Fifth Letter of Zeuxis to Arte -
Theories of Harmony of Colours after Chevreul

My dear Arte,

Many people have pondered over the harmony of colours. I describe hereafter some of their theories. Take patience: this is heavy stuff!

Wilhelm von Bezold (1837-1907)

Von Bezold’s theories on harmony joined those of Goethe and of Philipp Otto Runge. Analogous colours in the circle of twelve colours are contiguous colours, and for Bezold these were harmonious when combined. Bezold wrote on the notion of relative brightness of each hue. In harmonious colours, the relative bright ness of each hue had to concord also. Bezold found that colours that were further away from each other on the colour circle did not go well together. So, these hues were un-harmonious. Only when the distance between two colours became large, did Bezold find again harmonious contrasts. In combinations of three colours, harmony was thus obtained when the distance between the colours was the same.

Albert Henry Munsell (1858-1918)

Munsell was a north-American painter. He wrote a book with the title "The Grammar of Colour", in which he presented his concepts of colours. He proposed five major hues: yellow, green, blue, purple and red. He devised a colour wheel of twenty colours. Munsell defined these colours as the basic hues. He came to that conclusion from perceptions of afterimages, that is of hues perceived after one looks for some time at a hue and then diverts one’s glance away from that hue and on to a white background. Munsell placed the afterimage colours on opposite sides of his circle. Munsell also proposed a numbering system for hues, which was later adopted by the United States Bureau of Standards, and that system has remained influential to this day.

Munsell wrote on harmony and he proposed five rules for harmony.
Rule one was that as few hues as possible should be used; if more hues were combined together, they had to be similar for Munsell.
In rule two, he proposed to combine hues of different tone but he stated that a balance between these was needed so that for instance one part of brightness was balanced by three or four parts of less bright colours.
In rule three, Munsell proposed to combine very pure with less pure colours and again to hold these in balance.
Munsell’s fourth rule described these balances in surface areas. He stated that the dimensions of the areas should be inversely proportional to the products of purity and brightness of the colours of these surfaces.
Finally, in a last rule, he said that harmony was reached when three out of the four foregoing rules were realised. Munsell thus stated that there were three characteristics of colours: hue, purity and brightness. He also emphasised the notion of balance of areas of colour.

Wilhelm Ostwald (1853-1932)

Wilhelm Ostwald was a professor of chemistry and physics at the university of Leipzig in Germany. He won a Nobel Prize for chemistry. Ostwald also wrote on his notions of harmony of colours in a book called "The Harmony of Colours".
He wrote that there was one major rule by which colours go well together, and that was that their characteristics should be in simple relations to each other.
For instance in the grey scale, the relations between hues are indeed straightforward, as only the degree of white and black can vary. A simple relation was also when two hues could be combined with a third to obtain a neutral grey. Ostwald discussed many cases of combinations of colours, and his notion of "simple relations" that could be found between them to determine harmony, or the lacking thereof, and hence their discord. Ostwald stressed the importance of tone. He found that any colour could harmoniously be combined with any other, as long as their tone was similar. This however did not work well for hues that were already similar. Ostwald used a colour circle of twenty-four colours. He stated that mostly two complementary colours went well together, or three, or four or eight colours of the circle, as long as they were similarly situated at symmetric intervals on the circle.

Other writers

Other writers of the end of the nineteenth century and somewhat later were Adolf Hoelzel (1863-1934) and Paul Renner (1878-1956). Michel-Eugčne Chevreul made his discoveries on the changes in perception of juxtaposed colours in the 1830’s, and he then also formulated his views on harmony of colours. These are still much the soundest basis for contemporary theories on colour perception and on harmony. Very few scientists and artists of the twentieth century have studied colours so extensively as Chevreul, and fewer still published additional ideas.

Two of the best-known teachers on colours were Josef Albers (1888-1976) and Johannes Itten (1888-1967). They were both born in the same year, both Germans and both taught at the Bauhaus institute founded by Walter Gropius in Weimar. Itten taught form and colour from 1919 to 1923. Wassily Kandinsky followed him for the course on colour, whereas Albers taught later after the Bauhaus’ departure for Dessau.
Johannes Itten published his book "The Art of Colours" in 1961; Albers’ book "Interaction of Colours" was published in 1963.
Various other authors and painters wrote on colours, such as the painter Hajo Düchting. Düchting wrote a book that gave a synthesis of previous theories.
The psychologist Rudolf Arnheim also handled colours in his book "Art and visual perception", published in 1952, and revised in a new edition in 1974. We will also mention Arnheim’s ideas on colours.

