Color–tone analogies refer to the association of color scales to musical scales. Throughout history, such analogies have played the most diverse roles with regard to aspects of philosophy, the natural sciences, art theory, and music theory. Depending on the stage of development reached by the theory of colors and optics and the theory of music and acoustics, respectively, a variety of procedures for developing analogies have been applied, while the prevailing understanding of the world was used to justify these comparisons.
Color–sound correspondences appeared in prehistoric times as components of complex symbolic or cosmological analogies. In connection with the planets and different spheres of human existence, they were intended to demonstrate a reflection of the macrocosm within the microcosm or a comprehensive blueprint for nature in the sense of a global harmony.
From the ancient world onward, the number of analogical models was incrementally reduced and the first separate color–tone analogies were developed. These then also led to a definition of color harmonies through the transfer of the musical theory of consonance and to the establishment of a theory of harmony in painting.
It is only since the early eighteenth century that fully independent color–tone analogies have been developed. These were mainly intended to facilitate the visualization of music, usually on the basis of various types of light organ.
The first occurrences of color–tone analogies are to be found in symbolic and cosmological models of the prehistoric period that sought parallels between all natural phenomena. Such equations were based on the belief in a superior unity of nature and in the existence of an all-embracing correspondence between microcosm and macrocosm. Thus, following the integration of light and sound into the myths of creation, it was mainly in Eastern Asia that not only colors and tones, but also the seasons, the human body, climate conditions, the points of the compass, the planets, years of life, and so forth, were structured and symbolically associated with one another. As regards the incorporation of these analogies in comparisons that concern only colors and musical tones, the associations made in line with this tradition by Athanasius Kircher are particularly important. These are described in his book Ars magna lucis et umbrae, dated 1646, where he creates associations between intensities of light, different degrees of brightness, types of tastes, the elements, years of life, levels of knowledge, levels of being, and tones, always using the same subdivision into five parts.
The first reduction of the all-encompassing analogies of prehistoric times took place in the ancient world, when the numerous components involved were reduced to tone intervals, color pairings, taste qualities, and the planets, among which harmonious relations were established on the basis of seven-point scales.
Until the eighteenth century, seeing and hearing, as the human being’s predominant senses for the perception of the environment, and occasionally also smelling and tasting, were structured by creating analogies based on the concept of numerical equality.
These transfers were linked to the idea of a comprehensive theory of harmony, in which the world order and esthetics are based on numbers and numerical ratios and can also be expressed by these.
In this respect, the findings by the Pythagoreans that traced musical harmony back to relationships between whole numbers represented an important innovation.
The number seven played a fundamental role in music theory as it was then developing, given that it encompassed the entire musical scale. Accordingly, Aristotle also changed the color scale from white – black – red – ochre yellow to white – yellow – red – purple – green – blue – black, that is, with the colors arranged according to brightness and thus in correspondence with their perception. He also transposed the consonances of tone intervals (octave, fifth, fourth) to blends of colors.
During the seventeenth century, the clearly defined principles of consonance were applied to pairs of colors, which led to a kind of harmonic theory for painting. In this process, the analogy between tone intervals and color pairs was considered in isolation from the other senses. Thus, in 1650, Marin Cureau de la Chambre, following in Aristotle’s footsteps, first transferred the musical consonances of octave, fifth, and fourth to colors, and then continued to differentiate this system until he was able to determine degrees of consonance and even dissonance for all possible pairs of colors.
Athanasius Kircher had not only created symbolic classifications; in 1650, he also allocated colors to tone intervals. The color scale Kircher selected for his work was the system that had been newly developed by Franciscus Aguilonius in 1613, which was based on the three primary colors yellow – red – blue framed with white and black (following the Aristotelian tradition) and thus sorted according to brightness. Kircher then placed the color green, which had no collocation in this system, between the red and blue, correlated it with the octave, and allocated consonances to white and dissonances to black.
