Piano string stiffness causes musical harmonics to deviate from exact integer multiples
the verdict
SUPPORTED
the evidence backs this
confidence 87/100
Physical measurements and acoustic models consistently confirm that the stiffness of piano strings causes their overtone frequencies to sharp slightly, resulting in inharmonicity that deviates from exact integer multiples of the fundamental frequency.
Evidence for · 5
Normal Vibration Frequencies of a Stiff Piano String
1964 · cited by 86
Formulates normal modes and partial frequencies for stiff piano strings, showing how physical dimensions lead to deviations from ideal harmonic series.
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More for · 4
String Inharmonicity and Piano Tuning
1985 · cited by 10
Investigates measured inharmonicities in grand piano strings and confirms they correspond directly to predictions based on physical string stiffness.
Stiff-string theory: Richard Feynman on piano tuning
2009 · cited by 2
Discusses how the nonzero stiffness of piano strings impacts tuning harmonics.
String inharmonicity and piano tuning
1984 · cited by 0
Confirms that real piano strings exhibit string inharmonicity due to stiffness, causing deviations from ideal harmonic relationships.
Investigating the Inharmonicity of Piano Strings
2024 · cited by 0
Demonstrates experimentally and theoretically that real piano string vibrations deviate from exact integer harmonics due to string stiffness.