The myth of generic optimum room dimension ratios

Dec 13, 2010
253
1
18
#1
Hi all,

in 2012 in a thread relating to room dimension ratios Amir said:

There are no good dimensions per-se. Much if not all of the research there was relative to one speaker/position, one listening position, and ideal rectangular rooms. Change those assumptions and you invalidate them.

From Dr. Toole:

"None of this is wrong [research into magic dimensions], but, in sound reproduction, it is irrelevant!

I thought I’d expand a little bit on that, so here’s a short piece I’ve prepared some time ago.

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 rooms, 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 (Toole 2006).

It should further be noted that all formulas for the calculation of room mode frequencies 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).

The goal of all of these optimization methods is to arrange all of the modes evenly on the frequency axis. Therefore, 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). When playing music, 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. In my own listening room the modes are well audible at the listening position when playing pure sine tones, With music I have so far detected only three tracks where the second order width mode is, at the listening position, audibly excited. Hence, in my room of the 25 calculated modes below the Schroeder-frequency (because of the acoustical ceiling I’m not counting the tangential and oblique modes where the ceiling is involved) only 1 is actually disturbingly excited when playing music.

In listening tests using music samples Fazenda (2005) found: “A room that scores highly on a certain metric may still suffer from problems, since the detection cue is one of stimulus–room interaction rather than one of room response per se. The modification of modal distributions by the manipulation of room aspect ratios is therefore shown to be of doubtful utility in the reduction of the unwanted subjective effects of room resonances. Controlling the problems of room modes by the consideration of expressly degenerate modal superpositions may still be regarded as appropriate at a design stage. However, the results presented here clearly suggest that overly zealous considerations of the modal distribution are likely to be rather peripheral to subjective room performance.”

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).

“So it is not that the idea of optimum room ratios is wrong, it is simply that, as originally conceived, it 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).

In a conference paper from 1990 Toole says: „It has long been puzzling that music and speech can sound as natural as they do in rooms that are horrendously flawed by numerous resonances. The explanation seems to be that room modes are generally medium- to high-Q phenomena. In steady-state measurements, such as these, modes are very much in evidence. However, when excited by the sounds of speech and music, which are mostly transient or discontinuous events, they are not always as apparent to the ear as the measurements suggest.”



References

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 stereophonic sound reproduction”, Audio Engineering Society 8th International Conference 1990: The Sound of Audio

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)
 

FrantzM

Member Sponsor & WBF Founding Member
Apr 20, 2010
6,469
0
0
#2
Hi

Excellent well researched post. I had an intuition to that but this anchor my point of view. Thanks.
 
Last edited:
May 30, 2010
13,968
42
48
Portugal
#3
Analysis of room dimensions is mostly a question of common sense , together with some knowledge of acoustics - it can help you trace existing problems and if you are lucky enough and you have one room that pleases one of the several different criteria you pick this one as the best existing work in acoustics and create a big expectation bias in your room! ;)

The big issue is not the calculus - existing computing power could simulate with large accuracy and resolution the response of all small rooms with small pitch. The main question is what defines a good small room. There are always compromises and the way we weight them will return very different results. As you say, Toole considers that the importance of room dimensions are overestimated. In part perhaps because his perspective is mainly focused on home theater systems, that most of us accept have different bass requirements from stereo listening.

The optimum dimensions have cost me some trouble and money. My listening space was originally a long room - length is more than twice the width. When I found that building a wall could separate it in a room having the golden rule ratio dimensions and a good independent stowage space I decided to have it built. It was a disastrous decision, only corrected a few months later by removing it ...
 

JackD201

[WBF Founding Member]
Apr 21, 2010
10,994
8
38
Manila, Philippines
#4
It is over estimated, without a doubt because the construction is just as important. I wouldn't go as far as saying however that they are irrelevant. From a cost perspective, starting off with good dimensions makes the job of the acoustician much easier. Perhaps Toole was referring to very small rooms and systems with more typical bandwidth. Half wave will trump quarter wave. I don't think that there will be any debate about that. If he's saying, any dimension can be dealt with rendering the ratios irrelevant, in an absolute sense that may be true. It does not mean however that it will be just as easy.
 

Bruce B

WBF Founding Member, Pro Audio Production Member
Apr 26, 2010
6,569
5
38
Seattle, WA
www.pugetsoundstudios.com
#5
I don't think it's completely irrelevent. What if you have a cube room... 10' x 10' x 10' Wouldn't that not work at all?

