Complementary colors are colors that “complete” each other. This completion can be understood in terms of some physical relationship or in terms of how the colors are related in their appearance. There are different ways of establishing these relationships, two being widely accepted: By one definition, two paints, inks, or colored lights are complementary if their mixture can yield a neutral black, gray, or white. This is a physical relationship that can be demonstrated. By another definition, two colors are complementary if the afterimage of one color has the same hue as the other color. This is a phenomenal relationship that can also be demonstrated. It is also common simply to claim that colors opposite to each other on a color circle are complementary, without further explanation or justification. Complementary relationships can be helpful when mixing paints to produce particular results. Complementary relationships also feature in theories of color harmony.
The notion of complementary colors is caught between science and art, between what can be measured and what cannot. But this notion can also be seen as a bridge. If there are objective ways of establishing complementary color pairs, and if such pairs are found to be pleasing, then complementary colors may be a key to color harmony – harmony could be subject to measurement. One difficulty here is that different ways of establishing complementary relationships do not yield exactly the same results. A number of these ways are described and illustrated in the sections that follow. There is also the problem of what comes first, the objective methods or the experience of harmony. The idea that some color pairs are more pleasing than others is older than any demonstration of particular physical or phenomenal relationships of the kind associated with complementary colors. Perhaps the earlier judgments are endorsed by the later demonstrations, or perhaps the demonstrations show color relationships that are now widely agreed to be harmonious.
Harmony is a slippery word. Most definitions deal with harmony in music, but there it has more than one meaning. It can mean a combination of notes which have a pleasing effect . It can also mean a combination of notes organized according to a system of structural principles . The same definitions could be applied to color combinations. According to the first definition, only those color combinations that are found to be pleasing are harmonious. This could make color harmony a private matter; harmony, like beauty, would be in the ears of the listener or the eyes of the beholder. Only some kind of consensus could establish a wider claim for some color combinations to be accepted as more harmonious than others. Whether the judgment is made by an individual or a group, this definition depends on evaluation. With the second definition, there are also limitations. Only with certain relationships between notes or colors can a combination be called harmonious. The relationships can be measured so the definition depends on description. Philosophers might argue about the possibility or impossibility of any link between description and evaluation, but for most people, to say that there is an interval of a third between the notes C and E when they are sounded together in a chord is description, while to say that the chord is pleasing is evaluation. Similarly, to give Munsell or NCS notations for the two colors in a particular combination is description while to say that the combination is beautiful is evaluation. The idea of a link between description and evaluation as the basis for some theories of color harmony is discussed in a paper that was presented at a conference in Gothenburg in 1996 .
Pleasing Color Combinations
Before the invention of the color circle, or any notion of a special relationship between colors that are opposite to each other on a circle, there was a recognition that certain color pairings are more satisfying than others. Leon Battista Alberti, in fifteenth century Italy, claimed that “there is a kind of sympathy among colours whereby their grace and beauty is increased when they are placed side by side. If red stands between blue and green, it somehow enhances their beauty as well as its own” [4, p. 85]. Leonardo da Vinci introduced the notion of “contrary colors” and suggested that pairs of contrary colors enhance one another. “The colours which go well together are green with red or purple or mauve, and yellow with blue” [5, p. 73]. Martin Kemp points out that “this account of colours which ‘go well together’ comes close to the doctrine of ‘complementary colours’ as defined in the eighteenth and nineteenth centuries, but lacks the systematic base provided by the later colour wheels” [6, p. 284].
To find out whether people might intuitively choose particular colors as going well together, without appeal to a color wheel or any theories of complementary colors, a preliminary investigation was carried out at Curtin University of Technology in 1994. Students worked with colors of equal nuance from the Natural Color System (NCS). Each was assigned a particular color and asked to find a color to go with it so that the combination would be the most beautiful, most exciting, or most harmonious. The intention was to go back to the kind of judgments made by Alberti and Leonardo, to find colors that were most “sympathetic” or “contrary.” Students generally agreed on which color pairings were the most “beautiful” and the most “exciting”, but there were two schools of thought about what kind of color relationship is “harmonious” – colors of similar or contrasting hue. And it was not always the same colors that were selected as contrasting. There was a small range comparable to the “red or purple, or mauve” as nominated by Leonardo for “going well” with green. A more rigorous study, with a larger number of participants, might lead to firmer conclusions. But it does not seem likely that an approach, from this direction, to the identification of complementary colors would yield precise results. The “complementary” of a given hue would not be a single hue but a narrow range of similar hues. This can be set beside the imprecise results when the approach is from the other direction, starting with the theories.