Josef Albers’ views on Colours

Josef Albers mostly explained how colour effects could be made aware to students. He did not formulate new rules for harmony, and he barely touched the subjects that Chevreul had studied. He emphasised the subjectivity in the perception of colours, his scepticism with theory, and his belief in practical exercises in the teaching of colours. He described marvellous exercises to demonstrate the effects of simultaneous contrast.

Albers stated that his studies on the size of areas of colours, which he called his "quantity" studies, had taught him that independent of harmony rules, any colour "goes" or "works" with any other, presupposing that their quantities were appropriate. He wrote that it was fortunate that there were so far no comprehensive rules for such aims.

Josef Albers noted that effects of simultaneous contrasts often appear as shadows on one side of a boundary between two colours, and as light reflected on the other side. He remarked that these effects occurred most perceptibly between colours that were contrasting in their hues, but also similar in light intensity.
He much relativised the theories, as they had been devised with colour areas of particular sizes. He even stated that the boundary effects of simultaneous contrast were perceived under the same conditions by some people and not by others and that – though rarely perceived – the articulate boundaries could be made nearly invisible through the choice of appropriate colours of equal light intensity.
Moreover, he emphasised that colour harmonies were not the only desirable relationships between colours. He wrote, "As with tones in music, so with colour – dissonance is as desirable as its opposite, consonance."

Albers’ views are very wise. His views lack maybe in delicate analysis, but gain in synthesis. Albers, as other modern writers, proposed to prone individual taste over analysis of colour harmony.

Johannes Itten’s ideas on harmony and contrasts

Johannes Itten noted the obvious subjectivity of the concept of harmony. He wrote that the assertion of harmony or discord referred simply to scales of appreciations like agreeable-disagreeable or attractive-unattractive, which remained very subjective attitudes. Like Josef Albers, he found primarily that harmony implied balance and symmetry of forces.

Itten pulled the concept of harmony therefore into the purely objective domain, in order to be able to share a definition, and he based this definition soundly on the complementarity of colours.

Itten devised a colour circle logically derived from the three painters’ primaries yellow, blue and red.
These three colours give rise to three secondary colours as they are combined: green (blue plus yellow), violet (blue plus red) and orange (red plus yellow).
The three secondary colours can be combined in their turn with the three primary colours to give rise to six tertiary colours, whose names denote the combinations: yellow-orange, red-orange, red-violet, blue-violet, blue-green and yellow-green.
Itten thus obtained in all twelve different colours, which he positioned on his colour circle, but configured as a ring. We reproduce this in the following figure.

Itten gave an almost mathematical definition of harmony.
He stated that harmonious were the complementary pairs of colours, the colours that lay on opposing ends of the radius of the colour wheel.
Harmonious also were the combinations situated at the corners of the equilateral and isosceles triangles, rectangles and squares, as well as of the two hexagons that could be inscribed in the ring. Such combinations of colours yield in a subtractive mixture of paints a neutral grey.
All other combinations he called expressive or discordant in character.
But Itten quickly added that many great paintings used this expressive intonation to exciting and provocative effect. So, Itten very much relativised the necessity for harmony as an absolutely desired sensation of perception, that naturally evoked feelings of pleasure. He did not spend much time on elaborating rules for colour combinations that could explain what could have agreeable or disagreeable effects on viewers. He almost dismissed the notion, calling it an entirely subjective criterion that was in the realm of individual taste.
Itten preferred to remove the concept of harmony from that subjective sphere, to give it a definition of logical construction that was both universal and objective. This construction was derived from the subtractive mixing of paints. Itten therefore used a painter’s definition and view on harmony.

The concept of harmony according to Johannes Itten is entirely based on fully saturated hues, and on hue only. The properties of tone and intensity do not enter the definition of harmony for him.
Both Itten and Albers did away with the attempt of Chevreul to define criteria for harmony that included all three characteristics of colour, and they refused schemas like Chevreul had given. If Albers hardly spoke of harmony rules and had more the idea that "anything goes" in combinations of colours, as long as balance of quantity was preserved, Itten aimed to limit once and for all the polemics on harmony to a geometrical construction based on the subtractive complementarity of hues.

