Effect of inharmonicity on pitch perception and subjective tuning of piano tones

Funding Information: This research was supported by the Academy of Finland Project No. 289300, Niilo Helander Foundation, and Alfred Kordelin Foundation. The authors express their thanks to the piano tuners Harri Tuovinen (for a description of the aural tuning method), Elisa Visap€a€a (for contribution in development of the tuning experiment), and Matti Kyllonen (for assistance in the Steinway D grand piano recording session). Publisher Copyright: © 2022 Acoustical Society of America.The consensus in piano tuning philosophy explains the stretched tuning scale by the inharmonicity of piano strings. This study aimed to examine how variable inharmonicity influences the result of the piano tuning process, compare the tuning curves of aurally tuned pianos with the curves derived from subjective octave enlargement experiments, and evaluate whether the pitches of inharmonic or harmonic versions of the same tone are perceived differently. In addition, the influence of strings of other piano keys on the measured inharmonicity of a single piano string was investigated. The inharmonicity of all individual strings was measured on a Steinway D grand piano. Variable inharmonicity was implemented by additive synthesis with frequency-adjusted sinusoidal partials. Fifteen piano tuners and 18 orchestra musicians participated in the experiments. The results indicate that the inharmonic piano tones produced a keyboard tuning curve similar to the Railsback curve and differed significantly from the harmonic counterpart. The inharmonic tuning curve was reminiscent of the subjective octave enlargement curve. Inharmonic tone pitches were perceived to be higher than harmonic tones up to C » 7. The covibrating strings of the other keys did not exhibit any meaningful effect on the measured inharmonicity of a single string of the played key.Peer reviewe