Piano string stiffness causes musical harmonics to deviate from exact integer multiples

the verdict

SUPPORTED

the evidence backs this

Recorded sources

5 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

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.

The analysis

The claim addresses a well-established physical property of real piano strings known as inharmonicity. Multiple papers (1, 3, 9, 10) explicitly confirm and mathematically model how string stiffness causes partial frequencies to deviate from exact integer multiples. No papers refute this fundamental acoustic principle.

Evidence for · 5

Normal Vibration Frequencies of a Stiff Piano String

Recorded source metadata

Harvey Fletcher. Normal Vibration Frequencies of a Stiff Piano String. 1964. https://doi.org/10.1121/1.1918933

Formulates normal modes and partial frequencies for stiff piano strings, showing how physical dimensions lead to deviations from ideal harmonic series.

Source citation format

See more details

More for · 4

String Inharmonicity and Piano Tuning

Recorded source metadata

Rudolf A. Rasch, Vincent Heetvelt. String Inharmonicity and Piano Tuning. 1985. https://doi.org/10.2307/40285331

Investigates measured inharmonicities in grand piano strings and confirms they correspond directly to predictions based on physical string stiffness.

Source citation format

Stiff-string theory: Richard Feynman on piano tuning

Recorded source metadata

John C. Bryner. Stiff-string theory: Richard Feynman on piano tuning. 2009. https://doi.org/10.1063/1.3273016

Discusses how the nonzero stiffness of piano strings impacts tuning harmonics.

Source citation format

String inharmonicity and piano tuning

Recorded source metadata

Vincent Heetveld, Rudolf A. Rasch. String inharmonicity and piano tuning. 1984. https://doi.org/10.1121/1.2021760

Confirms that real piano strings exhibit string inharmonicity due to stiffness, causing deviations from ideal harmonic relationships.

Source citation format

Investigating the Inharmonicity of Piano Strings

Recorded source metadata

Eleanor Roy. Investigating the Inharmonicity of Piano Strings. 2024. https://doi.org/10.2218/esjs.9815

Demonstrates experimentally and theoretically that real piano string vibrations deviate from exact integer harmonics due to string stiffness.

Source citation format

The paper trail · every fact has a biography

first checked01 Aug 2026

judged → SUPPORTED · 8701 Aug 2026

More receipts

Is it true that Phonological evolution involves regular processes of phoneme elision, vowel nasalization, and tonogenesis?Is it true that Hemangiomas are treatable with medication?Is it true that Research identifies forms of intelligence that diverge from standard IQ measures?

Random receipt →The Trust Wiki →

Anyone with this link can read the claim and its public receipt, including any personal information in that text. Open permanent receipt.

Check your own claim

Challenge the receipt

I have a source that contradicts this verdict I have a source that supports it No source: request a receipt review Requests are recorded for review. This does not start an automatic check or guarantee a response time.

trust me, bro: win the argument, pass the class, survive peer review.

Citation formatting by citeproc-js (Frank Bennett) and the Citation Style Language project. Source and licenses.

This receipt is an automated verdict against our published method · not an opinion about any author or publication.
Terms · Privacy · How verdicts work · Dispute this receipt