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The myth of generic optimum room dimension ratios

Posted by KlausR. (A) on May 12, 2011 at 07:39:43

In Reply to: Room Dimensions posted by Bardo on May 10, 2011 at 10:43:34:

My standard answer:


In audiophile circles optimum room dimension ratios (height: width: length) such as 2:3:5, 1:1.6:2.5, 1.236:2:3.236 (Golden rule ratio), 1:1.4:1.9 (Louden) are recommended and used, further known are optimization criteria from (Bonello 1981) and (Walker 1996). One of the first to mention room dimension ratios was W.C. Sabine in “Collected papers on acoustics”, Harvard University Press (London) 1922:

“Thus the most definite and often repeated statements are such as the following, that the dimensions of a room should be in the ratio 2 : 3 : 5, or according to some writers 1 : 1 : 2, and others 2 : 3 : 4; it is probable that the basis of these suggestions is the ratios of the harmonic intervals in music, but the connection is untraced and remote. Moreover, such advice is difficult to apply; should one measure the length to the back or to the front of the galleries, to the back or the front of the stage recess? Few rooms have a flat roof, where should the height be measured?”

However, the concept of optimum dimensional ratios was originally conceived for reverberation chambers, where sound fields of mechanical devices are measured. Such devices often produce noise, i.e. the whole audible frequency spectrum, or major parts thereof, simultaneously and all the time. For measuring the sound field microphones are placed all around the device. Since the whole spectrum is constantly emitted, all of the possible room modes are excited all the time. In order to obtain useful readings from all microphones it was important to have a uniform distribution of the resonance mode frequencies on the frequency scale. Somehow this concept has migrated into home audio.

It should further be noted that all formula for the calculation of room modes are based on the assumption that the room is empty, has perfectly reflective walls, and no wall openings. Large absorbing furniture is capable of shifting mode frequencies and lower mode levels (De Melo 2007). Large reflective furniture is capable of splitting up modes, hence generating two modes instead of one (Bork 2005). Wall openings are structural weaknesses and locations of pressure maxima and minima are shifted (Welti 2006, Toole 2008). It has further been shown, that the mode frequencies measured in real rooms may be substantially different from those calculated (Toole 2008, fig.13.8).

In non-rectangular rooms these known “optimization criteria” do not apply anyway, and methods such as Finite Element Methods have to be used (Bolt 1939, Van Nieuwland 1979).

In domestic listening rooms, in order to experience the benefits of optimum ratios, all of the modes must be excited, simultaneously and at equal levels, and the listener must be able to perceive all of them, again simultaneously and at equal levels. This is possible only when source and listener are positioned in corners. Anywhere else not all of the modes are equally energized and are equally audible (Toole 2006). In any randomly selected position of source and listener only some of the modes will be (partially) excited and only some of those excited modes will be heard, so any ratio will be as good (or bad) as any other. None will be optimum.

By looking only at the eigenfrequencies of a room, the relative excitation of each mode by a real source at a particular position in the room is not accounted for. Equally, the sound pressure resulting in a particular listening position, which pressure varies greatly, is not accounted for. For instance, Bonello’s approach is moderately useful with a single source in a corner, and has reduced usefulness when the source is not in a corner (Welti 2009).

All of those optimization methods are hence, inherently, designed to obtain optimum conditions for room corners only. If possible, ratios where one dimension is a multiple of another (square, cube) should be avoided, but even in this case, the result is not necessarily worse (Fazenda 2005, Wankling et al. 2009).

Hence, “the idea of optimum room ratios is irrelevant in our business of sound reproduction” (Toole 2006).

The only possibility to employ the concept of optimum dimensional ratios is to know in advance the exact location of loudspeakers and listener. This in turn means that the benefits of such a ratio are experienced only in one single location in that room. In any other location a listener will experience different bass. For this listener (or listeners) the energy in the corresponding resonances must be attenuated, by absorption, equalization, or mode cancellation by use of multiple subwoofers (Welti 2002). In non-rectangular and asymmetrical rooms additional signal processing in the feeds to the subwoofers is necessary (Welti 2003, 2006).


Bolt, “Normal modes of vibration in room acoustics: experimental investigations in nonrectangular enclosures”, J. of Acoust. Soc. of America 1939, vol. 11, p.184

Bonello, „A new criterion for the distribution of normal room modes“, J. of the Audio Engineering Society 1981, p.597

Bork, „Modal analysis of standing waves (in German)“, Progress of Acoustics, DAGA ’05, 31st Annual Convention of Acoustics. (German Society of Acoustics), Munich 2005

Fazenda et al., “Perception of modal distribution metrics in critical listening spaces - Dependence on room aspect ratios”, J. of Audio Engineering Society 2005, p.1128
¬
Louden, „Dimension-ratios of rectangular rooms with good distribution of eigentones”, Acustica 1971, vol. 24, S.103

De Melo et al., “Sound absorption at low frequencies: room contents as obstacles”, J. of Building Acoustics 2007, vol. 14, no. 2, p.143

Toole, “Loudspeakers and rooms for sound reproduction – a scientific review”, J. of
the Audio Engineering Society 2006, p.451

Toole, „Sound reproduction - Loudspeakers and rooms”, Focal Press 2008

Van Nieuwland , “Eigenmodes in non-rectangular reverberation rooms”, Noise control engineering 1979, Nov., p.112

Walker, “Optimum dimension ratios for small rooms”, Audio Eng. Soc. preprint 4191 (1996)

Wankling et al., “Subjective validity of figures of merit for room aspect ratio designs”, Audio Eng. Soc. Preprint 7746 (2009)

Welti, “How many subwoofers are enough”, Audio Eng. Soc. preprint 5602 (2002)

Welti, “In-room low frequency optimization”, Audio Eng. Soc. preprint 5942 (2003)

Welti, “Low-frequency optimization using multiple subwoofers”, J. of Audio Eng. Soc. 2006, p.347

Welti, „Investigation of Bonello criterion for use in small room acoustics“, Audio Eng. Soc. Preprint 7849 (2009)


Klaus

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