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Effect of the inharmonicity of stiff strings on piano tuning

1984; Acoustical Society of America; Volume: 75; Issue: S1 Linguagem: Inglês

10.1121/1.2021273

1520-9024

Hideo Suzuki,

Diverse Musicological Studies

The presently used tuning theory [A. A. Reblitz, Piano Servicing, Tuning, and Rebuilding, 5th Printing (Vestal Press, Vestal, NY, 1981)] uses the beat rates calculated from the ideal harmonics of notes in the temperament octave. Following this theory, the note F3 is tuned sharp to C4 (middle C) with a 0.59-Hz beat rate. Then, the note F4 is tuned to the note F3, beatless. Theoretically, assuming the ideal harmonic relationship of partials, the best rate between notes C4 and F4 (test interval) is 1.18 Hz with F4 sharp. This is not true, however, for real piano strings with some amount of inharmonicity. If the inharmonicity index B, which describes the degree of inharmonicity of a string [H. Fletcher, J. Acoust. Soc. Am. 36, 203–209 (1964)], is assumed to be 0.0004 for notes F3, C4, and F4, the beat rate between notes C4 and F4 becomes 0.696 Hz with F4 flat. This is a self-contradiction inherent in the present tuning theory. A method will be presented to calculate the beat rates when the inharmonicity indexes are known for all thirteen notes of the F3–F4 octave.