Ways of Establishing Complementary Colors
With different ways of establishing complementary relationships yielding different pairs, no color can be said to have a single complementary hue unless a decision is first made about which way of establishing complementary relationships is “correct.”
In one of his diagrams, Leonardo da Vinci illustrates a spherical body (a) being lit by two lights (d) and (e). Two shadows are cast (b) and (c). He explains that “the shadow formed by the light e, which is yellow, will tend towards blue, because the shadow of the body a is formed on the floor at b, where it is exposed to the blue light, and accordingly the shadow made by the light d, which is blue, will be yellow at the location c, because it is exposed to the yellow light” [5, p. 74].
Colored shadows may be linked to the experience of afterimages. Martin Kemp identifies the Comte de Buffon as “the pioneer in the study of subjective colour.” Buffon described colored shadows and also afterimages at the French Academy of Sciences in 1742–1743 [7, p. 294–295]. Afterimages were introduced by Moses Harris when he explains how the world will look if green-tinted spectacles are worn for about 5 min and then removed: “every scene and object will look of a fiery red, opposite to green you will find red” [8, p. 8]. In the Harris color circle, colored shadow and afterimage color pairs are to be found opposite to each other. For Goethe, afterimages were the key to color harmony. He saw, in the experience of an afterimage, the eye’s search for completeness, and he concludes that “in this resides the fundamental law of all harmony of colours” [9, p. 317]. Goethe had only six colors in his color circle so, within each segment, there could be a range of different hues under the same name. Red would range from orange red to purple red and in that range the afterimage for a particular green might be found. If more precise identification of afterimage hues is required, there are two questions to be considered: If a particular red is the afterimage of a particular green, does it follow that the same green will be the afterimage of that red? Is the afterimage phenomenon reciprocal in this way? The second question takes account of afterimages as subjective experiences peculiar to the individual. So is it possible to know whether everyone experiences the same hue as the afterimage of a given color?
Afterimage Color Progression
Having painted a patch of reddish orange, Douglas stared at it, looked away, and matched its afterimage which she saw as a pale turquoise. She then increased the intensity of the turquoise, being careful to retain its hue, and repeated the process for the turquoise. The afterimage of the turquoise was slightly more yellowish than the original reddish orange. In a carefully controlled operation, where such color relationships were established in random order, she found, when she put it all together, a progression right round the circle.
Individual Variations in the Experience of Afterimages
The slight variations in hue may be due to inaccurate mixing but studies by Marian-Ortolf Bagley have confirmed that there are, indeed, variations in how individuals experience afterimages . Rather than have the participants in her study match the afterimages in paint, she asked them to identify their afterimage colors from the samples in the Munsell book of color.
Colors That Are Least Like Each Other
Wilhelm Ostwald points out how “if one moves away from a given hue in the hue circle, the colors become increasingly dissimilar” [12, p. 33]. Since the hue circle is continuous, there will come a point where this dissimilarity is at its greatest, and beyond which there will be a progressive return to similarity. For Ostwald, “there exists for every hue in the hue circle another that is most different from it. This relationship is mutual. The entire hue circle is filled with such pairs of contrasting colors, which shall be called complementary colors” [12, p. 34]. However, the determination of least similarity must depend on the judgment of observers, and such judgments are likely to vary. Ostwald preferred precision. Accordingly he appeals to mixture and proposes an alternative definition: “Complementary colors are colors which in an optical mixture yield a neutral gray” [12, p. 35].
Colors that Mix to a Neutral
When discussing color mixture, it is important to distinguish between the paints, inks, or lights that are being mixed on the one hand and, on the other hand, the appearance of those paints, inks, or lights and the resultant mixture. If a paint that appears red is mixed with a paint that appears blue, the mixture will appear purple, more bluish, or more reddish depending on how much of each paint is in the mixture. There are different ways of mixing: subtractive, additive, and partitive. The results of one way of mixing are not always a guide to the likely results of the other ways.
Moses Harris claims that if such colors (i.e., paints) are mixed and are “possest of all their powers, they then compose a deep black” [8, p. 7]. But he concedes that no pigments that are generally available, like those used for Fig. 4, have such “powers.” Instead of deep black, the result here is a neutral dark gray.
Additive and Partitive Mixture
Partitive mixture was the method used by Ostwald to establish complementary pairs which he then placed opposite to each other on his circle. Ostwald’s circle has yellow opposite blue, as in Fig. 5, where Harris has orange as in Fig. 4.