Johannes Itten started his book on colours by stating, "Colour effects are in the eye of the beholder. Yet the deepest and truest secrets of colour effects are, I know, invisible even to the eye, and are beheld by the heart alone. The essential eludes conceptual formulation".
Herein lies modern and contemporary analysis of colour harmony. The search for criteria or rules for harmony seemed to be over, as Albers and Itten relegated the notion either to the fully subjective or the mere arbitrary definition. The twelve-colour ring of Itten is an elegant and simple construction that has the great advantage that it is easily constructed, and thus can be easily remembered by painters and viewers alike. Its simplicity is its superiority.

Once Johannes Itten had dispensed with the controversy on harmony in a decisive manner, he distinguished between seven schemas of colour combinations that could serve as analysis models in paintings. He called these "colour contrasts". He identified seven such colour contrasts. I discuss these hereafter.

Itten's Contrast of Hues

Itten called these contrasts the combinations of the saturated primary and secondary colours, plus white and black.
These were the combinations of the undiluted colours that Goethe had called together the "splendid". Itten allowed the brilliances of the colours to be varied, as well as their quantitative proportions. Such combinations are splendid indeed, and the examples we have used in these lessons to illustrate them, date mostly from the Early Renaissance (Botticelli and Fra Angelico), as such combinations express grandeur, joviality and in Itten’s own words "cosmic universality".

Itten's Light-Dark Contrasts

Light-dark contrasts are series of colours of equal brilliance or of equal darkness, colours of the same tone.
These contrasts can be formed by all the shades of the grey-scale and for such a given grey-tone of all the hues of that same tone. Equality of tone relates colour hues, but some hues are simply too extreme in tone by themselves to be able to be configured in any scheme of constant tone. Yellow for instance is simply too brilliant a hue, so that it cannot find its place in schemas of darker tones. The same goes for violet in the brighter tones.
Light-dark contrast is created when a colour of a light tone (whatever its hue) is combined with a colour of a dark tone (whatever its hue). Itten wrote that when in a painting colours are not grouped by tone, then order, clarity and vigour of a composition are sacrificed. This however was not necessarily a wrong effect, and could even be desired in certain paintings.

Itten's Cold-Warm Contrasts

On Johannes Itten’s colour ring yellow is the brightest and violet the darkest hue. Itten positioned these on the vertical axis and opposing each other. On the horizontal axis we find red-orange facing blue-green. Itten called these the cold-warm contrasting colours, with red-orange the warmest and blue-green the coldest. Combinations and gradations of these yield paintings based on cold-warm antagonies of colour.

Itten's Complementary Contrasts

The pairs of complementary colours yellow and violet, blue and orange, and red and green create complementary contrasts. These pairs of course excite each other to maximum vividness, as Chevreul had proven. Itten found that such combinations, used in the proper proportions, gave the effect of statically fixed images, as each colour confirmed the other’s hue and intensity. He noted that complementary colours often occurred in elegant mixtures in nature, for instance in flowers.

Itten's Simultaneous Contrast

Itten recognised of course the effects of the laws of simultaneous contrast of Michel-Eugčne Chevreul. He confirmed the importance of these effects, which transformed single hues into other hues due to the relative position of such a hue in other, surrounding hues, so that the effect was a real challenge for painters.

Itten's Contrast of Saturation

This contrast relates to the degree of purity of a colour. A hue can be diluted by white or black, and thus be transformed over a scale. Contrast of saturation then was the contrast between pure, intense colours and dull, diluted colours. These are "dull-vivid" contrasts.

Itten's Contrasts of Extension

By this term, Itten denoted the proportions of relative areas of two or more colours patches, the contrast between large and small sizes of colour areas. We handled this notion in our previous chapter on balance of colour surfaces in size.

Johannes Itten wrote more on contrasts than on harmony. Thereby he drew attention away from harmony, to expression. Contrasts are expressive, create tension, and they emphasise emotions. Many modern writers seem to find this aspect more important than harmony. Whereas harmony induces gentle, equal feelings in viewers, contrasts are surprising, entice interest, create tension and thus form the dynamic, lively aspect that strikes and captures the viewer. For Johannes Itten, such effects were more necessary than the harmony of colours in pictures.

