The Physical Criterion for Determining the Pitch of a Musical Tone
Harvey Fletcher · Physical Review · 1924
Effects upon pitch and quality of musical sounds of eliminating certain component frequencies.---A high quality telephone system was used to reproduce musical sounds from the voice, the piano, the violin, the clarinet and the organ without any appreciable distortion. Into this telephone system electrical filters were introduced which made it possible to eliminate any desired frequency range. Results with this system show that only the quality and not the pitch of such musical sounds changes when a group of either the low or high frequency components is eliminated. Even when the fundamental and first seven overtones were eliminated from the vowel $\mathrm{ah}$ sung at an ordinary pitch for a baritone, the pitch remained the same. These results were checked by a study of synthesized musical tones produced by ten vacuum tube oscillators, with frequencies from 100 to 1000 at intervals of 100. It was found that three consecutive component frequencies were sufficient to give a clear musical tone of definite pitch corresponding to 100, and that in general when the adjacent components had a constant difference which was a common factor to all components, a single musical tone of pitch equal to this common difference was obtained, but not otherwise. Explanation of the results in terms of mechanism of the ear. Recent work on hearing has shown that the transmission mechanism between the air and the inner ear has a non-linear response which accounts for the so-called subjective tones. When the components of low frequency are eliminated from the externally impressed musical tone, they are again introduced as subjective tones before the sound reaches the nerve terminals. Calculation of the magnitude of these subjective tones from the non-linear constants of the ear shows that the results on pitch are what might be expected.Sound spectra of ten typical musical sounds, obtained with an electrical automatic harmonic analyser to be described by Wegel and Moore, are given for $\mathrm{ah}$ sung at pitch $d$, $\overline{a}$ sung at $a$, piano ${c}_{1}$, piano ${c}^{\ensuremath{'}}$, violin ${g}^{\ensuremath{'}}$, clarinet $c$, organ pipe ${c}_{1}$ for three pressures, and organ pipe ${c}^{\ensuremath{'}}$.