The effect of inharmonic partials on pitch of piano tones

Piano tones have partials whose frequencies are sharp relative to harmonic values. A listening test was conducted to determine the effect of inharmonicity on pitch for piano tones in the lowest three octaves of a piano. Nine real tones from the lowest three octaves of a piano were analyzed to obtain frequencies, relative amplitudes, and decay rates of their partials. Synthetic inharmonic tones were produced from these results. Synthetic harmonic tones, each with a twelfth of a semitone increase in the fundamental, were also produced. A jury of 21 listeners matched the pitch of each synthetic inharmonic tone to one of the synthetic harmonic tones. The effect of the inharmonicity on pitch was determined from an average of the listeners' results. For the nine synthetic piano tones studied, pitch increase ranged from approximately two and a half semitones at low fundamental frequencies to an eighth of a semitone at higher fundamental frequencies.