Timbre reduces to a weighted ratio of fundamental and resolved versus unresolved harmonics

Evidence

Instruments among those for which spectra have been presented, which have significant amplitudes in harmonics above the fifth or seventh during their steadystate phases, include organ reed stops (see Figures 4.22 and 5.2), the tenor saxophone (see Figures 4.24 and 5.3), the trumpet (see Figure 5.4), the violin and professional singing voice (see Figure 5.5). The timbres of such instruments might be compared with those of other instruments using descriptive terms such as “bright,” “brilliant” or “shrill.” — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1475 (#expands, via linked claim)

A psychoacoustic description of timbre perception must be based on the nature of the critical bandwidth variation with frequency, since this describes the nature of the spectral analysis carried out by the hearing system. The variation in critical bandwidth is such that it becomes wider with increasing frequency, and the general conclusion was drawn in the section on pitch perception in Chapter 3 (Section 3.2) that no harmonic above about the fifth to seventh is resolved no matter the value of f0. Harmonics below the fifth to seventh are therefore resolved separately by the hearing system (e.g., see Figure 3.11), which suggests that these harmonics might play a distinct and individual role in timbre perception. Harmonics above the fifth or seventh, on the other hand, which are not separately isolated by the hearing system, are not likely to have such a strong individual effect on timbre perception, but could affect it as groups that lie within a particular critical band. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1473 (#corroborates, via linked claim)

Categorization

• XREF: connects to: Instrument timbre differences stem from harmonic spectra that shape masking breadth — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 449; Instrument timbre determines how dissonant the same two-note interval sounds; Critical bands govern tonal discrimination and timbre, not overall hearing resolution (+14 more)

Related

• Only harmonics below the fifth to seventh are individually resolved in timbre perception (similarity 0.94)
• Bright timbres stem from strong energy in harmonics above the seventh (similarity 0.92)
• Only harmonics below the fifth to seventh are resolved individually by hearing (similarity 0.91)
• Note onsets have staggered harmonic entry times that define each instrument’s timbre (similarity 0.90)
• Instrument timbre differences stem from harmonic spectra that shape masking breadth (similarity 0.90)
• Only the first five to seven harmonics are resolved regardless of fundamental (similarity 0.89)
• Timbre is conditioned entirely by the strength and presence of overtones (similarity 0.88)
• Timbre perception arises from basilar membrane vibration patterns, not pitch alone (similarity 0.88)
• Each instrument’s timbre is defined by its unique recipe of harmonic partials (similarity 0.87)
• Harmonics resolve only while their spacing exceeds the ear’s ERB (similarity 0.87)
• Only the first five to seven harmonics are resolved by the ear’s place mechanism (similarity 0.85)
• Consonance perception depends on harmonics up to about the seventh (similarity 0.85)
• Harder blowing grows higher harmonics and brightens or rasps wind-instrument tone. (similarity 0.84)
• Timbre is defined negatively, as whatever differs between equal-pitch, equal-loudness sounds (similarity 0.84)
• Musicians describe sounds using pitch, loudness, and timbre descriptors (similarity 0.84)

Broader Connections

• Bright timbres stem from strong energy in harmonics above the seventh #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1475
• Dark or dull timbres lack energy in harmonics above the seventh #expands (0.85)
• Only harmonics below the fifth to seventh are individually resolved in timbre perception #corroborates (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1473