Across Acoustics

Preferred dimension ratios of small rectangular rooms

June 30, 2021 ASA Publications' Office Season 1 Episode 6
Across Acoustics
Preferred dimension ratios of small rectangular rooms
Show Notes Transcript

Preferred dimension ratios of small rectangular rooms

JASA Express Letters 1, 021601 (2021); https://doi.org/10.1121/10.0003450

Author: Jens Holger Rindel

 

How do the acoustics of a small room—such as one used for music rehearsal, sound studios, or control rooms—differ from those of larger rooms? In this episode, we interview Jens Holger Rindel of Odeon A/S about the best way to design small rooms for acoustic performance. 

JASA Express Letters page

 Acoustical Society of America Publications page

 Music: Min 2019 by minwbu from Pixabay. https://pixabay.com/?utm_source=link-attribution&utm_medium=referral&utm_campaign=music&utm_content=1022

SUMMARY KEYWORDS

acoustics, golden ratio, room, acoustical, aspect ratios, concert halls, height, sound, rehearsal rooms, frequency, ratio, distance, low frequencies, dimensions, frequency response, musical instrument, wavelength, frequency spacing index, timbre, tonal coloration, length, width

 

Kat Setzer (KS)

00:06

Welcome to Across Acoustics, the official podcast of the Acoustical Society of America’s Publications office. On this podcast, we will highlight research from our four publications: The Journal of the Acoustical Society of America, also known as JASA. JASA Express letters, Proceedings of Meetings on Acoustics, also known as POMA, and Acoustics Today. I'm your host, Kat Setzer, editorial associate for the ASA.

 

KS

00:39

Joining me today is Jens Rindel from Odeon. We'll be discussing his article, “Preferred dimension ratios of smaller rectangular rooms,” which appeared in the February 2021 issue of JASA Express Letters. Thank you for taking the time to talk with me today, Jens. How are you doing?

 

Jens Rindel (JR)

00:55

Thank you. I'm doing well. Thank you for having me. 

 

KS

So first, tell us a little bit about yourself. 

 

JR

Well, I first studied engineering, building technology and acoustics, at the Technical University of Denmark. And after my PhD, I continued teaching and doing research at the same university for more than 30 years. This was interrupted by periods as a visiting professor at universities of Australia and New Zealand and in Japan. Among my research projects was the development of an efficient computer model for room acoustic simulations. This has led to the software called Odeon, and in 2008, I left the university and established the company Odeon as an independent corporation. I also do some consultancy work. And I worked with acoustical refurbishment of concert halls like the Alberta Jubilee Halls, which are two nearly identical concert halls in Canada. For many years, I've been active in developing standards for ISO related to architectural acoustics. And the article that I'm talking about today is closely related to the work with an ISO standard for music rehearsal rooms. And a final draft of the standard is currently out for voting. By the way, talking about music, I could mention that I play the flute and I have experience from playing in symphony orchestras and in small music groups.

 

KS

02:53

That's great. Thank you. So to start out, what are the kinds of acoustical properties you look for in rooms used for music, speech, or acoustical measurements?

 

JR

03:04

Well, an acoustically good room should carry and support sound, without any disturbing or audible effects. So that implies that the sound should be supported equally well over the frequency range covered by the sound source. The response of the room is the sound pressure, or how loud the sound is, measured with a tone that sweeps slowly from low to high frequencies. The result is the frequency response, and this should be as smooth as possible. But the volume or reverberation time are also important properties for how well the sound is received and supported by the room. The reverberation time is a measure of how long the sound can be heard in a room after the sound source has stopped. The optimum reverberation time depends on the purpose of the room. Some kinds of music and singing require relatively long reverberation times, and rooms for speech, and especially talk studios, should have short reverberation times. Disturbing audible effects… Well, an example of that could be the so called “boxiness” which appears in smaller rooms when the reverberation time is too long at the low frequencies.

 

KS

04:30

Okay, that is very interesting. A lot of times people talk about the golden ratio in room acoustics, and shoe box concert halls. What are those?

