A tiny extra mass ruins a string’s harmonic spacing and makes it sound sour

Evidence

A real string has thickness and resists bending of its own accord, independent of the tension. For low-frequency, long-wavelength vibrations, this does not make much difference, since the curvatures of the string are low. However, at higher frequencies and shorter wavelengths, the bending is more severe, since so many wavelengths are packed into the length of the string. This extra resistance to bending sends the frequencies of a real string higher than they would be for the ideal string. — Eric J. Heller, Why You Hear What You Hear- An…, 860 (#expands, via linked claim)

Categorization

• XREF: connects to: Higher modes of a lumped bead string are not equally spaced, ruining periodicity; Adding mass at a node leaves a vibrating string’s mode unchanged; A string’s stiffness raises its higher-frequency modes above the ideal values — Eric J. Heller, Why You Hear What You Hear- An…, 860 (+2 more)

Related

• Higher modes of a lumped bead string are not equally spaced, ruining periodicity (similarity 0.93)
• A string’s stiffness raises its higher-frequency modes above the ideal values (similarity 0.88)
• Real string stiffness slightly raises wave velocity with frequency, affecting timbre. (similarity 0.84)
• Instrument stiffness versus tension determines how widely its modes are spaced (similarity 0.84)
• Adding mass at a node leaves a vibrating string’s mode unchanged (similarity 0.84)
• Adding mass at a node leaves that mode unchanged (similarity 0.83)
• String stiffness makes higher frequencies travel faster, changing timbre (similarity 0.83)
• Plucking a string at a node suppresses every Nth harmonic (similarity 0.83)
• The inharmonicity of real strings is a desirable feature, not a defect (similarity 0.82)
• When a string’s linear density is fixed, pitch is varied by tension and length (similarity 0.81)
• Slightly mistuned piano strings produce richer, longer-lasting sound (similarity 0.81)
• Increasing string tension raises the frequency of a single-bead oscillator (similarity 0.81)
• String stiffness raises the frequency of a piano’s higher modes relative to the fundamental. (similarity 0.81)
• Attaching mass to a string lowers odd harmonics and can trigger chaotic screech (similarity 0.80)
• String pitch depends on mass per unit length, length, and tension (similarity 0.80)

Broader Connections

• String stiffness raises component mode frequencies above the harmonic series, creating inharmonicity #expands (0.90)
• A string’s stiffness raises its higher-frequency modes above the ideal values #expands (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 860
• Harmonic spacing theories also fail once harmonics are non-adjacent #expands (0.80)