Pianos are stretch-tuned so low notes sit flat and high notes sharp

Evidence

Stretch tune. Modulates the Railsback effect. Stretch tuning makes the low range slightly flatter and the high range slightly sharper so you hear an in-tune piano across the full range. — Eric J. Heller, Why You Hear What You Hear- An…, 1849

Categorization

• DEFINE: Introduces the Railsback effect: real piano tuning stretches away from equal temperament.
• QUESTION: Why does stretching make the piano sound in-tune rather than out-of-tune? The implied mechanism (inharmonicity of stiff strings) deserves chasing.
• SHARE: Piano tuning is deliberately non-equal-tempered — a fact a musician friend who tunes instruments would appreciate.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 1849
• XREF: connects to: Moisture, cracking, and tension drift make every grand piano uniquely voiced over its lifetime; Physically correct octaves actually cause audible beats in a real piano; Stretched partials give the piano its characteristic musical color (+3 more)

Broader Connections

• Octave stretching on pianos emerges directly from string inharmonicity #expands (0.95) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1096
• Piano octave stretching grows with pitch as strings shorten #expands (0.90)