Rasch, R.A., Heetvelt, V. (1985). String inharmonicity and piano tuning. Music Percept. 3, 171-190

Inharmonicity is a well-known property of stiff strings such as those used in the modern piano. Effects on piano tuning (e.g., the stretched octave) have been suggested but have never been fully investigated. We have measured the inharmonicities of the strings of a medium-sized grand piano. The measured inharmonicities are in excellent correspondence with the predictions by formula from the physical properties of the strings. Strings with higher frequencies usually have higher inharmonicity than strings with lower frequencies; this cancels out part of the effect of inharmonicity on beat frequency.