The rate of beating between close partials determines whether they sound consonant or rough

Evidence

A clear connection between psychoacoustics and music has been shown. Roughness is closely related to consonance and dissonance perceived between two or more musical notes; the more the partials of the notes generate roughness, the higher the perceived dissonance is. This leads directly to basic melodic and harmonic structures in music. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1350 (#corroborates, via linked claim)

For the majority of listeners, beats are usually heard when the frequency difference between the tones is less than about 12.5 Hz, and the sensation of beats generally gives way to one of a “fused” tone that sounds “rough” when the frequency difference is increased above 15 Hz. As the frequency difference is increased further, there is a point at which the fused tone gives way to two separate tones but still with the sensation of roughness, and a further increase in frequency difference is needed for the rough sensation to become smooth. The smooth separate sensation persists while the two tones remain within the frequency range of the listener’s hearing. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 575 (#expands, via linked claim)

Categorization

• XREF: connects to: Perception of two tones progresses from beats to roughness to smoothness — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 575; Sensory consonance depends on roughness, sharpness, and tonalness — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 2040; Perceived musical dissonance reduces to roughness from beating partials. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1350 (+6 more)

Broader Connections

• Perceived musical dissonance reduces to roughness from beating partials. #corroborates (0.90) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1350
• Perception of two tones progresses from beats to roughness to smoothness #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 575
• Dissonance depends on musical interval, not a fixed beat rate across frequencies #qualifies (0.85)
• Sensory consonance depends on roughness, sharpness, and tonalness #expands (0.80) — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 2040
• Modulation frequency determines whether sound is heard as fluctuation, roughness, or multiple tones #expands (0.80) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1217
• Slow envelope fluctuations up to 16 Hz predict consonant-in-noise perception. #expands (0.75) — Dijk, Pim van, Physiology, Psychoacoustics and…, 5575
• Distinct high partials make tones sound cutting or rough and powerful #expands (0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1520
• Roughness grows faster with modulation depth for tones than for noise #expands (0.75)