Isaac Newton started experimenting with prisms in 1666 and in 1671 divided the spectrum of sunlight into five colors: red – yellow – green – blue – purple. (In 1672, he even briefly considered a division of the spectrum into eleven parts.) In order to reach a more elegant and balanced distribution of the proportions of these five colors, in 1672 he introduced two intermediate colors and thus obtained red – orange – yellow – green – blue – indigo – violet. On the basis of this subdivision he postulated a similarity to the tonal system, given that the seven steps of his color scale partition the spectrum in the same way in which the seven notes are arranged on a musical scale. He then concluded that there could be a harmony of colors that was analogous to the harmony of musical notes. In 1704, he therefore arranged the seven colors in circular form and compared the color bands to the intervals within a Dorian scale. Committed as he was to the Greek ideal of a cosmic harmony, Newton also produced a comparison to the seven planets in accordance with the idea of a unity of nature. He published this analogical model in Opticks (1704) and it was later incorporated by succeeding color-tone theorists. Whereas the theories propounded up to then had only referred to tone intervals, it was in Newton’s publication that a comparison to a musical scale was made for the first time in history. From there it was only a small step to reduce the tone intervals within a scale to individual tones and the bands of color to individual colors, as came about at the beginning of the eighteenth century.
In addition, Newton’s model dispensed with Aristotle’s ordering of the colors between black and white and thus overrode numerous preceding theories of color while giving his own analogical color-tone model a physical foundation.
Louis-Bertrand Castel was the first to produce a pure color-tone analogy (from 1726 onward). He based his work on previous analogical models, including those of Aristotle, Kircher, and Newton. In contrast to his predecessors, however, his aim was not to provide proof of an all-encompassing global harmony, but to visualize music, that is, to substitute tones with colors. In order to circumvent or suspend the transience of music as a time-based art form, he wanted to combine it with painting, a spatial art, and so form a new art: musique muette. Castel argued that as music consisted of notes and painting of colors, an analogy between colors and musical notes would make it possible to visualize music, especially given that analogical reasoning was accepted as a scientific method. For the purposes of a practical implementation and in order to prove his theory, he designed a color organ, which he called the clavecin oculaire.
At that time, there were two established theories of color: Aguilonius’s and Newton’s. Also, at the beginning of the eighteenth century, Joseph Sauveur’s overtone series had provided a scientific explanation for the derivation of musical occurrences, while only four years earlier, in 1722, Jean-Philippe Rameau had declared the ecclesiastical modes — on which Newton’s work had been based — as definitively outdated and had identified the triad in a major key as the core of his new harmonic theory.
Thus, there were two fundamentally different systems available both for tones and for colors: a physics-based and an artistic model, respectively.
For colors, there was the sequence of colors in the spectrum, on the one hand, and the color scale used in painting, on the other. For tones, there was a physically based order — the overtone series — that corresponded to the spectrum and, again in correspondence to colors, there was the scale (representing the tone material or keys) used by composers.
Moreover, each given color and tone system consisted of subdivisions of different levels which all served as foundations for the compatibility required to form the analogies.
With regard to color, painters and dyers used a three-point scale, while physicians worked with a seven-point scale. These were sometimes modified to aid a potential correlation with tones. Thus, the three-point scale can be extended to six points by adding intermediate colors (yellow – orange – red – violet – blue – green) and to twelve points by inserting additional intermediate colors. The seven-point scale can be reduced to three points, given that the first five colors (red – orange – yellow – green – blue) contain the painters’ three primary colors in the order red – yellow – blue. For the extension of the seven-point scale into a twelve-point closed color circle, purple, which is not contained in the spectrum, must be added. Moreover, if a linear arrangement of the spectrum is to be maintained, when intermediate colors are added at regular intervals then a seven-point scale can only be extended to a thirteen-point scale. If a circular structure is sought, then a fourteen-point scale can be achieved. Thus, when the two color systems are combined, divisions based on the numbers 3 – 6 – 7 – 12 – 13 – 14 are possible.
Eighteenth-century music also had both a three-part and a seven-part structure: on the one hand, the major chord, which consisted of three tones and was derived from the overtone series and, on the other, the extension of this chord to a seven-tone major scale. The three- and seven-point musical scales could also be extended to twelve parts, which resulted in the chromatic scale. Hence, within music, divisions based on the numbers 3 – 7 – 12 are possible.
