Jaatinen Jussi, Pätynen Jukka
Faculty of Arts, Musicology, University of Helsinki, P.O. Box 24, 00014 Helsingin yliopisto, Finland.
Akukon Ltd, Hiomotie 19, 00380 Helsinki, Finland.
J Acoust Soc Am. 2022 Aug;152(2):1146. doi: 10.1121/10.0013572.
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.
钢琴调音理念中的共识是用钢琴琴弦的非谐性来解释拉伸调音音阶的。本研究旨在探讨可变非谐性如何影响钢琴调音过程的结果，比较听觉调音钢琴的调音曲线与主观八度扩展实验得出的曲线，并评估同一音的非谐或谐和版本的音高是否被不同地感知。此外，还研究了其他钢琴琴键的琴弦对单根钢琴琴弦测量的非谐性的影响。在一台施坦威D型大钢琴上测量了所有单根琴弦的非谐性。通过对频率调整的正弦分音进行加法合成来实现可变非谐性。15名钢琴调音师和18名管弦乐音乐家参与了实验。结果表明，非谐钢琴音调产生的键盘调音曲线与雷尔斯巴克曲线相似，且与谐和对应曲线有显著差异。非谐调音曲线让人联想到主观八度扩展曲线。在高达C♯7的音高上，非谐音高被感知为高于谐音高。其他琴键的共振琴弦对所弹奏琴键单根琴弦测量的非谐性没有表现出任何有意义的影响。
