Instrument stiffness versus tension determines how widely its modes are spaced

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)

Categorization

• XREF: connects to: A string’s stiffness raises its higher-frequency modes above the ideal values — Eric J. Heller, Why You Hear What You Hear- An…, 860; Mass dominates impedance at high frequencies, stiffness at low frequencies — Eric J. Heller, Why You Hear What You Hear- An…, 87; Mass, stiffness, and friction each resist a distinct kinematic quantity (+11 more)

Broader Connections

• String stiffness makes higher frequencies travel faster, changing timbre #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 103