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

Abstract

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 [Formula: see text]. 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.

Laajentunut viritys ja kontekstisidonnainen intonaatio

“…Pystypianon alarekisterin virityksen voimakkaampi leviäminen selittyy osittain suuremman inharmoniteetin aiheuttamasta havaitun sävelkorkeuden noususta, koska viritykseltään ylävireiset osasävelet dominoivat sävelkorkeuden havaitsemista alimmissa äänissä johtuen kuuloaistin epäherkkyydestä äänenvoimakkuuteen matalilla taajuuksilla (Suzuki ja Takeshima 2004). Tämä vastaavasti aiheuttaa tarpeen fysikaalisen pohjataajuuden madaltamiselle, jotta äänet eivät kuulostaisi liian korkeilta (Jaatinen ja Pätynen 2022).…”

“…Värjätyt alueet: 95 %:n luottamusvälit. (Jaatinen ja Pätynen 2022. ) Mainittakoon vielä, että joissain vanhemmissa analogisissa syntetisaattoreissa ja sähköpianoissa, joissa asteikon laajentumista ei ole huomioitu, saattaa törmätä matemaattiseen tasaviritykseen, joka kattaa koko instrumentin käytettävissä olevan sävelasteikon.…”

Subjectively preferred octave size is resolved at the late stages of cerebral auditory processing

“…The slightly enlarged preferred octave interval has been observed when sinusoidal, complex (a tone with harmonics) or Huggins' (Cramer & Huggins, 1958) tones are used (Hartmann, 1993) or when two tones are presented successively or simultaneously (Demany & Semal, 1990; Ward, 1954). The most common example of stretched tuning can be heard in modern pianos, where it is a de facto tuning standard (Jaatinen & Pätynen, 2022; Schuck & Young, 1943). Some variability has been observed in the preferred enlarged octave size between listeners, but no systematic differences have been reported.…”