Harald Küppers

Harald Küppers is a German engineer who was very active in the German colour industry. He wrote several books on colours. In 1989 he edited a book on the theoretical foundation of the basic colours called "The Theory of Harmony of Colours".
Küppers based his theory on the three colours upon which the retina of the eye reacts: red (slightly orange-tinted), green and blue (slightly violet-tinted). These three allow eight combinations, but including the three primary colours and also white (formed when the three primary colours are present) and black (when the three primary colours are absent).
Like his predecessors Runge, Chevreul and Ostwald, Küppers built a three-dimensional system to represent colours of the additive process in hues, tones and intensities. Whereas Runge used a sphere, Chevreul half a sphere and Ostwald a double cone, Küppers found that a rhomboidal form best allowed representing all colours. To explain practical concepts of harmonies, he devised a colour circle of twelve colours, and he represented changes in intensity by gradually varying the degree of white and black towards the centre.

Küppers' circle looks like the following figure. Three of the colours received names given by Küppers, which are hard to translate so we left them in Küppers’ original German notation.

Harald Küppers laid particular emphasis on the three primary colours of the additive process, red, green and blue, especially as compared to the painter’s basis of yellow, red and blue. Küppers claimed red, green and blue to be the colours of the real physical processes that form our eyesight. Yet we do not know how distinctive perception of colours is created in our mind by the stimuli of the red, green and blue receptors in our retina. Colour is created by a complex opponents process of transforming the mere first physical signals, so in our view painters like Johannes Itten and Wassily Kandinsky can claim as much feeling for colours as could be deduced from the additive process. Moreover, we know that colour perception depends on the relative reflectances from neighbouring zones, so more complex processes are at work than merely an addition of hues.

Küppers summarised his theory of harmony by stating that harmony exists when there are relations between colours of visual nearness or of contrasts.
Contrasts are between one or two of the four aesthetical differences (hue, tone, intensity, area), or when related to one or two combinations of green, red and blue. Analogous hues constructed from one colour and varying the intensity always pleases, but is of course a very easy effect. One may remain with close colours on the circle, but should not go too far away from contiguous colours of the colour wheel. Contrasting, complementary combinations are also good, proposes Küppers, but the colours should meet each other somewhat, tending somewhat to each other on the wheel. One can build combinations of three, four or six colours, by staying at symmetrical distances on the colour wheel and in the same intensity. Other combinations are difficult to find, but not impossible.

Küppers concluded by stating that a theory of harmonies cannot be a simple recipe that automatically, by applying a few rules, would lead to certain harmony, whereas also artists will need to use dissonant, un-harmonious colours for specific effects. Küppers wrote however that, in general, dissonance between colours comes when there are no regular relations between the chosen colours, when the colours are not chosen in some logical way.

Synthesis of the theories of Chevreul and Itten

The various theories of contrasts of colours and of harmonies refer to the changes in the qualities of colours. As we have seen before, colours have three qualities: their hue, tone and intensity. One or two of these qualities can be kept fixed while the other qualities are varied, so that different colours are created. It is about and within these variations that Chevreul and Itten proposed their contrasts and harmony.

In the following table we present the six possible cases. To explain the concept of this table, consider the first row. This row explains how Chevreul and Itten have handled the case when a certain hue is chosen for an area, for instance red, and then other areas are juxtaposed with the same tone but with varying intensities.

N/A indicates "not applicable", or not directly handled by the authors.

Hue	Tone	strong> Intensity	Comment	Handled by Chevreul in	Handled by Itten in
Fixed	Fixed	Variable	One hue in one tone only but the intensity (saturation) varies as white or black is added to dilute or dull the colour	Harmony of contrast of scale	Contrast of saturation
Fixed	Variable	Fixed	One hue and one and the same intensity or saturation, but the brightness or darkness of the hue is varied	Harmony of scale; Harmony of contiguous hues of different tones (when several hues of these properties are considered together)	Light-dark contrast
Variable	Fixed	Fixed	For a certain tone and intensity, look at various hues of colours	Harmony of contrasts (very different hues); Harmony of approximate hues; Harmony of a dominant colour	Contrast of hue; Complementary contrast (only between the complementary colours); Harmony definition
Variable	Fixed	Variable	Take one tone and then look at all hues that have that same tone, diluted or not with white or black	N/A	Light-dark contrast
Fixed	Variable	Variable	All modifications of one and the same hue	N/A	N/A
Variable	Variable	Fixed	Take one intensity and look at all colours of various tones and hues	N/A	N/A

Table - Plate 79. Variations in the qualities of colours

This table teaches us that variations of contrasts exist, which have not been handled by writers on contrasts and harmonies. Chevreul distinguishes harmonies within one category, whereas Itten defines harmony just in one category of variation. In each category however, we can speak of harmony and of contrast. We can categorise paintings according to the categories of this table, and analyse which means of variation the painter used and try to find out for what reason.