 

JR

04:40

Well, let's begin with the golden ratio. It's known from art and architecture. If you divide a line into two sections according to the golden ratio, the ratio of the smaller to the larger section is the same as the ratio of the larger section to the whole line. Mathematically, the golden line, the golden ratio, is approximately 1.62. An example is that we have in the human proportions, as was suggested by the ancient Roman architect Vitruvius. So, this was illustrated later on. In the famous drawing by Leonardo da Vinci, is showing, shows that the height of a standing person is divided into Golden Ratio by the person’s belly button.

 

KS

That's interesting.

 

JR

In acoustics, it’s often mentioned in connection to room dimension ratios. However, as showed in my article, the golden ratio is not particularly good for small rooms and cannot be recommended. There's no scientific background supporting the use of the golden ratio in acoustics. But some people think that acoustics is not science, but an art, with a lot of mysticism, and that the golden ratio is this universal law. Then about the shoe box concert hall. Well, this is a hall that basically has the shape of a rectangular cuboid. However, my article deals with small rooms only, and the upper limit I have suggested is 300 cubic meters. So concert halls are much bigger, and my findings for preferred dimension ratios do not apply to concert halls.

 

KS

06:43

Okay, got it. So what are room modes and how do they relate to normal modes? How does sound frequency relate to room modes?

 

JR

06:51

Room modes or normal modes are the same. And sound. Let's start to say that sound is an invisible wave in the air. And the wavelength of this wave is the speed of sound divided by the frequency. Since the speed of sound is around 340 meters per second, the wavelength of for example, 100 hertz sound is 3.4 meters. However, half the wavelength is more important for what happens in the room. So if the distance between two walls is half the wavelength of the sound, this will be the fundamental normal mode. Then the sound level varies, being very loud near the walls and reaching a minimum in the middle, between the walls. I've experienced a small dining room, which was 3.4 meters wide. And behind one of the walls, there was installed an electric refrigerator that generates a 50 hertz tone. This is common for electric equipment in Europe. In the US, I think it's 60 hertz. However, then this 50 hertz tone coincides with the fundamental normal mode for the dining room, having the width of 3.4 meters. So for those sitting close to the walls, the noise was very disturbing. Now those sitting in the middle of the room, they couldn't hear the noise at all. 

 

KS

That's so interesting. 

 

JR

So in this case, the distance between the walls match half the wavelength of the sound. And we call that the fundamental mode in the series of one-dimensional modes, where the distance matches a whole multiple of the half wavelength. So each of the corresponding frequencies is a natural number times the fundamental frequency. So for this room, we would have the series of 50 hertz, 100, 150, 200, etc, etc. In a room, there are normally three such series related to each of the three main dimensions of the room. In addition to that, there are two-dimensional modes involving four surfaces of a room, and there are three-dimensional modes involving all six surfaces. This means that the room modes are few and clearly separated at low frequencies. But the number of modes increases rapidly at higher frequencies.

 

KS

09:37

Tell us about room aspect ratios with regards to acoustics. How have they been viewed in previous research?

 

JR

09:44

Well since 1940s, the aspect ratios have been studied basically in two different ways, either by analyzing frequency distribution of the room modes, or by analyzing the shape of the transfer function. In all previous research, the aspect ratios have been displayed relative to the shorter dimension, which is normally the height. So, results have been displayed as function of width divided by height and length divided by height.

 

KS

10:17

How did you use aspect ratios differently in this study?

 

JR

10:21

In this study, I realized that it would be much better to use the aspect ratio of the two larger dimensions as one parameter and then the aspect ratio of the two smaller dimensions as the second parameter. Then it becomes clear that the first aspect ratio is of decisive importance, while the second aspect ratio is of minor importance. And I think this observation is new. If we can assume that the room height is the smaller dimension of the room, then the important aspect ratio is the length to width.

 

KS

11:01

Okay, what is coupling between a musical instrument and a room?

 

JR

11:06

Yeah, this maybe not so easy to explain. but just recently, I bought myself an electric bike. I don't know if you are familiar with how it works. 

 

KS

Oh, yes.

 

JR

You need to use your legs as on a normal bike. But a motor will add power and makes it much easier to run the bike. Playing a musical instrument is like using your muscles to run the bike. The acoustics of the room are like the electric motor assisting you. So in combination, you feel much stronger and can go up hill with less effort. Similarly, when the musical instrument is coupled with a good room, you can better master the music, the dynamic range is increased ,and you have greater freedom in the musical expression. On the other side, playing in a room with poor acoustics and little support makes you feel like going uphill without any assisting motor.

