XXIII. On the physical constitution and relations of musical chords
Alexander John Ellis · Proceedings of the Royal Society of London · 1864
Abstract When the motion of the particles of air follows the law of oscillation of a simple pendulum, the resulting sound may be called a simple tone. The pitch of a simple tone is taken to be the number of double vibrations which the particles of air perform in one second. The greatest elongation of a particle from its position of rest may be termed the extent of the tone. The intensity or loudness is assumed to vary as the square of the extent. The tone heard when a tuning-fork is held before a proper resonance-box is simple. The tone of wide covered organ-pipes and of flutes is nearly simple. Professor G. S. Ohm has shown mathematically that all musical tones whatever may be considered as the algebraical sum of a number of simple tones of different intensities, having their pitches in the proportion of the numerical series 1, 2, 3, 4, 5, 6, 7, 8, &c. Professor Helmholtz has established that this mathematical composition corresponds to a fact in nature, that the ear can be taught to hear each one of these simple tones separately, and that the character or quality of the tone depends on the law of the intensity of the constituent simple tones.