.
D, Dial records color values in terms of standard white (100), the opposite end of the scale being absolute blackness (0).
E, Eye-peiece: to shield eye and sample from extraneous light while color determinations are being made. Fatigue of retina should be avoided.
G, Gear: actuates cat’s-eye shutter, which controls amount of light admitted to right half of instrument. Its shaft carries index-hand over dial.
H, Field-Holder: retains sample and standard white in same plane, and isolates them, Is hinged upon lower edge, and secured by pivot clamp.
M, Mirror: permits observation of the isolated halves of the holder, bearing standard white and the color to be measured. Should be clean and free from dust on both sides of central partition. 3
N$^5$, as will also N$^7$ and N$^3$, N$^8$ and N$^2$, or N$^9$ and N$^1$. But N$^9$ and N$^3$ will unite to form N®, which is midway between 3 and 9.
(66) When this numbered scale of values is familiar, it serves not only to describe light and dark grays, but the value of colors which are at the same level in the scale. Thus R’ (popularly called a tint of red) is neither lighter nor darker than the gray of N?. A numeral written above to the right always indicates value, whether of a gray or a color, so that R$^1$, R$^2$, R$^3$, R$^4$, R$^5$, R$^6$, R$^7$, R$^8$, R$^9$, describes a regular scale of red values from black to white, while G$^1$, G$^2$, G$^3$, etc., is a scale of green values. ​(67) This matter of a notation for colors will be more fully worked out in Chapter VI., but the letters and numerals already described greatly simplify what we are about to consider in the mixture and balance of colors.
Mixture of light hues with dark hues.
(68) Now that we are supplied with a decimal scale of grays, represented by divisions of the neutral axis (N$^1$, N$^2$, etc.), and An image should appear at this position in the text. a corresponding decimal scale of value for each of the ten hues ranged about the equator (R}, R$^1$,—YR$^1$, YR$^2$,—Y$^1$, Y$^1$,—GY$^2$, GY$^1$,— and so on), traced by ten equidistant meridians from black to white, it is not difficult to fore- see what the mixture of any two colors will produce, whether they are of the same level of value, as in the colors of the equator already considered, or whether they are of different levels.
(69) For instance, let us mix a light yellow (Y$^7$) with a dark red (R$^3$). They are neighbors in hue, but well removed in value. A line joining them centres at YR$^5$. This describes the result of their mixture,—a value intermediate between 7 and 3, with a hue intermediate between R and Y. It is a yellow-red of middle value, popularly called “dark orange.” But, while this term “dark orange’? rarely means the same color to three different people, these measured scales give to YR$^5$ an unmistakable mean- ing, just as the musical scale gives an unmistakable significance to the notes of its score.
(70) Evidently, this way of writing colors by their degrees of value and hue gives clearness to what would otherwise be hard to express by the color terms in common use.
(71) If Y$^9$ and R$^5$ be chosen for mixture, we know at once that ​they unite in YR$^7$, which is two steps of the value scale above the middle; while Y$^6$ and R$^2$ make YR$^4$, which is one step below the middle. Charts prepared with this system show each of these colors and their mixture with exactness.
(72) The foregoing mixtures of dark reds and light yellows are typical of the union of light and dark values of any neighboring hues, such as yellow and green, green and blue, blue and purple, or purple and red. Next let us think of the result of mixing different values in’ opposite hues; as, for instance, YR$^7$ and B$^3$ (Fig. 11). To this combination the color sphere gives a ready answer; for the middle of a straight line through the sphere, and joining them, coincides with the neutral centre, showing that they An image should appear at this position in the text. balance in neutral gray. This is also true of any opposite pair of surface hues where 3 the values are equally removed from the equator.
(73) Suppose we substitute familiar flowers for the notation, then YR$^7$ becomes the buttercup, and B$^3$ is the wild violet. But, in comparing the two, the eye is more stimulated by the buttercup than by the violet, not alone because it is lighter, but because it is stronger in chroma; that is, farther away from the neutral axis of the sphere, and in fact out beyond its surface, as shown in Fig. 11.
