Chapter III: Color Mixture and Balance

+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.[17]

(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.[17]
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.

[Footnote 17: Orange is a variable union of yellow and red. See
Appendix.]

(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.[18] 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.

[Footnote 18: Green is often wrongly assigned as the opposite of
red. See Appendix, on False Color Balance.]

(62) This is a table of five mixtures which make neutral gray:

{ Red & Blue-green }
{ Yellow Purple-blue }
Opposites { Green Red-purple } Each pair of which unites
{ Blue Yellow-red } in neutral gray.
{ Purple Green-yellow }

(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, which 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 make Yellow-gray }
Yellow Blue Green-gray } Each pair unites in a _colored_
Green Purple Blue-gray } gray, which is an intermediate hue
Blue Red Purple-gray } of weak chroma.
Purple Yellow Red-gray }

+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 gray 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)[19] 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.

[Footnote 19: 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.]

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 eyepiece, 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.

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 N1, N2, N3, N4, N5, N6, N7, N8, N9, N10. Such a scale makes it easy to foresee the result of mixing light values with dark ones. Any two gray values unite to form a gray midway between them. Thus N4 and N6 being equally above and below the centre, unite to form N5, as will also N7 and N3, N8 and N2, or N9 and N1. But N9 and N3 will unite to form N6, which is midway between 6 and 9.

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-PIECE: 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.
_S_, DIFFUSING SCREEN, placed over front apertures, to evenly
distribute the light.]

(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 R7 (popularly called a tint of red) is neither lighter nor darker than the gray of N7. A numeral written above to the right always indicates _value_, whether of a gray or a color, so that R1, R2, R3, R4, R5, R6, R7, R8, R9, describes a regular scale of red values from black to white, while G1, G2, G3, 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 (N1, N2, etc.), and a corresponding decimal scale of value for each of the ten hues ranged about the equator (R1, R2,-- YR1, YR2,-- Y1, Y2,-- GY1, GY2,-- and so on), traced by ten equidistant meridians from black to white, it is not difficult to foresee 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 (Y7) with a dark red (R3). They are neighbors in hue, but well removed in value. A line joining them centres at YR5. 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 YR5 an unmistakable meaning, 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 Y9 and R5 be chosen for mixture, we know at once that they unite in YR7, which is two steps of the value scale above the middle; while Y6 and R2 make YR4, 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, YR7 and B3 (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 _balance in neutral gray_. This is also true of any opposite pair of surface hues where the values are equally removed from the equator.

(73) Suppose we substitute familiar flowers for the notation, then YR7 becomes the buttercup, and B3 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 3/4,--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? Artists 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 Maxwell 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 buttercup. 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 downward 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,--YR 8/9, Y 7/8, GY 6/7, G 5/6, BG 4/5, B 3/4,--and is shown graphically in Fig. 12. Its hue sequence is described by the initials YR, Y, GY, G, BG, and B. Its value-sequence appears in the upper numerals, 8, 7, 6, 5, 4, and 3, while the chroma-sequence is included in the lower numerals, 9, 8, 7, 6, 5, and 4. This gives a complete statement of the sequence, defining 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 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 æsthetics 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.