Small rooms—ratios and modes
This article is a small piece of room acoustics history and a brief overview of previous work and research in the special field of room acoustics, dealing with 3-dimensional ratios of small rooms and their significance to modal distribution.
Since Bolt (1946) , in the aim for evenly spaced modes, came up with a method for determining preferable room ratios, researchers have continued to search for the optimum room dimensions based on various criteria. A review of papers in this special field of small room acoustics was given in a paper by Cox and D’Antonio in 2004.
Some highlights from research in small room acoustics in general in the period from the early 1940’s until present follows.
The 2:3:5 ratio recommended by Volkman  becomes less supported as time goes by, and the same goes for Boner’s  1:1.26:1.59 from the following pages of the same publication (1942). The importance of axial modes are pointed at by Gilford (1959) , who also reports from an interesting study of coloration in radio broadcasting studios, corresponding to frequencies in the range of 100-175Hz by male voices and 200-300Hz by female voices.
Another development is the shift from studying average mode spacing to standard deviation of mode spacing, the latter being suggested as a single figur of merit by Louden (1971). Bonello  differs from other authors by leaving the interest for mode spacing in favour of his own criterion of non-decreasing density of modes within increasing third-octave-bands (1981). Work by Walker  influence Broadcasting Union recommendations (1998), which as discussed by Walker leaves the golden ratios alone and rather aims at avoiding the worst cases. Cox and D’Antonio  presented a new approach in small room acoustic planning, aiming for the flattest possible frequency response (2000 and 2004).
Cuboid rooms dominates in detailed studies of geometry and acoustic quality. Other geometries have been examined by finite element methods (FEM), but such studies have been few since they require high computational capacity. Results from Nieuwland  and Weber includes pressure amplitude contour plots of rooms with splayed walls compared with rooms with parallell walls. Splaying the walls apparently reduces pressure gradients, but it is not clear if it provides less area having peaks and dips and reduced standard deviation of levels in the average receiver point. At least 5% splaying of walls is necessary to have an effect on degeneracy of modes . Thumb rules of 6 to 12 degrees deviation from parallell have been common, but strangely enough not related to distance between such wall pairs. This author has suggested that splaying or other deviation from parallell should be related to distance between wall pairs , since one and the same degree of slanting is expected to have larger effect on a standing wave if wall distance was shorter.
Sommerville and Ward (1951) reported that geometrical diffusing elements reduced fluctuations in a swept-sine steady-state transmission test. For a noticeable effect, such geometrical diffusors had to be at least 1/7 of a wavelength, and in their study of cylindrical, triangular and rectangular elements, the rectangular shape proved the more effective for both steady-state and transient phenomena.
Splaying one or two walls may improve diffusion, but does not eliminate modal problems. Geometries deviating from rectangular sections (slanted walls, etc) does not make coloration dissapear, only harder to predict, Gilford 1972) .
Related AKUTEK papers:
External source: Room dimensions for small listening rooms
1. J.E.Volkman, ”Polycylindrical Diffusers in Room Acoustical Design”, J.Acous.Soc.Am., 13 (July 1942), p 234-243.
2. C.P.Boner, ”Performance of Broadcast Studios Designed with Convex Surfaces of Plywood”, J.Acous.Soc.Am., 13 (July 1942), p 244-247.
3. R. H. Bolt, “Note on The Normal Frequency Statistics in Rectangular Rooms,” J. Acoust. Soc. Am., vol. 18, pp. 130–133 (1946).
4. T.Sommerwille, F.L.Ward, ”Investigations of Sound Diffusion in Rooms by means of a Model”,
5. Nimura, Tadamoto and Kimio Shibayama, ”Effect of Splayed Walls of a Room on Steaty-State Sound Transmission Characteristics”, J.Acoust.Soc.Am., 29,1 (January 1957), p85-93.
6. C. L. S. Gilford, “The Acoustic Design of Talk Studios and Listening Rooms, 1959, reprinted in “J. Audio. Eng. Soc., vol. 27, pp. 17–31 (1979 Jan./Feb.).
7. M. R. Schroeder and K. H. Kuttruff, ‘‘On Frequency Response Curves in Rooms. Comparison of Experimental, Theoretical, and Monte Carlo Results for the Average Frequency Spacing between Maxima,’’ J. Acoust. Soc. Am. 34, 76–80 1962.
8. M. M. Louden, “Dimension Ratios of Rectangular Rooms with Good Distribution of Eigentones,” Acustica, vol. 24, pp. 101–104 (1971).
9. C.L.S.Gilford, ”Acoustics for Radio and Television Studios”, (1972), London, Peter Peregrinus Ltd.
10. J.M. van Nieuwland and C.Weber, ”Eigenmodes in Non-Rectangular Reverberation Rooms”, Noise Control Eng., 13, 3 (Nov/Dec 1979), 112-121.
11. O. J. Bonello, “A New Criterion for the Distribution of Normal Room Modes, “J. Audio. Eng. Soc., vol. 29, pp. 597–606 (1981 Sept.); Erratum, ibid., p. 905 (1981 Dec.).
12. R. Walker, “Optimum Dimension Ratios for Small Rooms,” presented of the 100th Convention of the Audio Engineering Society, J. Audio Eng. Soc. (Abstracts), vol. 44, p. 639 (1996 July/Aug.), preprint 4191.
13. R. Walker, “A Controlled-Reflection Listening Room for Multichannel Sound,” Proc. Inst. Acoust. (UK),vol. 20, no. 5, pp. 25–36 (1998).
14. EBU R22-1998, “Listening Conditions for the Assessment of Sound Programme Material,” Tech. Recommendation, European Broadcasting Union (1998).
15. F. A. Everest, ”The Master Handbook of Acoustics”, 4th ed., McGraw-Hill, New York, 2001,
16. T.Cox, P.D’Antonio, M.R.Avis, “Room Sizing and Optimization at Low Frequencies”, J. Audio Eng. Soc., Vol. 52, No. 6, 2004 June. https://www.researchgate.net/profile/Trevor_Cox2/publication/28578741_Room_sizing_and_optimization_at_low_frequencies/links/558131be08aed40dd8cd40e1.pdf
17. M.Skålevik, ”Schroeder Frequency Revisited”, Forum Acusticum 2011, Aalborg.
First published 17.01.2012, latest change 17.01.2012