Monotonic mode growth predicts perceptually smooth room response

Evidence

As an example, let us calculate the critical frequency of our typical living room. The second equation predicts a slightly lower critical frequency compared with the first one. However, the agreement is surprisingly good. Although the modal overlap has been calculated using a reverberation time and hence a diffuse field assumption, this is probably just valid at this frequency, which represents the boundary between the two regions. The critical frequency results show that, for this room, frequencies below 213 Hz must be analyzed using modal decay time rather than reverberation time. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2038 (#expands, via linked claim)

Between the orderly low-frequency room resonances, and the different higher frequency reflection/ray-acoustical behavior, is a transition zone, the middle of which, in large rooms such as concert halls and auditoria, would be defined as the Schroeder frequency or, as Schroeder himself calls it, the cross-over frequency fc (Schroeder, 1954, 1996): where T is the reverberation time in seconds, and V is the volume of the enclosure in cubic meters. The multiplier constant changed from the original 4000 to 2000 in the 1996 paper, emphasizing that this is not a precision calculation. — Toole, Floyd E, Sound reproduction- the acoustics and…, 475 (#qualifies, via linked claim)

Categorization

• XREF: connects to: PIR predicts preference via smoothness cues, not the room curve itself; Critical bandwidth marks the perceptual shift from rough to smooth tone resolution; A transition frequency separates modal from ray acoustical behavior in rooms — Toole, Floyd E, Sound reproduction- the acoustics and…, 475 (+1 more)

Broader Connections

• Critical bandwidth marks the perceptual shift from rough to smooth tone resolution #corroborates (0.85)
• Modal decay analysis governs room acoustics below the critical frequency #expands (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2038
• A transition frequency separates modal from ray acoustical behavior in rooms #qualifies (0.75) — Toole, Floyd E, Sound reproduction- the acoustics and…, 475