Timbre can be graphed as relative energy across fundamental, resolved, and unresolved harmonics.

Evidence

The graph is plotted based on the proportion of energy in (1) the second, third and fourth harmonics or “mid” frequency components (Y axis) and (2) the highfrequency partials, which here are the fifth and above, or “high” frequency components (X axis) and (3) the fundamental or f0 (where X and Y tend toward zero). The corners of the plot in Figure 5.7 are marked: “mid,” “high” and “f0” to indicate this. A point on a tristimulus diagram therefore indicates the relationship between f0, harmonics that are resolved, and harmonics that are not resolved. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1488

Categorization

• DEFINE: Defines the tristimulus diagram’s three axes: mid harmonics, high partials, and the fundamental f0.
• XREF: Connects to earlier chapters on critical bands and harmonic resolution — resolved vs unresolved harmonics is the core of that analysis. — connects to: Timbre comprises spectral content and how frequencies and amplitudes shift over a note — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1427; Instrument timbre develops over time as higher harmonics fade in after the fundamental. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1452; Timbre lacks a correct answer, so it must be measured via adjective-pair ratings. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1481 (+17 more)

Broader Connections

• Timbre is determined by the relative amplitudes of partials, not their frequencies alone #corroborates (0.90) — Eric J. Heller, Why You Hear What You Hear- An…, 2201
• Timbre reduces to a weighted ratio of fundamental and resolved versus unresolved harmonics #expands (0.85)
• Harmonic amplitudes shape timbre and loudness but not pitch. #corroborates (0.85) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1195
• Each instrument’s timbre is defined by its unique recipe of harmonic partials #corroborates (0.85)
• Spectrum magnitude, not phase, drives the perceived timbre of a sound #corroborates (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2756
• Harmonic content alone produces recognizable, describable timbre qualities #corroborates (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 2202
• Instrument timbre differences stem from harmonic spectra that shape masking breadth #qualifies (0.80) — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 449
• Timbre distinguishes sounds sharing pitch, loudness, and duration. #responds-to (0.80) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1179
• Bright timbres stem from strong energy in harmonics above the seventh #complicates (0.75)
• Timbre depends on staggered harmonic entry times and spectral extent #complicates (0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1475
• Spectra of only odd harmonics produce a clarinet-like timbre #qualifies (0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 3014
• An oboe-like timbre is reproduced by four harmonics with exponentially decreasing amplitudes #qualifies (0.75) — Dijk, Pim van, Physiology, Psychoacoustics and…, 5290
• Timbre depends on sound order over time, not just spectral content. #complicates (0.75)
• Helmholtz derived timbre’s spectral dependence from theory alone, without critical-band data #responds-to (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1492
• Timbral differences between instruments can be plotted dynamically through critical bands #expands (0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1514