Piano tuning must sacrifice perfect octaves to avoid beating against sharp harmonics

Evidence

In reality, the partials are sharp, so what to do? If the base frequencies of each key are set to be rigidly at the mathematically correct frequencies—perfect octaves—then they will beat against the out-of-tune harmonics of lower notes. If they are instead stretched—that is, tuned to the sharp harmonics— then they are no longer strictly using the octave as a musical interval. — Eric J. Heller, Why You Hear What You Hear- An…, 1824

Categorization

• DEEPTHINKING: The piano as physically impossible instrument — its very construction forces a compromise between tuneability and pure musical intervals — is a genuinely dense point about embodied materiality forcing aesthetic norms.
• XREF: connects to: Higher piano notes require progressively greater octave stretching — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1097