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Bonello and Schroeder

Bonello : A new criterion for the distribution of normal room modes,
JAES 1981, p.597

For optimum room dimensions the following conditions should be met:
1. The curve spectral density of modes vs frequency should increase monotonically. Each one-third octave should have more modes than the preceding one.
2. There should be no double modes. At most, double modes only in
one-third-octave bands with densities equal to or greater than 5.


Schroeder : The "Schroeder frequency " revisited, JASA 1996, vol.99,
p.3240

The Schroeder frequency fc is the frequency above which the standing waves are so closely spaced that they do not substantially affect the sound. It is dependent on room volume and reverberation time. The larger the room or the shorter the reverberation time, the lower that frequency. A low Schroeder frequency tends to make the frequency response smooth over a wider range.

The Schroeder frequency marks the transition from individual, well
separated resonances to many overlapping normal modes. It is
calculated as follows :

fc = 2000 sqrt T/V

T = 60 dB reverberation time in seconds
V = Room volume in m3

which has a a consequence that at least three resonances fall within the half-power bandwidth B (B = 2.2/T) of one resonance at frequencies above fc.


I choose to use Bonello rather than any of the other proposed methods (fixed ratio, Golden Ratio, Walker) because it's in line with the concept of the Schroeder frequency: the number of modes per 3rd-octave band rises up to a point where there are that many modes per 3rd-octave band that the individual mode is no longer distinguishable. Thanks to the acoustically effective ceiling our living/listening rooms has a (calculated) reverb time of 0.4 - 0.5 seconds which results in a Schroeder frequency of about 138 Hz.


Klaus

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