Slightly mistuned piano strings produce richer, longer-lasting sound

Evidence

This equation, although it is derived assuming an infinitely thin string, is applicable to most strings that one is likely to meet in practice. But it is applicable to only pure transverse vibration; it does not apply to other modes of vibration. However, transverse waves are the dominant form of vibration for thin strings. The main error in Equation 1.7 is due to the inherent stiffness in real materials, which results in a slight increase in velocity with frequency. This effect does alter the timbre of percussive stringed instruments, like the piano or guitar, and gets stronger for thicker pieces of wire. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 103 (#expands, via linked claim)

The notes of a piano are usually tuned to equal temperament (see Chapter 3), and octaves are then tuned by minimizing the beats between pairs of notes an octave apart. When tuning two notes an octave apart, the components that give rise to the strongest sensation of beats are the first harmonic of the upper note and the second harmonic of the lower note. These are tuned in unison to minimize the beats between the notes. This results in the f0 of the lower note being slightly lower than half the f0 of the higher note due to the inharmonicity between the first and second components of the lower note. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1096 (#expands, via linked claim)

Categorization

• XREF: connects to: The inharmonicity of real strings is a desirable feature, not a defect; Piano strings and soundboards can exchange energy producing audible loudness shimmer; Octave stretching on pianos emerges directly from string inharmonicity — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1096 (+2 more)

Broader Connections

• String stiffness makes higher frequencies travel faster, changing timbre #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 103
• Octave stretching on pianos emerges directly from string inharmonicity #expands (0.82) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1096
• String-instrument inharmonicity is testable as contributing to sound quality #corroborates (0.78)