Many methods and optimum room ratios have been suggested over the years to minimise coloration. Essentially these methods try to avoid degenerate modes, where multiple modal frequencies fall within a small bandwidth, and also bandwidths with absences of modes. The assumption being that as music is played in the rooms, the absence or boosting of certain tonal elements will detract from the audio quality. The starting point for these previous methods to determine room dimensions, is usually the equation defining the eigenfrequencies within a rigid rectangular enclosure:

(1)

Where nx, ny and nz are integers and Lx, Ly and Lz the length, width and height of the room. Often the best dimensions are given in terms of the ratios to the smallest room dimension. Previous methods for determining room ratios differ, however, in how they utilize Equation (1).

Bolt produced design charts that enabled him to determine good room ratios. His method investigated the average modal spacing to try and achieve evenly spaced modes; the assumption being that if the modal frequencies are evenly spaced, then there will fewer problems with peaks and dips in the modal response. It is now known, however, that 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) are suggested, but Bolt also notes that there is a broad area over which the average modal spacing criterion is acceptable. (Note, this later ratio is often rounded to the commonly quoted figures of 1:1.25:1.6).

Gilford 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 to undertake by hand, but this type of iterative search is easily accomplished using modern computers using numerical optimisation techniques. It is this type of computer controlled optimisation that is set out below as a method for choosing room dimensions. Furthermore, in addition to the use of numerical optimisation to ease the burden of searching, a better basis than modal spacing for evaluating the effects of modes will be detailed. Gilford also states that the 2:3:5 ratio suggested by Bolt is no longer popular and that the axial modes cause the major difficulty in rooms.

Louden calculated the modal distribution for a large number of room ratios and published a list of preferred dimensions based on a single figure of merit. The figure of merit used to judge room ratios is the standard deviation of the intermode spacing, so again this is a regime to achieve evenly spaced modes. The method produces the well known room ratio of 1:1.4:1.9. Louden undertook the investigation by examining 125 combinations of room ratios at a spacing of 0.1. This type of discretized search can limit the potential solutions found. With the optimised techniques developed since Louden published his work, such as the one used below, the search for the best ratios can be undertaken in a more intelligent manner without the need to artificially discretize the ratios tested.

Bonello developed a criterion based on the fact that the modal density should never decrease when going from one third octave band to the next highest band in frequency. Modes with coincidental frequencies are only tolerated in one-third octave bands with five or more modes present. Bonello compares his criterion against others used by Knudsen, Olson and Bolt. Justification for his methodology is drawn from his experience as a consultant in 35 rooms.

Walker develops a low-frequency figure of merit based on the modal frequency spacing. The method leads to a range of practical, near-optimum room shapes. Walker discusses how blind application of optimum room ratios does not necessarily lead to the best room, because room quality is volume dependent. The Room Sizer does not use generalized room ratios, and so avoids this problem.

All the above methods have limitations. Equation (1) is only applicable for rigid surfaces. Absorption has a number of effects, for instance it shifts the eigenfrequencies. This is critical for evaluation criteria, as is the case of all the above methods, which examine the modal frequencies or spacing of modes. The new method set out below uses a theoretical model, which although not perfect, is a more accurate model of low frequency room behaviour than Equation (1). Another effect of absorption is that it acts differently on axial, tangential and oblique modes - for example, axial modes will have the greatest magnitude and least damping. None of the above methods account for this fully unlike the new method given below, although Gilford, for example, does discuss the prominence of axial modes. A further difficulty with the above methods is the choice of criterion used for evaluation. For example, Bonello's method makes several assumptions - such as the use of a one-third octave bandwidth, and that five modes in a bandwidth mask the effects of coincident modes - which are empirical rather than fundamental in nature. The new method outlined below acts directly on the modal response of the room, so a criterion based on mode spacing is no longer required. Although an evaluation criterion is still required, as this can be based on the modal response of the room, it is much easier to relate to human perception. This is because the mode spacing is one level more removed from the actual signals received by the listener than the modal response.

Standards and recommendations also stipulate good room ratios for activities such as listening tests and broadcasting. European Broadcasting Union recommendations are discussed by Walker. Walker states that the aim of the regulations appears to be to avoid the worse cases, rather than to provide proscriptive optimum ratios. Consequently, the recommendations cover a wide range of room proportions.

(2)

(3)

(4)

In addition, it is stipulated that ratios of Lx, Ly and Lz which are within ±5% of integer values should also be avoided.

The British Standards Institute and International Electrotechnical Commission give slightly different criteria for Equation (2):

(5)

The criteria given by Equation (3) and (4) are also stipulated along with recommended floor areas. A recommended room size of 7 x 5.3 x 2.7m (2.59:1.96:1) is given. Older versions of the standard give different recommendations, with a standard room of 6.7 x 4.2 x 2.8m (1.59:1.5:1). These values are also reported in a popular textbook.