Higher piano notes require progressively greater octave stretching

Evidence

Inharmonicity on a piano increases as the strings become shorter, and therefore the octave stretching effect increases with note pitch. The stretching effect is usually related to middle C, and it becomes greater the further away the note of interest is in pitch. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1097

Categorization

• XREF: connects to: Piano octave stretching grows with pitch as strings shorten; Piano octaves are stretched because lower notes’ overtones are inharmonic; Octave stretching on pianos emerges directly from string inharmonicity — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1096 (+5 more)

Broader Connections

• Piano octave stretching grows with pitch as strings shorten #expands (0.92)
• Finite wire thickness raises higher piano partials, producing stretched harmonics #expands (0.88) — Eric J. Heller, Why You Hear What You Hear- An…, 1820
• String stiffness raises the frequency of a piano’s higher modes relative to the fundamental. #expands (0.86) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1116
• Pianos are stretch-tuned so low notes sit flat and high notes sharp #exemplifies (0.84) — Eric J. Heller, Why You Hear What You Hear- An…, 1849
• Octave stretching on pianos emerges directly from string inharmonicity #corroborates (0.82) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1096
• Piano tuning must sacrifice perfect octaves to avoid beating against sharp harmonics #corroborates (0.80) — Eric J. Heller, Why You Hear What You Hear- An…, 1824
• Real piano strings force a stretched tuning to avoid audible beats #corroborates (0.78) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1098
• Piano octaves are stretched because lower notes’ overtones are inharmonic #complicates (0.75)