Piano bass tones raise questions related to the perception of multicomponent, inharmonic tones. In this study, the influence of the relative phases among partials on pitch and timbre was investigated for synthesized bass tones with piano-like inharmonicity. Three sets of bass tones (f0 = 527.5 Hz, 100 partials, flat spectral envelope) were generated; harmonic, low inharmonic, and high inharmonic. For each set, five starting phase relations among partials were applied; sine phases, alternate (sine/cosine) phases, random phases, Schroeder phases, and negative Schroeder phases. The pitch and timbre of the tones were influenced markedly by the starting phases. Listening tests showed that listeners are able to discriminate between tones having different starting phase relations, and also that the pitch could be changed by manipulating the relative phases (octave, fifth, major third). A piano-like inharmonicity gives a characteristic randomizing effect of the phase relations over time in tones starting with nonrandom phase relations. A measure of the regularity of the phase differences between adjacent partials is suggested for quantifying this randomization process. The observed phase effects might be of importance in synthesizing, recording, and reproducing piano music.
Galembo, Alexander; Askenfelt, Anders; Cuddy, Lola L.; and Russo, Frank A., "Effects of relative phases on pitch and timbre in the piano bass range" (2001). Psychology Publications and Research. Paper 1.