The influence of inharmonicity on piano tuning
Taro Mori, Ingolf Bork · The Journal of the Acoustical Society of America · 1999
It is well known that octaves of piano sounds are stretched to more than a 2 : 1 ratio. One reason is that partials of piano tones are not exactly harmonic because of the flexural rigidity of the string. This inharmonicity is characterized by the coefficient B, which depends on the tension, length, Young’s modulus, the area of cross section, and the radius of gyration of the string. Piano technicians are trained to tune the octave as ‘‘beautifully’’ as possible, but the inharmonicity of the string hinders perfect tuning without beat. For example, when the second partial of the lower sound and the first partial of the upper sound are tuned without beat, all other partial pairs show beats. On the other hand, since the timbre structure of partials is unique for each instrument, the tuned octaves of two different instruments may differ. Some piano sounds were simulated by additive synthesis with different octave, inharmonicity, and timbre in order to perform subjective hearing tests with some piano tuners. It could be shown that the tuned octave width depends not only on the coefficient B but also on the timbre. The influence of the sound board is also discussed.