In the eighteenth century, then, the formation of analogies was based on divisions of 3 – 7 – 12, which were common to both systems. However, there were differences depending on the chosen starting point and the direction of the color scale.
In music, the initial starting point was the major as opposed to the minor mode and, within this, the key of C major. This form of allocation started with Castel (from 1726 onward) and was continued by Johann Gottlob Krüger who, like Castel, in 1743 had also designed a light organ (called the Farbenclavecymbel).
The most frequent analogy applied reduced the six possible combinations of the three primary painters’ colors to the combination contained from left to right in the spectrum: red – yellow – blue. This combination was correlated with the triad tones of the C-major chord, while a parallel was drawn between the remaining intermediate tones and the intermediate colors: c red, d orange, e yellow, f green, g blue, a indigo, b violet. Another way of arriving at the same analogy is to reduce Newton’s analogy between colors and tone intervals to an analogy between colors and tones, and to replace the Dorian scale used by Newton with the C-major scale. Hence, the physical and artistic derivations concur, which is why a clear separation between the two is not always possible, given that they tend to mutually confirm each other. Moreover, even after Newton, there was still no consensus with regard to the allocation of colors to tones. The diversity of these analogical models becomes evident when the variety of positions assigned on the scale to the color red, for example, is considered.
Around 1800, research into color-tone relations received new inspiration when the physicist Thomas Young succeeded in proving that light did not consist of particles, as Newton had maintained, but of waves.
Thus, wavelength correspondence became the basis for a new color-tone analogy, which (at least arithmetically) seemed to be more objective than Newton’s subdivision of the prism. In this approach, if a major scale is chosen as counterpart, then the ambitus of the spectrum must exhibit the same proportions as those of the major scale, that is, in musical terms, the interval must be a major seventh (15:8 = 1.87) or an octave (2:1 = 2.0). Newton had worked with a smaller spectrum, but its boundaries were extended thanks to improvements in optical equipment over the course of the nineteenth century. Today, it is assumed that the wavelength range of the spectrum visible to the human eye spans from approximately 360–410 nm (extreme violet) to approximately 680–800 nm (extreme red), depending on where the boundaries are drawn. If a mean value is chosen, e.g., 400–700 nm, this corresponds to a frequency range of 4.3 x 1014 Hz (extreme red) to 7.5 x 1014 Hz (extreme violet), with fluent transitions at the boundaries to infrared and ultraviolet.
The points of contact between the two systems were also determined. For example, the frequencies of tones could be exponentiated until they reached the numerical range of the light frequencies. Thus, the color correspondence of the concert pitch a = 44 Hz, for example, was reached at 4.4 x 1014 Hz after a fortyfold octavation, which corresponds to the spectral color red. Given that the interval from the tone a to the next c represents a minor third (5:6), the resulting value for c was 5.28 x 1014 Hz, which leads to yellow green. However, because the C-major scale was often used as a musical point of reference and because the note c therefore played a predominant role, this tone had to be assigned a primary color instead of yellow green. Thus, for correspondence purposes, a point at the beginning of the color spectrum, that is, within the red area, was usually chosen for c and further analogies progressed from there, usually in accordance with the proportions of the overtone series and more rarely following the tempered tuning that had been in common use since the eighteenth century.
Colors and tones differ in principle both as physical phenomena and with regard to their perception and are thus not subject to the same classification systems. When comparing spectral colors and musical tones, the following problems have to be taken into consideration. First, within the prism, colors have fluent transitions, whereas individual notes are clearly separated from each other on a theoretically constructed scale. Therefore, some points within the spectrum cannot be clearly defined by color names. Second, the boundaries of the spectrum cannot be clearly defined because the sensitivity of the human eye does not stop abruptly at the boundaries of the light spectrum, rather does so gradually. Third, the colors are unevenly distributed within the prism. The color red is dominant, which is why it should really be allocated several halftones on the musical scale. Whereas only minor color changes are perceivable in the wavelength range from approximately 600 to 700 nm, all the intermediate colors between red, orange, yellow, and green are to be found between 500 and 600 nm. The notes on a scale, by contrast, are evenly distributed. Fourth, the number of prism colors cannot be precisely defined as seven. Even in the eighteenth century, other subdivisions varying from five to eight colors were proposed.
