Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

Complementary Colors

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_264



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.

Color Harmony

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 [1]. It can also mean a combination of notes organized according to a system of structural principles [2]. 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 [3].

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.”

Colored Shadows

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].

Later observers noticed that a blue shadow would be cast by a yellow light even if another light, shining on the shadowed area, was not blue but white. A systematic study of colored shadows was carried out by Count Rumford who reported his results to the Royal Society of London in 1794. Rumford concluded that the phenomenon was subjective. He went further and suggested that his results might serve as a guide to artists in “the magic of colouring,” and he introduced what was then a new term: “one shadow may with propriety be said to be the complement of the other” [7, p. 295]. Moses Harris, in 1766, also describes the colored shadow phenomenon and points out how the colors of the light and the shadow are opposite to each other on his color circle [8, p 8]. Johann von Goethe explains how to conduct the colored shadow experiment with a candle and the full moon as light sources. And he has a beautiful account of how he experienced a sequence of colored shadows on a walk in the Harz Mountains. The ground and trees were covered in snow and hoar frost. Toward the end of the day, the shadows cast by the trees were “decidedly blue, as the illumined parts exhibited a yellow deepening to orange.” Then, as the sun began to set, it “began to diffuse a beautiful red colour over the whole scene around me, the shadow colour changed to a green, in lightness to be compared to a sea-green, in beauty to the green of the emerald. The appearance became more and more vivid: one might have imagined oneself in a fairy world, for every object had clothed itself in the two vivid and so beautifully harmonising colours” [9, pp. 34–35]. Colored shadows may be a subjective phenomenon, but it is possible to record them in photographs, as shown in Fig. 1.
Complementary Colors, Fig. 1

Demonstration of complementary colors as seen in colored shadows. At top left the candlestick is lit by two white lights and casts gray shadows. In the other photographs, colored filters were placed in front of the light shining from the right while neutral filters were placed in front of the other light to equalize the illumination. The shadow colors can be described as being complementary


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

The assumption that two colors could be each other’s afterimage was investigated by Nathan Cabot Hale. Cabot Hale claimed to have found what he called “after-image color progression” [10, p. 262]. Having experienced a yellow as the afterimage of a blue, he found that the afterimage of the yellow was a violet. Then the afterimage of the violet was a green and this progression continued right round the circle. Cabot Hale’s claim was investigated, in turn, by Western Australian artist Sally Douglas. Douglas did not find such strong hue shifts as those reported by Cabot Hale, but she did find progression all round the circle. Her method and results are shown in Fig. 2.
Complementary Colors, Fig. 2

Afterimage color progression as recorded from her observations by Sally Douglas

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

To see if individuals have the same afterimage experiences from given colors, students at Curtin University of Technology were assigned specific paints and asked to match the colors they experienced as the afterimages. Some of the results are shown in Fig. 3.
Complementary Colors, Fig. 3

Afterimage colors as recorded by individual students at Curtin University of Technology

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 [11]. 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.

Subtractive Mixture

Subtractive mixture occurs when paints are mixed in the palette, when inks are premixed before being used on the press, and when transparent inks or paints are applied in layers one over the other. Subtractive mixture also occurs when two differently colored filters are placed in front of a single light source. Experiment with different paint combinations can lead to the discovery of a pair of paints that can be mixed to a dark gray as shown in Fig. 4.
Complementary Colors, Fig. 4

Dark gray in the middle of a sequence of colors mixed from varying amounts of two paints which appear blue and orange when used straight from the tube

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

Additive mixture occurs when beams projected from two filtered light sources overlap on a screen. Partitive mixture occurs when a disc with segments painted in different colors is spun at high speed. The results of additive and partitive mixture are shown in Fig. 5.
Complementary Colors, Fig. 5

Similar colors in filtered lights and on painted paper discs can mix additively and partitively to a neutral – white or gray

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.

