This paper describes the mathematical model used for computing both the frequency and angular distribution of the normal modes in rectangular rooms. The criteria adopted were computed for each half-octave band over the first 4 octaves of normalized frequency for rooms with dimension ratios ranging from 313:1 to 1:1. Considerable variation in the frequency-spacing criterion exists not only for changes in room dimensions but also from one half-octave band to the next. No clearly defined optimum room dimension, as predicted by Bolt, emerges from this study. The angular-distribution index is more regularly behaved with rather definite stratification apparent as a function of the room height/length ratio, when the height direction is taken as the angular reference. When both the frequency and angular criteria are combined, only a few small regions of dimension ratios appear to be good. From these regions, p = 0.69, q = 0.43; p = 0.83, q = 0.65; p = 0.82, q = 0.72, together with p = 1/21/3, q = 1/41/3, appear to be among the best. For rooms having satisfactory mode distribution, an approximate formula has been developed for determining the lowest midband frequency for which a room may be used for measurements of continuous spectrum sounds. The formula turns out to be a constant divided by the cube root of the volume, where the constant is a function of the measuring bandwidth and the number of normal modes required therein. For 20, 12, and 9 modes in 1-, 12-, or 13-oct bands, the constants are 1150, 1280, and 1355 cps, respectively.
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L. W. Sepmeyer (1965) studied this question.