The term overtone numbers components above the fundamental, offset by one from harmonics

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: Overtone numbering is offset one step behind harmonic numbering; String stiffness raises component mode frequencies above the harmonic series, creating inharmonicity; 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

• Overtone numbering is offset one step behind harmonic numbering (similarity 0.84)
• The harmonic overtone series of strings is a lucky gift, not a fixable property (similarity 0.82)
• A string’s stiffness raises its higher-frequency modes above the ideal values (similarity 0.81)
• Higher modes of a lumped bead string are not equally spaced, ruining periodicity (similarity 0.81)
• Overtones count from the first frequency above f0, offset by one from harmonic numbering. (similarity 0.81)
• A tiny extra mass ruins a string’s harmonic spacing and makes it sound sour (similarity 0.79)
• An open-open pipe’s modes form a complete harmonic series at integer multiples (similarity 0.79)

Broader Connections

• A string’s stiffness raises its higher-frequency modes above the ideal values #expands (0.90) — Eric J. Heller, Why You Hear What You Hear- An…, 860
• String stiffness raises component mode frequencies above the harmonic series, creating inharmonicity #expands (0.85)
• An open-open pipe’s modes form a complete harmonic series at integer multiples #exemplifies (0.85)