Abstract
Inharmonicity is a well‐known property of the stiff strings as used in the modern piano. Effects on piano tuning (e.g., the stretched octave) have been suggested but never fully investigated. We have measured the inharmonicities of the strings of a medium‐sized grand piano. The measured inharmonicities were in excellent correspondence with the predictions by formula from the physical properties of the strings. Six models, differing in three pairs of assumptions, were developed for describing the effects of the inharmonicity on the tuning of the piano and on the beat frequencies used when tuning. The correspondence between the model predictions and the actually applied tuning could be used to test the validity of the assumptions. One of the surprising outcomes was that the fact that higher harmonics of lower strings beat with lower harmonics of higher strings (which have, as a rule, higher inharmonicity) cancels out a part of the effects of inharmonicity on beat frequency.
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