So if you know the speaker/listener location and could build a room around it, wouldn't the inverse be true? You could take the dimensions of the room and know exactly where the speakers/listener "should" be? Where's the calculation for that?
 

JackD201

[WBF Founding Member]
Apr 21, 2010
10,994
8
38
Manila, Philippines
#6
I don't think it's completely irrelevent. What if you have a cube room... 10' x 10' x 10' Wouldn't that not work at all?

So if you know the speaker/listener location and could build a room around it, wouldn't the inverse be true? You could take the dimensions of the room and know exactly where the speakers/listener "should" be? Where's the calculation for that?
How does one deal with a cube? Build into it so it's no longer a cube. Sounds like a joke but it isn't. Perfect example Bruce.
 
Jul 8, 2010
1,232
0
0
70
New Milford, CT
#7
I thought I’d expand a little bit on that, so here’s a short piece I’ve prepared some time ago.
Nice post Klaus. As Bruce explained, room ratios are not irrelevant. But I agree their importance is often overstated. One key point that many overlook is that even with "ideal" dimensions in a suitably large room, you still have flutter echo, peaks and deep nulls, comb filtering, and modal ringing. the notion that a purpose-built room doesn't need bass traps and other acoustic consideration is misguided.

--Ethan
 

FrantzM

Member Sponsor & WBF Founding Member
Apr 20, 2010
6,469
0
0
#8
I don't think it's completely irrelevent. What if you have a cube room... 10' x 10' x 10' Wouldn't that not work at all?

So if you know the speaker/listener location and could build a room around it, wouldn't the inverse be true? You could take the dimensions of the room and know exactly where the speakers/listener "should" be? Where's the calculation for that?
Hi
If you read carefully, this is covered ..
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).
I am reminded of one gary L. Koh installation in a round room. According to Gary it worked. I was skeptical and would always avoid a round or cubic room but ... The other point that is worth mentioning is the position of the listener and the speakers in the room. The nulls and peaks relative positions and levels are also a function of those. You move a sub or add another and the level, distribution and frequencies of the modes change.
 
May 30, 2010
13,968
42
48
Portugal
#9
My relative inexperience in these matters has shown me that one of the biggest problems in small rooms are nulls caused by cancellation due to reflections. I am not aware that the optimum dimensions often referred consider this aspect.
 

garylkoh

WBF Technical Expert (Speakers & Audio Equipment)
#12
Excellent post, Klaus. Thank you for taking the time and effort to research this thoroughly and providing us with the references.

Mods - this should be a sticky IMHO.

I am reminded of one gary L. Koh installation in a round room. According to Gary it worked. I was skeptical and would always avoid a round or cubic room but ... The other point that is worth mentioning is the position of the listener and the speakers in the room. The nulls and peaks relative positions and levels are also a function of those. You move a sub or add another and the level, distribution and frequencies of the modes change.
Yes - I traveled all the way to Morocco to see/hear it for myself. The speakers and seating had to be very carefully positioned, all the calculations was done by the owner of the room. I'm still impressed.

I once had to do a show in a room that was almost perfectly a half-cube. 18 x 18 x 9. And when I asked the dealer for room treatment, all he did was to give me a blank look. It worked perfectly with the system firing along the diagonal.
 
Jul 8, 2010
1,232
0
0
70
New Milford, CT
#13
My relative inexperience in these matters has shown me that one of the biggest problems in small rooms are nulls caused by cancellation due to reflections. I am not aware that the optimum dimensions often referred consider this aspect.
Indeed, nulls are usually the larger problem, except maybe in square and cube shaped rooms. Peaks are typically 6 dB or less, but nulls are often 30 dB deep or even deeper. Further, the worst null is usually due to reflections from the wall behind you. The frequency of that null is related more to your distance from that wall than the room dimensions.

--Ethan
 
Dec 13, 2010
253
1
18
#14
Hi,

First, thanks for all the positive comments.

Toole is referring to small rooms for the purpose of sound reproduction in general. Small means small in comparison to wavelengths at low frequencies (11.3 m at 30 Hz). A Schroeder-frequency of 30 Hz means a room of about 4,400 cbm (RT60=1 s), that’s a room of 30 x 21 x 7 m (1,800 cbm at RT60= 2 s, or 18 x 14 x 7 m).