The head of a pin stuck in toward the axis on the 7th level of YR may represent the 9th step in the scale of chroma, such as the buttercup, while the “modest” violet with a chroma of only 4, is shown by its position to be nearer the neutral axis than the brilliant buttercup by five steps of chroma. This is the third dimension of color, and must be included in our notation ​So we write the buttercup YR 7/9 and the violet B 3/34,—chroma always being written below to the right of hue, and value always above. (This is the invariable order: HUE VALUE/CHROMA).
(74) A line joining the head of the pin mentioned above with B 3/4 does not pass through the centre of the sphere, and its middle point is nearer the buttercup than the neutral axis, showing that the hues of the buttercup and violet do not balance in gray.
The neutral centre is a balancing point for colors.
(75) This raises the question, What is balance of color? Ar- tists criticise the color schemes of paintings as being “too light or too dark” (unbalanced in value), “too weak or too strong” (unbalanced in chroma), and “too hot or too cold” (unbalanced in hue), showing that this is a fundamental idea underlying all color arrangements.
(76) Let us assume that the centre of the sphere is the natural balancing point for all colors (which will be best shown by Max- well discs in Chapter V., paragraphs 106-112), then color points equally removed from the centre must balance one another. Thus white balances black. Lighter red balances darker blue-green. Middle red balances middle blue-green. In short, every straight line through this centre indicates opposite qualities that balance one another. The color points so found are said to be “complementary,” for each supplies what is needed to complement or balance the other in hue, value, and chroma.
(77) The true complement of the buttercup, then, is not the violet, which is too weak in chroma to balance its strong opposite. We have no blue flower that can equal the chroma of the butter-cup. Some other means must be found to produce a balance. One way is to use more of the weaker color. Thus we can make ​a bunch of buttercups and violets, using twice as many of the latter, so that the eye sees an area of blue twice as great as the area of yellow-red. Area as a compensation for inequalities of hue, value, and chroma will be further described under the harmony of color in Chapter VII.
(78) But, before leaving this illustration of the buttercup and violet, it is well to consider another color path connecting them which does not pass through the sphere, but around it (Fig. 12). Such a path swinging around from yellow-red to blue slants down- ward in value, and passes through yellow, green-yellow, green, and blue-green, tracing a sequence of hue, of which each step is less chromatic than its predecessor.
This diminishing sequence is easily written thus,Y 8/7, GY 7/9, G 6/5, BG 5/4, B 4/3, PB 3/2,—and is shown graphically in Fig. 12. Its hue sequence is described by the initials Y, GY, G, BG; -B,: and PB 3/2. Its An image should appear at this position in the text. value-sequence appears in the upper numerals, 8, 7, 6, 5, 4, and 3, while the chroma-sequence is included in the lower numerals, 7, 6, 5, 4, 3, and 2. This gives a complete statement of the sequence, Achaing its peculiarity, that at each change of hue there is a regular decrease of value and chroma. Nature seems to be partial to this sequence, constantly reiterating it in yellow flowers with their darker green leaves and underlying shadows. In spring time she may contract its range, making the blue more green and the yellow less red, but in autumn she seems to widen the range, presenting strong contrasts of yellow-red and purple-blue.
(79) Every day she plays upon the values of this sequence, ​from the strong contrasts of light and shadow at noon to the hardly perceptible differences at twilight. The chroma of this sequence expands during the summer to strong colors, and contracts in winter to grays. Indeed, Nature, who would seem to be the source of our notions of color harmony, rarely repeats herself, yet is endlessly balancing inequalities of hue, value, and chroma by compensations of quantity.
(80) So subtle is this equilibrium that it is taken for granted and forgotten, except when some violent disturbance disarranges it, such as an earthquake or a thunder-storm.
The triple nature of color balance illustrated.
(81) The simplest idea of balance is the equilibrium of two halves of a stick supported at its middle point. If one end is heavier than the other, the support must be moved nearer to that end.
