The Chromatic Octave

Abstract

I HAVE to thank “M. A.” for his letter in NATURE of June 9th, suggesting that the wave-frequency to which the complementary of any tint is due, may be, not the geometric mean between that tint and its octave, as I suggested in a letter in NATURE of 28th April, but the harmonic mean. I can scarcely doubt that there must be some simple arithmetical relation between the wave frequencies of any tint and its complementary, but I see no à priori reason for expecting to find one such law rather than another; we must try which assumed law will most nearly coincide with fact, and the hypothesis of a harmonic mean does so coincide pretty nearly. The following table (see my previous letter) gives the ratios of the wave-frequencies of red, orange, and yellow as observed, of their complementaries as observed, and of the same as calculated on the hypothesis of the harmonic mean:—