Possibilities from Physics
In the introduction to his book The Principles of Harmony and Contrast of Colors and their Application to the Arts, Michel-Eugène Chevreul suggests a precise definition: “if we re-united the total quantity of the coloured light absorbed by a coloured body, to the total quantity of coloured light reflected by it, we should reproduce white light: for it is this relation that two differently coloured lights, taken in given proportions, have of reproducing white light, that we express by the terms Coloured lights complementary to each other, or complementary colours” [13, p. 54]. From this one can imagine a spectral reflectance curve which would serve as a kind of template for a second curve – where one curve had peaks, the other would have valleys. This may be a theoretical ideal; it is doubtful whether two surfaces could be found with such perfectly matched reflectance curves.
Color relationships that could be regarded as complementary can be seen in a close examination of Newton’s rings. Isaac Newton describes the phenomenon that bears his name in his book Opticks. He found that “By looking through … contiguous object glasses … that the interjacent air exhibited rings of colours, as well by transmitting light as by reflecting it… Comparing the coloured rings made by reflection, with those made by transmission … I found that white was opposed to black, red to blue, yellow to violet and green to a compound of red and violet” [14, book 2, part I, observ. 9].
Polarized Light and Cellophane Tape
The colors that are seen in the stripes depend on the relationship between the axes and on how many layers of tape there are – in this case one, two, and three layers, the three-layer stripes being the ones in the center. The colors change radically as one filter is rotated in relation to the other. The colors on the left in Fig. 6 could be described as being complementary to those in the corresponding positions on the right. A more detailed, but simple, explanation of this effect is provided for the “Polarized Light Mosaic” which is included in the Science Snackbook compiled by the Exploratorium Teacher Institute [15, p. 78].
While carrying out the study, it was assumed that two colors can be each other’s afterimage. Given the findings of Sally Douglas, shown above in Fig. 2, such a color circle cannot be constructed except to suggest that opposite colors are close to being each other’s afterimage. The afterimage of unique blue may be a yellow orange, but the afterimage of that yellow orange may be a blue that is very slightly reddish.
An Elastic Color Circle
Complementary Colors as a Guide to Mixing
Painters are often advised to use complementary colors, rather than black, white, or gray, to modify the appearance of colors in their painting that they feel are too vivid. Black, white, and gray paints are felt to have a deadening effect.
Complementary Colors as a Guide to Color Harmony
Choosing a Single Definition as the Key to Harmony
Robert Hirschler discusses the potential for confusion arising from different ways of defining complementary colors. Hirschler quotes David MacAdam who was concerned with problems of measurement: “only that definition which states that the optically additive mixture of two complementary colors must match some arbitrarily assigned ‘neutral’ stimulus is sufficiently specific” [18, p. 1]. This way of establishing complementaries appealed to Ostwald and he used it as the basis for his theories of color harmony. And it is certainly true that optical mixture with spinning discs (partitive mixture) was the easiest way to establish precise complementary relationships during the study described above. A large range of vivid and consistent colors can be produced when gouache paints are used straight from the tube. Paper discs were painted and interleaved in very many combinations of two. The proportions were adjusted until particular combinations in particular proportions were found which would spin to appear neutral gray. These are illustrated in Fig. 7. However, it does not follow that the degree of precision obtainable with this process means that this must be the only “correct” way of establishing complementary color pairs which would be, by definition, harmonious. For Goethe, the key to harmony was afterimages, “a natural phenomenon immediately applicable to aesthetic purposes” [9, p. 320]. Afterimages, as subjective experiences, are not so easy to measure but they involve the observer more intimately, and the experience of an afterimage suggests that the visual system is seeking some form of completeness. Chevreul imagined two spectral reflectance curves which would produce white light when combined. A color stimulus and its afterimage could be the perceptual equivalent.
Complementary Colors as a Fuzzy Concept
Artists and designers, who are looking for some formula that will lead to harmonious color combinations, may be perplexed to find that the color circle is unstable as it adjusts to comply with different definitions of complementary colors. Rather than worry about which definition, and its corresponding color circle, is “correct,” it might be more fruitful to accept complementary colors as a fuzzy concept and make decisions based on personal judgment. After studying the color combinations illustrated in Figs. 11 and 12, a choice can be made. If one combination seems more satisfying and harmonious than the other two, the corresponding color circle could be adopted and Itten’s ideas applied. This could give the artist or designer a feeling of ownership while still providing a sense of security with a clear framework for developing harmonious color combinations. Alternatively a more flexible approach could be taken. If information about the likely results of mixing is needed, then reference could be made to the subtractive or additive circles as appropriate. But as a framework for developing harmonious color combinations, the color circle could be regarded as offering a choice within limits. While a given color may have more than one complementary, as different definitions are applied, those complementary colors will not be radically different in hue. Even in the most extreme example illustrated here, the alternative complementaries for blue, there is not a large spread between yellow and orange. This range can be considered as offering a choice with the decision being left to the judgment of the artist or designer. It is worth noting that Alberti and Leonardo both nominated more than one color as being “sympathetic” or “contrary.” Alberti mentions red in relation to blue and green and Leonardo lists red or purple or mauve as going well with green.