But, since color unites three qualities, we must seek some type of triple balance. The game of jackstraws illustrates this, when the disturbance of one piece involves the displacement of two others. The action of three children on a floating plank or the equilibrium of two acrobats carried on the shoulders of a third may also serve as examples.
(82) Triple balance may be graphically shown by three discs An image should appear at this position in the text. in contact. Two of them are suspended by their centres, while they remain in touch with a third supported on a pivot, as in Fig. 14. Let us call the lowest disc Hue (H), and the lateral discs Value (V) and Chroma (C). Any dip or rotation of the lower disc H will induce sympathetic action in the two lateral discs V and C. When H is inclined, both V ​and C change their relations to it. If H is raised vertically, both V and C dip outward. If H is rotated, both V and C rotate, but in opposite directions. Indeed, any disturbance of V affects H and C, while H and V respond to any movement of C. So we must be prepared to realize that any change of one color quality involves readjustment of the other two.
(83) Color balance soon leads to a study of optics in one direction, to esthetics in another, and to mathematical proportions in a third, and any attempt at an easy solution of its problems is not likely to succeed. It is a very complicated question, whose closest counterpart is to be sought in musical rhythms. The fall of musical impulses upon the ear can make us gay or sad, and there are color groups which, acting through the eye, can convey pleasure or pain to the mind.
(84) A colorist is keenly alive to these feelings of satisfaction or annoyance, and consciously or unconsciously he rejects certain combinations of color and accepts others. Successful pictures and decorative schemes are due to some sort of balance uniting “light and shade” (value), “warmth and coolness” (hue), with “brilliancy and grayness”’ (chroma); for, when they fail to please, the mind at once begins to search for the unbalanced quality, and complains that the color is “too hot,” “too dark,”’ or “too crude.” This effort to establish pleasing proportions may be unconscious in one temperament, while it becomes a matter of definite analysis in another. Emerson claimed that the unconscious only is complete. We gladly permit those whose color instinct is unerring— (and how few they are!)—to neglect all rules and set formulas. But education is concerned with the many who have not this gift.
(85) Any real progress in color education must come not from a blind imitation of past successes, but by a study into the laws ​which they exemplify. To exactly copy fine Japanese prints or Persian rugs or Renaissance tapestries, while it cultivates an appreciation of their refinements, does not give one the power to create things equally beautiful. The masterpieces of music correctly rendered do not of necessity make a composer. ‘The musician, besides the study of masterpieces, absorbs the science of counterpoint, and records by an unmistakable notation the exact character of any new combination of musical intervals which he conceives.
(86) So must the art of the colorist be furnished with a scientific basis and a clear form of color notation. This will record the successes and failures of the past, and aid in a search, by contrast and analysis, for the fundamentals of color balance. Without a measured and systematic notation, attempts to describe color harmony only produce hazy generalities of little value in describing our sensations, and fail to express the essential differences between “good” and “bad” color.
* ↑ Orange is a variable union of yellow and red. See Appendix.
* ↑ Green is often wrongly assigned as the opposite of red. See Appendix, on False Color Balance.
* ↑ Adopted in Course on Optical Measurements at the Massachusetts Institute of Technology. Instruments have also been made for the Harvard Medical School, the Treasury Department in Washington, and various private laboratories, and commercial industries.
False Color Balance. There is a widely accepted error An image should appear at this position in the text. that red, yellow, and blue are “primary,” although Brewster’s theory was long ago dropped when the elements of color vision proved to be Red, Grren, and Violet-Blue. The late Professor Rood called attention to this in Chapters VIII.—XI. of his book, “Modern Chromatics,” which appeared in 1879. Yet we find it very generally taught in school. Nor does the harm end there, for placing red, yellow, and blue equidistant in a circle, with orange, green, and purple as intermediates, the teacher goes on to state that opposite hues are complementary.
Red is thus made the complement of Green, Yellow thus made the„ complement„ of Purple, and
Blue is thus made the„ complement„ ofOrange.
