Room resonances necessarily overlap because high Q would ruin intelligibility

Evidence

At 300 Hz, the density of modes in a modest-sized room (about 8.5 by 10 by 2.7 meters) is about eight modes per Hz. To stand out alone, the full width at half maximum (FWHM) of the resonances would have to be less than about 0.1 Hz, corresponding to a Q of 3000. But a Q of 3000 corresponds to 10 seconds before sound around 300 Hz reaches 4% of its initial amplitude. Such a high Q would render speech unintelligible, and make a cathedral seem like a dead acoustic space in comparison. The conclusion is that the room resonances cannot be isolated from each other—they must overlap, their widths are greater, even much greater, than the spacing between them at 300 Hz. — Eric J. Heller, Why You Hear What You Hear- An…, 1124

Categorization

• DEEPTHINKING: A tight quantitative argument: if room resonances were sharp enough to be individually isolated, the Q would be so high that speech would smear into unintelligibility. Isolation and intelligibility are mutually exclusive constraints on room acoustics.
• XREF: Relates to the author’s definition of Q and the intensity-decay picture of resonance; also connects to reverb time in the earlier chapters on rooms.