Modes in small rooms often lead to extended sound decays and uneven frequency responses. In critical listening spaces, this causes unwanted coloration effects that can be detrimental to the sound quality. The problem arises at low frequencies because of the relatively low modal density. Many designers try to overcome the problems of modes by choosing an appropriately proportioned room and by the use of bass absorbers. This paper is interested in the former, the choice of room dimensions to minimise the coloration effects of modes. The paper starts by discussing previous studies by others, which have suggested optimum room ratios or design methodologies. Then a new method is outlined - this is based on numerical optimisation - and the old and new methods are compared philosophically. Results in the form of modal responses are given to demonstrate the power of the new method.

Problem
Many methods and 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 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. All the above methods have limitations. The eigenfrequency solution 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.

Solution
RPGŪ is now offering a new approach that automatically determines optimal room dimensions in rectangular rooms given an absorption coefficient for each surface and a minimum and maximum dimensional range for the length, width and height. The new method (Read more) uses a theoretical model, which although not perfect, is a more accurate model of low frequency room behavior than the simple eigenfrequency solution. 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 previous methods account for this fully. A further difficulty with previous 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 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. The new method is based on producing the flattest possible modal frequency response for the room. It uses an optimizing computer algorithm to search for the best solutions.

Full screen view showing Room view, Optimization data, Frequency responses and Error parameter progress graph.

Detailed view of Error parameter progress graph, showing bad guesses (peaks) and good guesses (valleys) during the automated intelligent search for optimal dimensions. Two solutions, with confirmations, are shown.

The Room Sizer allows for the use of electronic equalization. If electronic equalization is planned the user will instruct the program to minimize all valleys in the modal response at the expense of peaks, which can be electronically attenuated.

The worst, best and current modal responses are shown, along with predictions of the wall surfaces involved.

Screen view illustrating minimum and maximum entry menu for length, width and height.