COLOR MIXTURE AND BALANCE.
+All colors grasped in the hand.+
[Illustration: Fig. 6.]
(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.
[Illustration: Fig. 7.]
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.+
[Illustration: Fig. 8.]
(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.)
[Illustration: 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.
[Illustration: PHOTOMETER.
Back View. Front View.]
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.
[Illustration: Vertical Section through light openings.
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.
[Illustration: Fig. 10.]
(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.
[Illustration: Fig. 11.]
(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.
[Illustration: Fig. 12.]
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.
[Illustration: Fig. 14.]
(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.
APPENDIX TO CHAPTER III.
[Illustration]
FALSE COLOR BALANCE. There is a widely accepted error 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, GREEN, 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 " " Purple, and
Blue " " Orange.
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 unbalanced and inharmonious effects
of color.
The fundamental color sensations are RED, GREEN, and VIOLET-BLUE.
RED has for its true complement BLUE-GREEN,
GREEN " " RED-PURPLE, and
VIOLET-BLUE " " YELLOW,
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 green-yellows can be matched by certain
proportions of red and green light, all blue-greens, blues, and
purple-blues can be obtained 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.
[Illustration:
{ Vermilion
Spectra {
{ Em. Green
P. B. G. Y. R.]
Spectral analysis shows that no pigment is a pure example of the
dominant hue which it sends to the eye. Take, for example, 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.[20]
[Footnote 20: See Rood, Chapter VII., on Color by Absorption.]
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 yellow. Did the eye discriminate, as does the ear
when it analyzes the separate tones of a chord, then we should recognize
that yellow 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.