5 Calculation of wavelengths as a basis for color-tone analogies

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.