Johannes Itten, and also other writers, talk of additional effects and qualities of colour. These qualities are then other qualities but hue, tone and intensity. They are qualities of colours of one hue, one tone and one intensity.

Itten talks of cold/warm differences in qualities of colours, more specifically between red-orange and blue-green.

Another quality of colours is the nearness quality. All colours have a property by which they seem to lie in different planes of space. Blue is further off and more distant to viewers, orange-red in closer to viewers.

Itten defined contrasts between colours also based on these notions, even though he did not indicate a contrast category specifically for the intrinsic spatial quality of colours.

Finally, Johannes Itten handled simultaneous contrast as a category of contrasts, but we know that this is an effect of any colour when it is juxtaposed to other colours. This is a quality not of one colour as confronted with other colours, but more the mutual influence of colours upon each other. Michel-Eugčne Chevreul described this effect extensively.

As an analysis based on this table, we might first conclude that harmonious are the pictures in which one hue is used but in which this hue is varied in tone and in intensity, as long as the variations are gradual and preserve structural balance.

A second conclusion might be that when some or many hues are used together in a picture, then some colour combinations seem to be better than other. Not too many colours should be used, lest the viewer be lost in the number of impressions that are forced upon him or her.
Which colour combinations are agreeable and which not? Michel-Eugčne Chevreul presented long lists of appreciations of colour combinations, and Johannes Itten tried to state simple rules for harmony of hues. We will elaborate some more on these notions in the next paragraph.

It has to be noted that so far, no real conclusive analysis and testing has been presented on what harmony of hues could mean when in one painting various hues are combined in many tones and intensities. The number of combinations are simply too staggering and defy analysis. This is one of the wonders of the art of painting. We have come a long way in our discussion of colours, only to find that the wonder of colours remains much as mysterious as when we started.

An Analysis of the Combinations of Hues

Rudolf Arnheim wrote a book in 1952, revised in 1974, "Art and visual perception – A psychology of the perceptive eye", in which he also handled colour. Arnheim also wrote about harmony without defining specific rules, but he did produce a schema and annotation of colours to enable appreciating the value of colour combinations. We will continue on his notation schema and his ideas in this chapter.

Arnheim noted the three primary colours yellow, blue and red as Y, B and R.
The secondary colours (see the colour wheel of Johannes Itten) were then YB (green), YR (orange) and BR (violet).
The other secondary colours had one primary hue dominant and the other subordinate, so Arnheim used small and capital letters to indicate the relative proportion. Thus Yr meant Yellow-red with yellow dominant and red subordinated. In this notation all the hues of the Itten colour wheel are R, Y, B, RY, YB, BY, Yr, Yb, Ry, Rb, By and Br.
There are three primary hues, three secondary hues with two primaries mixed equally and six secondary hues based on a dominant primary.

Arnheim’s question was to find which combinations of these hues were agreeable, and which combinations were not. He only provided a schema for combinations of two of these colours.
We know of course that many more combinations are possible, for instance of three or more hues, as Johannes Itten had embarked on to consider. But is a fact that painters do not and cannot use so many different hues in near combinations, which then also do not vary much in tone and intensity. So a classification of just the combinations of pairs among the twelve basic colours might learn us much.
Itten’s construction of complementarity inside the colour wheel, as well as the concept of the isosceles triangles, rectangles, squares and hexagonal inside the colour circle seem to be somewhat too arbitrarily deterministic to remain unchallenged. Michel-Eugčne Chevreul defined his famous six rules for harmony, but he added long lists of colour combinations and advised on their being agreeable or disagreeable. Can we systematise such analysis?

The twelve colours of the colour wheel of Johannes Itten can be subdivided in three groups:

Group 1:	R, Y and B
Group 2:	RY, RB and YB
Group 3:	Yr, Yb, Ry, Rb, By and Br.

Then seven kinds of combinations between these three groups can be considered:

Combination set 1:	combinations of R, Y and B
Combination set 2:	combinations of RY, RB and YB
Combination set 3:	combinations within Yr, Yb, Ry, Rb, By and Br
Combination set 4:	combinations of R, Y and B with the hues of group 3
Combination set 5:	combinations of R, Y and B with the hues of group 2
Combination set 6:	combinations of hues of group 2 with hues of group 3
Combination set 7:	combinations of hues chosen at random from the three groups together.

Among these combinations Rudolf Arnheim analysed the sets 3 and 5, and he gave indications on set 1. We discuss briefly the combination sets. See also Plate 80, which illustrates the notation we will use.