I can’t quite see how good dimensions make an acoustician’s job easier? The number of mode frequencies doesn’t change, the fact that excitation amplitude depends only on the loudspeakers’ location doesn’t change, the fact that perception amplitude depends only on the listener’s location doesn’t change, the fact that you don’t excite 100% of the modes at the same time when playing music doesn’t change.

Simply stating that room dimension ratios are not irrelevant in our business of sound reproduction is not very convincing I’m afraid, so I would like to see some arguments or evidence.



Bruce B said:
What if you have a cube room?
Wankling et al. said: “It does remain clear however, that basing room ratios upon modal spacing metrics would appear somewhat flawed. It has been shown that predicted 'bad' rooms, such as cubes, may be scored highly by listeners.”

So if you know the speaker/listener location and could build a room around it, wouldn't the inverse be true? You could take the dimensions of the room and know exactly where the speakers/listener "should" be? Where's the calculation for that?
That calculation is given in my piece: when you take the room as a given, the only place where all modes are excited equally strong and perceived equally strong are the corners.

Bolt et al., “Frequency response fluctuations in rooms”, J. of the Acoustical Society of America 1950, vol. 22, no. 2, p.280: “To this point we have required all normal modes to be fully excited and to contribute equally to the room response. In general these conditions are not met, but they are met in the special case of a rectangular room with source and receiver placed at corners within a limiting distance which we can estimate [1/20th wavelength].”

Still, the temporal factor remains: you do not excite, with music program material, 100% of the modes at the same time.

microstrip said:
My relative inexperience in these matters has shown me that one of the biggest problems in small rooms are nulls caused by cancellation due to reflections. I am not aware that the optimum dimensions often referred consider this aspect.
Reflections at room boundaries generate standing waves with stationary locations of amplitude peaks and dips. Since the standing wave always has zero particle displacement at the boundary, the location within the room of these peaks and dips are always the same, regardless of the location of the source. What does change with a change of source location is the amplitude of these peaks and dips. The amplitude also changes with a change in material of which the boundary is made. Perfect cancellation is only possible when there is a perfect reflection, in all other cases the standing wave amplitude has no true null at a dip location but only a minimum.

Optimum dimension concepts exclusively consider the frequencies, not the amplitudes at dip and peak locations. On a sidebar, humans do not hear loudness in terms of dB SPL so looking at these only is somewhat uselesss. A factor 4 on the dB SPL scale can become less than 1.5 when converted to Sone, which is the linear scale of how humans perceive loudness. After all, it’s about what we hear not about what we measure.


Klaus
 
Jul 8, 2010
1,232
0
0
70
New Milford, CT
#15
I can’t quite see how good dimensions make an acoustician’s job easier? The number of mode frequencies doesn’t change, the fact that excitation amplitude depends only on the loudspeakers’ location doesn’t change, the fact that perception amplitude depends only on the listener’s location doesn’t change, the fact that you don’t excite 100% of the modes at the same time when playing music doesn’t change. Simply stating that room dimension ratios are not irrelevant in our business of sound reproduction is not very convincing I’m afraid, so I would like to see some arguments or evidence.
The number of mode frequency doesn't change, but their proximity to one another certainly does. When a room has modes that are more or less evenly spaced, each creates a peak of about 6 dB that decays over some amount of time. But in a square room, say 10 by 10 feet, each mode creates twice the energy increasing the peak response and extending the decay times even more. In a cube shaped room the problem is worse still. That's why my Graphical Mode Calculator has a graphical display. So you can see how nearby modes combine to be worse than modes that are spaced farther apart. This is the main reason for wanting a "good" ratio.

--Ethan
 
Dec 13, 2010
253
1
18
#16
Ethan Winer said:
The number of mode frequency doesn't change, but their proximity to one another certainly does.
Gilford states that “in practice the minimum separation for audibility appears to be about 20 Hz.”

Fazenda et al. have found that for two test tones the optimal spacing is 25-40% of the modal bandwidth. However, the authors conclude: “Finally, these results open up further research avenues. For example, will the masking effects of a musical stimulus cause a difference in result, or will the same detection of the shortest decay and onset of beats remain? Further work currently being undertaken also looks at the effects of multiple modes rather than the simple pair used in this test.”



