Beats, roughness, and separation emerge at different frequency differences

Evidence

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. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 575

Categorization

• XREF: The rough/smooth boundary prefigures critical bandwidth concepts used later in audio compression and masking research.
• SHARE: Share with a musician or tuner: the ~12.5 vs 15 Hz thresholds for beats vs roughness explain why slight detuning sounds urgent while larger detuning sounds dissonant.