Combination set 1

These are combinations of the three primary colours re, blue and yellow.
Rudolf Arnheim wrote on this, "these three fundamental primaries behave like the three legs of a stool. All three are needed to create complete support and balance. When only two of them are given they demand the third. The tension aroused by incompleteness of the triplet subsides as soon as the gap is filled".
He linked to this statement the theory of complementarity. Complementary colours (determined as colours apposite the centre of the colour wheel) go well together. The use of the three primary colours and of complementary colours to a harmonious, agreeable effect can be found in many Renaissance and late Gothic paintings, even if the three primary colours of the additive process (being red, blue and green) were used as much as red, blue and yellow.

We could speculate on the use of these hues instead of on the subtractive primaries in painting, due to the basic reactions on our retina of the additive primaries. Indeed, which hues should be called primary colours, those of the additive process or those of the subtractive process? Painters use paint, and thus prefer to think in terms of yellow, red and blue. The subtractive process generally generates the colours we perceive from nature such as the green of pastures or the red of leaves in autumn. So the "natural" colours are mostly created by reflection of light. But the additive process is physiologically more "natural", as our eyes react more on green, red and blue. However again, to what colour sensations do our brain processes react? One can build a schema of colours on the basis of the triplet red, yellow and blue, but when one talks of matters of natural harmony and equilibrium between the three fundamental hues, it may be more logical to consider red, green and blue as the basis.
Josef Albers, Johannes Itten, Rudolf Arnheim, Wassily Kandinsky and Michel-Eugčne Chevreul stuck to the painters’ primary colours, to yellow, red and blue. But Chevreul was candid about the primary colours. He stated that graphical constructions had been proposed for the purpose of representing colours and their various modifications, either by numbers or by a rational nomenclature, and that these were the primary colours red, yellow and blue. He himself formulated no prove or justification for any choice of primary colours. Chevreul did not really need the notion of primary colours. His analysis and his law were based on complementarity of colours and all colours of the colour wheel have a complementary (the hue opposite the centre). The concept of complementarity does not need the concept of primary colours.
So, when we conclude that the three primary colours need each other to establish a harmonious equilibrium, we might state that any three complementary colours suffice for this effect.

Johannes Itten also stressed the agreeable effect of the complementary hues. Itten and Arnheim remarked that the three primaries need each other in combinations and in paintings these combinations – always taken into account the necessity of structural balance or the necessities of expression – are agreeable.

Combination set 2

Combination set 2 is constituted of combinations among the secondary colours orange, violet and green. This is for the combinations RY+YB, RY+BR, and BR+YB.

Each of these colours when juxtaposed in pairs of RY, BR and YB, holds one primary colour in common and one different. Therefore they seem at the same time to destroy and to enhance each other. When juxtaposed, and according to Chevreul’s theory, the common component will be subdued on both sides as its complementary will be added, which hurts the common component, but the effect intensifies the other component. Combinations of these hues can be quite agreeable.

Arnheim discussed these combinations and spoke of the "highly dynamic pattern of attractions and repulsions in such a scheme", of "classicist stability". The secondary colours are lively hues, which help in combinations to brighten and to enhance contrasts in scenes.

Combination set 3

The combinations of set 3 are among the secondary colours, but the first derived ones (orange, violet and green). These are the combinations Yr+Br, Yr+Ry, Yr+By, Yr+Rb, Yr+Yb, Br+Ry, Br+By, Br+Rb, Br+Yb, Ry+By, Ry+Rb, Ry+Yb, By+Rb, By+Yb and Rb+Yb. There are in all fifteen possible combinations.

Arnheim found that when in these pairs the one colour in common was a subordinate, then the effect was agreeable. This is for the three combinations Yr+Br, Ry+By and Rb+Yb. This is probably because as the colour in common is only subordinated, the mutual destruction effect of adding the complementary remains of little importance. So the colours do not mutually destroy, and since the three primaries are present in these combinations, the result is lucky.

Agreeable also were the colour combinations that Arnheim called to be of "structural inversion". These are colour combinations which hold each colour subordinate and each the same colour dominant, whereby in the juxtaposed colours the common hue in inversed. These are the combinations Yr+Ry, Br+Rb, and By+Yb. These three combinations are agreeable. We cannot but think of the harmony of analogues of Chevreul in this regard.

