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Room dimensions for small listening rooms

Methods for choosing correct dimensions

These web pages gives some more detailed numerical results from an Audio Engineering Society journal paper which appeared in June 2004. The journal paper gives more details of the method used and can be downloaded from the AES web site.

Many optimum room ratios have been suggested over the years to minimize coloration. Essentially these methods try to avoid degenerate modes, where multiple modal frequencies fall within a small bandwidth, and the corollary of bandwidths with absences of modes. The starting point for these previous methods is usually the equation defining the modal frequencies within a rigid rectangular enclosure. Often the best dimensions are given in terms of the ratios to the smallest room dimension.

Bolt [1] investigated the average modal spacing to try and achieve evenly spaced modes, but using the average mode spacing is not ideal, and the standard deviation of the mode spacing is a better measure. Ratios of 2:3:5 and 1: 21/3:41/3 (1:1.26:1.59) were suggested, but Bolt also noted that there is a broad area over which the average modal spacing criterion is acceptable. (Note, this later ratio appears to be often rounded to the commonly quoted figures of 1:1.25:1.6).

Gilford [2] discusses a looser methodology whereby the modal frequencies are calculated and listed. The designer then looks for groupings and absences assuming a modal bandwidth of about 20Hz. The dimensions are adjusted and a recalculation is carried out until a satisfactorily even distribution is achieved. This is a cumbersome process. Gilford also states that the 2:3:5 ratio suggested by Bolt is no longer popular and that the axial modes need to be given a stronger weighting in calculations as they cause more problems.

Louden [3] calculated the modal distribution for a large number of room ratios and published a list of preferred dimensions based on the standard deviation of the intermode spacing to achieve evenly spaced modes. The method produces the well known room ratio of 1:1.4:1.9.

Limitations:
• The work is only applicable to rectangular geometries with rigid surfaces.
• Absorption neglected
• All modes (axial, tangential, oblique) treated the same

Standards and recommendations also stipulate good room ratios for activities such as listening tests and broadcasting and recent versions have drawn on work by Walker [4]. Walker states that the aim of the regulations is to avoid the worse cases, rather than to provide proscriptive optimum ratios. Consequently, the recommendations cover a wide range of room proportions.

Room dimensions equations

In addition, it is stipulated that ratios of Lx, Ly and Lz which are within about 5% of integer values should also be avoid. The British Standards Institute and International Electrotechnical Commission give slightly different criteria.

New Method

The new method has been produced based on producing the flattest possible modal frequency response for the room to determine the best room size. It uses a computer algorithm to search for best solutions [5]. Furthermore, the algorithm has been further advanced since reference [5] to look at room dimensions which are robust to changes in room size due to construction tolerances in terms of the room size and the properties of the construction material (the details of the analysis and method have been submitted to the Journal of the Audio Engineering Society..

Previous: Why choose the right room size?

Next: So what are the best room dimensions

Might also be of interest: Another article of studio design, How to design diffusers

[1] R.H.Bolt. Note on the normal frequency statistics in rectangular rooms. J.Acoust.Soc.Am. 18(1) 130-133. (1946).

[2] C.L.S.Gilford. The acoustic design of talk studios and listening rooms. J.Audio.Eng.Soc. 27. 17-31. (1979).

[3] M M Louden. Dimension ratios of rectangular rooms with good distribution of eigentones. Acustica. 24. 101-104 (1971).

[4] R. Walker. Optimum Dimension Ratios for Small Rooms. Preprint 4191. 100th Convention of the AES. (5/1996).

[5] Trevor J Cox and Peter D'Antonio. Determining Optimum Room Dimensions for Critical Listening Environments: A New Methodology. Proc 110th Convention AES. paper 5353 (2000)

 

Trevor Cox's research pages

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