This more flexible attitude to the color circle is recommended by Deryck Healey. Having introduced a 12-hue color circle based on subtractive mixture, with the printers’ cyan, magenta, and yellow as primaries (the so-called process inks), Healey illustrates combinations that deviate somewhat from strict adherence to Itten’s rules. He advises the reader to “study these examples of harmony and contrast. Few are strictly precise triads, split complementaries and so on; rather they illustrate how such themes may be subtly interpreted and still retain the desired characteristics of their general category” [19, p. 40].
Complementary colors, as defined by mixture to a neutral or by afterimages, provide reference points for the relationships between hues in a color circle. When the relative positions of hues are determined by mixture, the different results from subtractive and additive/partitive mixtures can be recognized and the appropriate circle used as a guide. More problematic is the role of complementary colors in theories of color harmony. Different definitions lead to different relationships between the hues in the color circle. This could lead one to question the theories or abandon them altogether. Nevertheless, the theories are interesting and can be helpful, especially for those who lack confidence in their own intuition. If a choice has to be made between the different circles, there are arguments in favor of objectivity and subjectivity. On the side of objectivity, there is the circle based on additive/partitive mixture where the color pairs are most readily measurable. This has the support of MacAdam and Ostwald. On the side of subjectivity is the circle based on afterimages which relates more directly to the personal experience of color and the judgments of beauty and harmony as made by the observer. This has the support of Goethe. In the end it is up to the artist or designer to choose a single circle or to take a more flexible approach as recommended by Healey. An advantage of the elastic color circle is that it allows one to stretch the rules without breaking them.
- 1.Thompson, D. (ed.): The Concise Oxford Dictionary. Oxford University Press, Oxford (1995)Google Scholar
- 2.Sadie, S. (ed.): The New Grove Dictionary of Music and Musicians. Macmillan, London (1980)Google Scholar
- 3.Green-Armytage, P.: Complementary colours – description or evaluation? In: Sivik, L. (ed.) Colour and Psychology: From AIC Interim Meeting 96, Colour Report F 50, pp. 205–209. Scandinavian Colour Institute, Stockholm (1996)Google Scholar
- 4.Alberti, L.B.: On Painting. Penguin, London (1991). 1435Google Scholar
- 5.da Vinci, L.: Leonardo On Painting. Yale University Press, New Haven (1989 )Google Scholar
- 6.Kemp, M.: Note. In: Leonardo on Painting. Yale University Press, New Haven (1989)Google Scholar
- 7.Kemp, M.: The Science of Art. Yale University Press, New Haven (1990)Google Scholar
- 8.Harris, M.: The Natural System of Colours. Whitney Library of Design, New York (1963 )Google Scholar
- 9.von Goethe, J.W.: Theory of Colours. MIT Press, Cambridge, MA (1970 )Google Scholar
- 10.Cabot Hale, N.: Abstraction in Art and Nature. General Publishing Company, Toronto (1993 )Google Scholar
- 11.Bagley, M-O.: Color in design education. In: Arnkil, H., Hämäläinen, E. (eds.) Aspects of Colour. University of Art and Design, Helsinki (1995)Google Scholar
- 12.Ostwald, W.: The Color Primer. Van Nostrand Reinhold, New York (1969 )Google Scholar
- 13.Chevreul, M.-E.: The Principles of Harmony and Contrast of Colors and their Application to the Arts. Reinhold Publishing, New York (1967 )Google Scholar
- 14.Newton, I.: Opticks. Impression Anastaltique, Culture et Civilisation, Brussels (1996 )Google Scholar
- 15.Institute Exploratorium Teacher: Science Snackbook. The Exploratorium, San Francisco (1991)Google Scholar
- 16.Itten, J.: The Art of Color. Van Nostrand Reinhold, New York (1961)Google Scholar
- 17.Itten, J.: The Elements of Color. Van Nostrand Reinhold, New York (1970)Google Scholar
- 18.Hirschler, R.: Teaching colour wheels and complementary colours. In: Kortbawi, I., Bergström, B., Fridell Anter, K. (eds.) Colour – Effects and Affects, Interim Meeting of the AIC, Proceedings, paper 98. Scandinavian Colour Institute, Stockholm (2008)Google Scholar
- 19.Healey, D.: Living with Colour. Macmillan, London (1982)Google Scholar