The overtone series proved to be unsuitable as a basis for comparison for several different reasons. First, the sequence of tones progresses logarithmically and thus at changing intervals, whereas this is not true for the sequence of colors. Second, even within the first four tones, the same note is named three times. Third, there is an overtone series for every musical note, which means that there are numerous different overtone series, whereas the spectrum is not based on individual colors but on light as a whole.
In addition to the problems which have already been mentioned with regard to the design of analogies based upon spectral colors, there are two further difficulties regarding analogies based on the calculation of wavelengths.
First, in contrast to mechanical sound waves, light waves are electromagnetic waves, so that the transformation of tones into colors lacks any common physical foundation.
Moreover, the upward transposition of sound does not bring it into the range of visible light, but into the range of ultrasound.
Second, the progression of colors is arithmetical, whereas the progression of tones is logarithmical, which is why the two lack any comparable mathematical foundation.
In addition to the problems inherent in color-tone analogies that have already been described, a large number of further problems were recognized over time.
As early as the eighteenth century, objections were raised that could apply to any form of color-tone analogy. These objections are still valid today and demonstrate, moreover, that the many theories of the nineteenth and twentieth century with their individually slightly modified mathematical and physical procedures did not take into account the intense discussion that had taken place during the eighteenth century.
Thus, Jean-Jacques d’Ortous de Mairan, for example, mentioned the following aspects in 1737 and 1738. First, color harmony depends on habits and fashion, whereas the definition of consonances in music remains constant over time. Second, the effect of a color dissonance such as red with orange, for example, is less unpleasant than a dissonance in music such as a halftone. Third, colors blend to form a unity that can be analyzed — yellow and blue become green, for example; two tones, however, do not form the tone found in between, that is, c with d does not create D#. Fourth, the perception of a color is always absolute, whereas notes always refer to a tonic keynote.
Among other things, Hermann von Helmholtz discovered in 1854 that a melody maintains its basic character even when it is transposed a third higher or lower, for example. However, a painting loses its meaning if one replaces all its colors with those whose frequency ratio corresponds to a third.
Developments in music during the nineteenth and twentieth centuries led to further points of criticism with regard to the creation of analogies. For example, there is no predominance of major keys in atonal music and even less so of the C-major key, which had served as the basis for most analogies. As very differently structured non-European scales became known, the significance given to the numbers 3 – 7 – 12 in Western music systems was put into new perspective. Even the number seven in relation to the planets, which was taken as a sign of the reflection between microcosm and macrocosm, is no longer valid today.
Although the physical and perception-based prerequisites for color-tone analogies have been gradually proven wrong (which, however, does not stop many artists and theorists from still developing analogical models today), the fascination of artists with the transformation of tones into colors and thus with visualizing music is still alive today and has even increased due to the possibilities (such as parameter mapping) offered by contemporary computer technology.
 The concept of the harmony of the spheres is based on the same idea, according to which the movement of the planets generates sounds that together result in celestial harmonics, which we cannot, however, hear. Cf. Hans Schavernoch, Die Harmonie der Sphären. Die Geschichte der Idee des Welteinklangs und der Seeleneinstimmung (Freiburg: Alber, 1981).
 The overtone series consists of the sinus tones contained in each tone. The frequencies of these consecutive tones are 1:2:3:4:5:6:7:8:9:10:11:12, etc. In relation to the note C, for example, the following series applies: C – c – g – c1 – e1 – g1 – [b1] – c2 – d2 – e2 – [F#2] – g2, etc., where the tones in square brackets do not precisely correspond to the name of the note.
 In order to calculate the distance between one halftone and the next, the frequency of the first tone is multiplied by the 12th root of 2.
 Uranus was discovered in 1781, Neptune in 1846, and Pluto in 1930. Since 2006, the latter has no longer complied with the definition of solar system planets used by the International Astronomic Union. Thus, the current number of planets is eight (Mercury – Venus – Earth – Mars – Jupiter – Saturn – Uranus – Neptune).
1610 until today