When a room has modes that are more or less evenly spaced, each creates a peak of about 6 dB that decays over some amount of time. But in a square room, say 10 by 10 feet, each mode creates twice the energy increasing the peak response and extending the decay times even more.
If I put the listener halfway between the walls he will not hear the first order modes. If I put the source halfway between the walls it will not excite those first order modes. So in order to obtain twice the mode energy the source has to be placed such that both modes are driven equally strong.

In a cube shaped room the problem is worse still.
Wankling, once more:” Finally, it is interesting to compare the results between the samples in the three test rooms [A: cuboid; B: Louden ratio; C: Louden ratio, different source position]. It becomes apparent that the subjects have not rated those cases in the 'bad' cubic room as particularly worst than cases in the best Louden ratio room.”

That's why my Graphical Mode Calculator has a graphical display. So you can see how nearby modes combine to be worse than modes that are spaced farther apart. This is the main reason for wanting a "good" ratio.

That in itself could be considered as a valid reason. But, how do you define "nearby"? What's the bandwidth of modes, is this bandwidth a strict limit, meaning that every neighboring mode within this limit is excited and every mode outside is not?

Directly neighboring axial modes don't travel in the same directions, so what happens when two nearby modes at 37 and 41 Hz are (0,1,0) and (2,0,0,)? When the first is excited fully, what happens to the other? Will it be fully excited or only partially? When the first is only partially excited, what happens to the other? When the first mode is not excited at all, what happens to the other? For these two modes, when I place the source against the front wall, and ¼ length distance from the side wall, it will be in the pressure maximum of the 37 Hz mode and in a pressure minimum of the 41 Hz mode. Will the 41 Hz mode be excited?

The next question is, how long does the duration of a signal need to be to excite a mode? If the bass guitar plays DO-RE-MI-FA-SO-LA-TI-DO quickly, and FA is at a mode frequency, is that mode excited?

Now say you’ve got this room with evenly spaced modes. How many of these modes do you drive at the same time? One? Two? Three? Five? None? When it’s three, if one is driven at 100% strength, the second at 50%, the third at 20%, what’s the use to have them evenly spaced? If one is at 25 Hz, the 2nd at 50 Hz, the 3rd at 100 Hz, what’s the use to have them evenly spaced? If only one mode is driven, what’s the use to have the others evenly spaced? What is the trick to drive several neighboring modes equally strong and at the same time, when playing music???

The above example with modes at 37 and 41 Hz is from my own room. The speakers are placed without any consideration to room acoustics whatsoever. Do these neighboring modes pose a problem? No, they don’t, with music I have managed to excite the (0,2,0) mode audibly disturbing at listening position.

Klaus

Gilford, “The acoustic design of talk studios and listening rooms”, J. of the Audio Engineering Society 1979, p.17

Fazenda et al., “Optimal modal spacing and density for critical listening”, Audio Engineering Society Preprint 7584 (2008)
 

FrantzM

Member Sponsor & WBF Founding Member
Apr 20, 2010
6,469
0
0
#17
Shouldn't we make of this thread a sticky?
 
May 30, 2010
13,968
42
48
Portugal
#18
Shouldn't we make of this thread a sticky?
Why a sticky? Just one more thread that concludes that acoustic of small rooms is mainly a question of luck or empirical expertise?
That the few people who have done it scientifically have proprietary tools that they do not want to share for free with WBF members? ;)
 

FrantzM

Member Sponsor & WBF Founding Member
Apr 20, 2010
6,469
0
0
#19
microstrip

Is that what you get from the thread that is "mainly" a question of luck?
 
May 30, 2010
13,968
42
48
Portugal
#20
microstrip

Is that what you get from the thread that is "mainly" a question of luck?
Frantz,

If you have a better summary than mine please post it. BTW I said "mainly a question of luck or empirical expertise" Please do not separate.
 
Last edited:

About us

  • Founded in 2010 What's Best Forum invites intelligent and courteous people of all interests and backgrounds to describe and discuss the best of everything. From beginners to life-long hobbyists to industry professionals we enjoy learning about new things and meeting new people and participating in spirited debates.

Quick Navigation

User Menu

Steve Williams
Site Founder | Site Owner | Administrator
Ron Resnick
Site Co-Owner | Administrator
Julian (The Fixer)
Website Build | Marketing Managersing