Newton’s Rings

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

Polarized light can also reveal striking color contrasts when cellophane tape is sandwiched between two polarizing filters. The filters only transmit light that is vibrating in one plane which means that each filter has what might be called an axis. When two filters are superimposed, they will transmit more or less light depending on the relationship between the axes. If the axes are at right angles to each other, no light is transmitted. The cellophane tape has the effect of modifying the light as it passes through so that certain wavelengths, visible as colors, are transmitted even when the axes are at right angles. This is demonstrated in Fig. 6.
Complementary Colors, Fig. 6

Colors revealed when cellophane tape is sandwiched between two polarizing filters. The axes of the filters are parallel on the left, at 45° in the center, and at 90° on the right

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].

Contradictory Complementaries

It is clear from the above that there is no single complementary color for each hue in the color circle. A study to establish complementaries by different definitions was carried out in 1981. Gouache paints, manufactured by Winsor and Newton (WN) and Pelikan (P), were used for this study. The results are illustrated in Fig. 7.
Complementary Colors, Fig. 7

Chart showing the results of a study to find complementary color pairs (partners) according to different definitions

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

The issue of contradictory complementaries is discussed in the entry on the color circle in this encyclopedia. An elastic color circle is proposed as a way of illustrating how the number of steps between the unique hues would need to be increased or decreased to bring differently defined complementary pairs opposite to each other. The illustration from the color circle entry is repeated here as Fig. 8.
Complementary Colors, Fig. 8

Color circles based on subtractive mixture complementaries (left), afterimage complementaries (center), and additive mixture complementaries (right). The color circles illustrated here were developed from the results of the study shown above in Fig. 7

Complementary Colors as a Guide to Mixing

Complementary colors can be used as a guide to mixing paints, inks, or lights. Given that the results of subtractive and additive/partitive mixture are not the same, the elastic color circle can help to clarify the situation. Figure 9 shows an extreme example of the way in which the same two paints can be used to produce radically different results from subtractive and partitive mixture. Here the blue and the yellow are more reddish than the blue and yellow in Fig. 5. The result of subtractive mixture is a dull green, but on the spinning disc, the result is a dull pink.
Complementary Colors, Fig. 9

The same two paints mix subtractively to a dull green and partitively to dull pink

Lines connecting that blue and yellow pass though green on the subtractive circle but through pink (red) on the additive/partitive circle, as shown in Fig. 10.
Complementary Colors, Fig. 10

Dotted lines trace the possible results from subtractive (left) and additive/partitive mixtures (right) of a reddish blue and a reddish yellow

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

Complementary colors underpin many theories of color harmony, notably the theories of Johannes Itten, author of what may still be the most influential and widely used books on color theory for students of art and design today [16, 17]. Itten argues that “the concept of color harmony should be removed from the realm of subjective attitude into that of objective principle” [17, p. 19]. He is unequivocal when he claims that “we can make the general statement that all complementary pairs … are harmonious” [17, p. 21]. And he supports this claim by offering three objective means of establishing complementary relationships: “the after-image always turns out to be of the complementary color … colors (lights) are harmonious if they mix to give white … colors (paints or pigments) are … harmonious if their mixture yields a neutral gray” [17, pp. 19–20]. These three definitions cannot coexist in a single color circle. There would need to be separate circles, one for each definition, if complementary colors are to be opposite to one another, and that would mean three possible frameworks for harmonious color combinations. If blue is to be one of the colors in a harmonious two-color combination, the other color would be orange, orange yellow, or yellow, depending on which circle was used. These combinations are shown in Fig. 11.
Complementary Colors, Fig. 11

Blue with three different complementary colors for three different definitions: (left to right) subtractive mixture, afterimages, and additive/partitive mixture

According to Itten, any regular geometric figure can be placed inside the color circle, and its vertices will connect with colors that will form a harmonious combination. An equilateral triangle can be used to find three-color combinations, or triads. Again, with blue as a constant, three rather different combinations would be found in the three circles. These are shown in Fig. 12.
Complementary Colors, Fig. 12

Blue as one of three colors in combinations found by an equilateral triangle placed inside each of three color circles where complementaries are established by, from left to right, subtractive mixture, afterimages, and additive/partitive mixture

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.



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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Design and ArtCurtin UniversityPerthAustralia