Music and the Making of Modern Science

Helmholtz and the Sirens 221

Figure 14.4

(a) Helmholtz ’ s representations (from his Handbook of Physiological Optics , 1866) of Newtonian color theory

using a “ color circle ” in which more saturated colors are near the circumference; this leaves out differences in

luminosity. (b) Helmholtz contrasts this with a markedly asymmetric curve showing the relation between colors

of equal luminosity.

A

B

wave-lengths are in the same ratio as the interval of a semi-tone between two musical

notes are always at equal distances apart in the drawing [ figure 14.5a ]. ”^9 Helmholtz

approached this parallelism in terms of Newton ’ s imposition of the musical scale on the

chromatic spectrum ( figure 14.5b ).

The different sensations of color in the eye depend on the frequency of the waves of light in the

same way as sensations of pitch in the ear depend on the frequency of the waves of sound; and so,

many attempts have been made to divide the intervals of color in the spectrum on the same basis as

that of the division of the musical scale, that is, into whole tones and semitones. Newton tried it

first. However, at that time the undulatory theory was still undeveloped and not accepted; and not

being aware of the connection between the width of the separate colors in the prismatic spectrum

and the nature of the refracting substance, he divided the visible spectrum of a glass prism, that is,

approximately the part comprised between the lines B and H [in figure 14.5a], directly into seven

intervals, of widths proportional to the intervals in the musical scale ... ; and so he distinguished

seven corresponding principal colors: red , orange , yellow , green , blue , indigo , and violet.^10