Unfortunately, each of these statements is wrong, and, if tested by the mixture of colored lights or with Maxwell’s rotating discs, their falsity is evident.
There can be no doubt that green is not the complement of red, nor purple of yellow, nor orange of blue, for neither one of these pairs unites as it should in a balanced neutrality, and a total test of the circle gives great excess of orange, showing that red ​and yellow usurp too great a portion of the circumference. Starting from a false basis, the Brewster theory can only lead to un-balanced and inharmonious effects of color.
The fundamental color sensations are red, green, and violet-blue.
| Red has for | its true complement | blue-green, |
| Green | its true„ complement„ | red-purple, and |
| Yellow | its true„ complement„ | violet-blue |
all of the hues in the right-hand column being compound sensations. The sensation of green is not due to a mixture of yellow and blue, as the absorptive action of pigments might lead one to think: Green is fundamental, and not made by mixing any hues of the spectrum, while Yellow is not fundamental, but caused by the mingled sensations of red and green. This is easily proved by a controlled spectrum, for all yellow-reds, yellows, and ereen-yellows can be matched by certain proportions of red and green light, all blue-greens, blues, and purple-blues can be ob- tained by the union of green and violet light, while purple-blue, purple, and red-purple result from the union of violet and red light. But there is no point where a mixture gives red, green, or violet-blue. They are the true primaries, whose mixtures produce all other hues.
Studio and school-room practice still cling to the discredited theory, claiming that, if it fails to describe our color sensations, yet it may be called practically true of pigments, because a red, yellow, and blue pigment suffice to imitate most natural colors. This discrepancy between pigment mixture and retinal mixture becomes clear as soon as one learns the physical make-up and behavior of paints.
​Spectral analysis shows that no pigment is a pure example of the dominant hue which it sends to the eye. Take, for example, An image should appear at this position in the text. the very chromatic pigments representing red and green, such as vermilion and emerald green. If each emitted a single pure hue free from trace of any other hue, then their mixture would appear yellow, as when spectral red and green unite. But, instead of yellow, their mixture produces a warm gray, called brown or “dull salmon,” and this is to be inferred from their spectra, where it is seen that vermilion emits some green and purple as well as its dominant color, while the green also sends some blue and red light to the eye.
Thus stray hues from other parts of the spectrum tend to neutralize the yellow sensation, which would be strong if each of the pigments were pure in the spectral sense. Pigment absorption affects all palette mixtures, and, failing to obtain a satisfactory yellow by mixture of red and green, painters use original yellow pigments,—such as aureolin, cadmium, and lead chromate,— each of them also impure but giving a dominant sensation of yel- low. Did the eye discriminate, as does the ear when it analyzes the separate tones of a chord, then we should recognize that yel- low pigments emit both red and green rays.
White light dispersed into a colored band by one prism, may have the process reversed by a second prism, so that the eye sees again only white light. But this would not be so, did not the balance of red, green, and violet-blue sensations remain undisturbed. All our ideas of color harmony are based upon this fundamental relation, and, if pigments are to render harmonious effects, ​we must learn to control their impurities so as to preserve a balance of red, green, and violet-blue.
Otherwise, the excessive chroma and value of red and yellow pigments so overwhelm the lesser degrees of green and blue pigments that no balance is possible, and the colorist of fine perception must reject not alone the theoretical, but also the practical outcome of a “red-yellow-blue” theory.
Some of the points raised in this discussion are rather subtle for students, and may well be left until they arise in a study of optics, but the teacher should grasp them clearly, so as not to be led into false statements about primary and complementary hues.
* ↑ Ultramarine, the pigment often selected as a typical blue, has a violet or purple quality which makes it the complement of yellow, not of orange. Typical blue should contain no hint of violet or purple, and is best represented by Cerulean (cyan-blue), which is the true complement of yellow-red. See charts B and Y of the Color Atlas.
* ↑ See Rood, Chapter VII. on Color by Absorption.