But Arnheim considered that combinations that had a similar dominant primary in the pairs were repulsive. Again, we can apply Chevreul’s law of simultaneous contrast to explain the destruction effect. Therefore, the combinations Yr+Yb, BR+By, Ry+Rb are not so agreeable. The two dominant colours destroy each other and this effect interferes too much with the subordinate hue.

Then remain the six combinations in which there is structural contradiction in one common element: Yr+By, Yr+Rb, Br+Ry, Br+Yb, Ry+Yb and By+Rb. These were not so good combinations. The contrasts seem to produce a conflict, and thus mutual repulsion.

Combination set 4

Combinations of the three primary colours R, Y and B with their secondary colours Ry, Rb, Yr, Yb, Br and By yield the combinations R+ Ry, R+Rb, R+Yr, R+Yb, R+Br and R+BY as well as Y+Ry, Y+Rb, Y+Yr, Y+Yb and Y+By and B+ Ry, B+Rb, B+Yr, B+Yb, B+Br and B+BY. Here we have eighteen combinations.

Arnheim wrote on these combinations in two variants. He said that when a primary was the subordinate element in the composition, then the colour combination was not so agreeable. Chevreul would have stated that the primary hue constituent in the secondary would be much hurt by the complementary of the primary hue, and so the colours destroyed. When the primary is dominant in the secondary colour, the effect is even more severe.
So the combinations R+Yr, R+Br, Y+Ry, Y+By, B+Yb, B+Rb are not very agreeable, and the combinations R+Ry, R+Rb, Y+Yr, Y+Yb, B+Br, B+By are even worse. In all, that makes for twelve not so lucky combinations.

As for the combinations R+By, Y+Br, B+Ry, R+Yb, Y+Rb and B+Yr, we may assume that the combinations re-enforce each other, as the three primaries are together and the hues tend to complementary colours.

Combination set 5

These combinations have much in common with the combinations of set 4, which were handled by Rudolf Arnheim. Combination set 5 is constituted of combinations between the three primaries R, Y and B on the one hand and the first derived secondary colours RY (orange), RB (violet) and YB (green). The combinations are thus R+RY, R+RB, R+YB as well as Y+RY, Y+RB, Y+YB and B+RY, B+RB, B+YB.

When the primary that is juxtaposed, for instance R, is placed next to a secondary colour that contains the same primary, here then RY and RB, the secondary colour will be much disturbed by mutual influences and the effect will not be agreeable. This counts for the combinations R+RY, R+RB, Y+RY, Y+BY, B+RB and B+YB.

The remaining combinations however, that is R+YB, Y+RB and B+YR, will enhance each other and be agreeable. These are combinations of the primaries with their complementary colours in the colour wheel.

Combination set 6

These are combinations of the secondary colours RY, YB and RB with the other secondary hues Yr, Br, Ry, By, Rb and Yb. This set consists hence of eighteen possible combinations: RY+Yr, RY+Br, RY+Ry, RY+By, RY+Rb and RY+Yb and also RB+Yr, RB+Br, RB+Ry, RB+By, RB+Rb and RB+Yb plus BY+Yr, BY+Br, BY+Ry, BY+By, BY+Rb and BY+Yb.

Combinations among these colours, which are very similar, are perceived as agreeable, as Chevreul wrote on his contrast of analogues. That is obvious for the six combinations RY+Yr, RB+Br, YB+By and RY+Ry, RB+Rb, BY+Yb.

Combinations in which one of the two primary hues of RY, UB and RY is present only as the subordinate hue in the other juxtaposed colour, will be rather agreeable, as the combination tends complementarity. The subordinate will not disturb too much the other colour in which it is dominant, whereas the complementary of the first derived secondary will enhance the other. That is the case of the combinations RY+Br, RY+By, BR+Yr, BR+Yb, BY+Ry and YB+Rb.

The remaining combinations have a primary hue dominant on both sides. The result will be mostly repulsive. That is the case for the combinations RY+Rb, RY+Yb, YB+ Yr, YB+ Br, BR+Yb and BR+By.

Combination set 7

We can combine all colours chosen from the three groups that we defined. Any two combinations have been discussed in the above paragraphs. Further combinations in triplets or more colours could be treated in the same way as the above analysis, but of course yield a massive amount of possible combinations. And then, we could variegate these colours by considering for each hue other tones and intensities. The possible number of combinations is infinite.