 

KS

12:13

Okay, that's really interesting. What is this frequency spacing index and how does it relate to a room's acoustical properties?

 

JR

12:22

Yes, I use this frequency spacing index for my article, and to explain it, I would think of a long telephone cable, you know, as used before the age of the modern cell phone. The cable is supported by a row of poles and thus, they cable exhibits a shape that peaks at every pole. The frequency response of the room is analog to the cable, and the poles correspond to the room modes. Then cable spans, the cable spans over a distance, which represents the frequency range from 20 hertz to 200 hertz, in my case, and the height of the cable represents sound level. The poles are then positioned at the frequencies of the room modes, and the frequency interval between the room modes corresponds to the distance between the poles. So, imagine in a square room many modes coincide at the same frequency. So, this would correspond to many of the poles being in the same position, and consequently there will be longer distances between poles or groups of poles. And this leads to greater variation in the height of the telephone line compared to the situation where the distance between the poles is more evenly distributed. The frequency spacing index, as I used it, is the variance of the distances between the room modes or the poles. The variance is the sum of the distances squared. So aiming at a low frequency spacing index ensures that the space is as evenly distributed as possible. In the article it’s shown that using the frequency spacing index as a criteria gives very similar results, as with more complicated methods that use the smoothness of the frequency response.

 

KS

14:30

Okay, interesting. So after your study, what conclusions were you able to make about the effect a small room’s dimensions have on its acoustical properties?

 

JR

14:41

The conclusion is that the aspect ratio of length to width should be within a relatively narrow range, whereas the width to height ratio can be chosen more freely, without compromising the acoustic quality. This will ensure that the frequency response is relatively smooth. During my work with this idea, I had a meeting in the ISO working group that I mentioned in the beginning. The convener of the working group is a musician who has gathered information about hundreds of music rehearsal rooms, and from his experience, the length-to-width ratio should not exceed 1.6. When he suggested that, I looked into my calculations, and in fact, his experience was confirmed; the aspect ratio should not exceed 1.6. And by the way, the golden ratio that we talked about before is 1.62, and just outside the range.

 

KS

15:48

That's funny. How do you recommend applying these findings to room design?

 

JR

15:53

My recommendation comes in various versions depending on how serious the acoustic quality must be taken. Three very good aspect ratios have been identified. And the very best results are obtained by choosing one of these, but that can be very full of constraints for practical use, so in most cases, I believe it is sufficient to choose the length-to-width ratio between 1.15 and 1.45. This should work fine for music studios and rehearsal rooms. If the concern is merely to avoid acoustical problems, a more relaxed recommendation is to choose a length-to-width ratio between 1.1 and 1.6. However, even if we can select the room heights quite freely, the height still needs a careful consideration in a music rehearsal room. If the sound is reflected from the ceiling with a very short delay, tonal coloration of the sound can appear. Tonal coloration means that certain frequencies are exaggerated, and provides the sound with an artificial, not natural, timbre. So the height must be sufficient to avoid tonal coloration. In a rehearsal room for a group of instruments or singers, a sufficient height is also important for a good blend of the sound. 

 

KS

Okay, do you have any closing thoughts? 

 

JR

Well, I think it's interesting that the most obvious and useful conclusions from the article come from rearranging the aspect ratios. Using the traditional way of displaying the results obscures how important the ratio between the larger dimensions, length and width, is. So this shows that finding a better way to display your results can be essential. These days, there's a lot of research that relies on advanced mathematical tools, and that's fine. But the risk can be that the researcher does not spend sufficient time to think about the context of the problem or the meaning of the results or to search for simplifications of the problem. Among the vast number of papers dealing with room aspect ratios, there are examples where the final recommendation would lead to unrealistic low rooms in which you can hardly stand upright.

 

KS

18:52

That is a very interesting point. Thank you for again for taking the time to talk to us. It's been great having you on the show. I think our listeners will be really interested in what you had to say. 

 

JR

Thank you for having me. 

 

KS

Thank you for tuning into Across Acoustics. If you'd like to hear more interviews from our authors about their research, please subscribe and find us on your preferred podcast platform.