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 . 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.
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August 2022
August 24 2022
Effect of inharmonicity on pitch perception and subjective tuning of piano tones
Jussi Jaatinen
;
Jussi Jaatinen
a)
1
Faculty of Arts, Musicology, University of Helsinki
, P.O. Box 24, 00014 Helsingin yliopisto, Finland
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Jukka Pätynen
Jukka Pätynen
b)
2
Akukon Ltd
, Hiomotie 19, 00380 Helsinki, Finland
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a)
Electronic mail: [email protected]
b)
Also at: Department of Computer Science, Aalto University, Konemiehentie 2, 02150 Espoo, Finland.
J. Acoust. Soc. Am. 152, 1146–1157 (2022)
Article history
Received:
December 20 2021
Accepted:
July 29 2022
Citation
Jussi Jaatinen, Jukka Pätynen; Effect of inharmonicity on pitch perception and subjective tuning of piano tones. J. Acoust. Soc. Am. 1 August 2022; 152 (2): 1146–1157. https://doi.org/10.1121/10.0013572
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