Painters rarely use more than two or three colours from the colour wheel. Usually, they use just two colours for large parts of their composition. They do that because otherwise also for them the combinations to harmony or breaking of harmony in particular expressions are too difficult to control. Moreover, many colours may distract and confuse the viewer in the composition.
Many painters have therefore told or written that just a few basic colours were preferable and necessary in a painting. These colours then they could evolve in analogous hues or by gradually changing tone and intensity. The above analysis of the six combinations taught us thus most we need to understand of the harmony of hues.

Conclusion on the combinations of two colours

After this analysis the following combinations of two colours are nice:

RY + YB, RY + BR, BR + YB: combinations of the secondary colours

Yr + Br, Ry + By, Rb + Yb, Yr + Ry, Br + Rb, By + Yb

R + By, Y + Br, B + Ry, Y +Rb, B +Yr

R +YB, Y + RB, Y + YR: combinations of primary colours and their complementary colours

RY + Yr, RB + Br, YB + By, RY + Ry, RB + Rb, BY + Yb

RY + Br, RY + By, BR + Yr, BR + Yb, BY + Ry, YB + Rb

Comparison with the rules for harmony of Johannes Itten

Johannes Itten only allowed six combinations of pairs of colours: the pairs of the complementary colours. In an analysis as we made in this chapter, many more combinations are allowed as colours that match each other reasonably well (29 combinations of two colours in the set of 12 colours in all).

Arnheim made no formal analysis on combinations of more than two colours. Itten, however, stated that harmonious combinations of three colours were the sets of colours on equilateral and isoscele triangles in his colour circle. Such combinations are nothing more than emphasis on the contrast of colours. Itten says in fact to take any two colours on the colour circle and then to take as a third either one of the two colours that are farthest away of each, in the middle between the two picked hues. Take for instance Rb and RB, then Itten would propose as third colour either B or RY. These last are the colours most complementary to the two originally chosen colours, and the painter would do best to place this colour in between the two first. Itten’s rule is a rule of maximum contrast.

Final recommendations for harmony of colours

After the review of the theories on the harmonies of colours we can define a few simple recommendations to which most of the authors would agree.

We might follow Harald Küppers in that the best basis in our current knowledge would be to use the primary colours of the additive process, which is the colours red, green and blue, even if the red should be somewhat tinted orange and the blue somewhat tinted violet.
We use a colour circle of twelve colours like the colour wheel of Harald Küppers, and we let the hues vary in tone from the darkest tone at the rim to the palest tones in the centre. Then the simple recommendations of harmony of colours can be as follows in ten rules.

Harmonious are the combinations of colours of one hue for which we vary the tone very slightly.
Harmonious are the combinations of colours of one hue for which we use contrasting tones. In this way contrast of tone plays, and we always have to remain cautious with contrasts. The contrasts must balance each other out.
Harmonious are the combinations of hues that are contiguous on the colour wheel, in combinations of not too many hues, so just two or three colours taken together and arranged in only slightly varying tone and intensity.
Harmonious are the combinations of contiguous hues arranged in contrast of tone and intensity, but taken care with balance of areas especially.
Harmonious are combinations of true complementary colours, even of differing tone and intensity, and always taken care of balance of areas. These colours then enhance each other through what Chevreul called "simultaneous contrast" effects.
Harmonious also are combinations of more than just two colours, when taken together, and taken from symmetric distances to each other on the colour wheel. Here we can use Johannes Itten’s constructs inside the colour wheel. The colours are best arranged according to the sequence of the colour wheel instead of in a random order. The colours can be of differing tone and intensity, even to the point that one colour is dominant. But care should be taken of balance of coloured areas.
Colours that do not go well together, so in combinations that are random or that do not satisfy the above recommendations can favourably be separated by grey, black or white, and most favourably by a grey hue and tone that matches the tones of the other colours.

Three additional recommendations can be formulated and these can be applied together with each of the foregoing.

8. Very harmonious and agreeable are the pictures of one mood, one overall and the same tone, even if the tone is a bright or a dark one. Such a mood is immediately recognised by the viewer, and thus has generally a very pleasing effect.
9. In one and the same picture, do not use too many zones in which the above rules change and vary. Have preferably an unpaired number of zones in which the combinations change, and order these well in a logical and easily recognisable way. This recommendation may be adapted according to the dimensions of the frame, as one can with less impunity vary combinations in larger pictures than in smaller ones.
10. Always keep balance between the surface areas of the colours. A good guideline for that are the numbers Goethe assigned to colours.

Yours truly,

Zeuxis

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Last updated: August 2010

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Fifth Letter of Zeuxis to Arte - Theories of Harmony of Colours after Chevreul