Room Dimensions and Volume

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Room Dimensions and Volume

Postby avare » Tue Aug 17, 2004 3:27 pm

This started on another site, but the direction I am taking the discussion in is more in the style of this site.

Over on RSD there is thread where Thomas Barefoot referenced a paper in the June 2004 AES journal regarding "critical listening environment" optimum ratios and their varying with room size.

http://www.johnlsayers.com/phpBB2/viewtopic.php?t=2078

I had posted asking about the similarities in results to Walker's paper

http://www.bbc.co.uk/rd/pubs/reports/1993-08.pdf

Eric posted on it and gave a link to Salford pages giving additional information about the paper and spreadsheets of optimum and almost optimum ratios for rooms of three sizes (50, 100, and 200m^3).

http://www.acoustics.salford.ac.uk/acoustics_world/room_sizer/room_sizing.htm

The paper is an evolution of the work detailed in

http://www.rpginc.com/cgi-bin/byteserver.pl/news/library/roomsizer.pdf


I have not read the latest paper. Everything written here is based on the above referenced documents and my personal knowledge. Many of the ambiguities I have may be addressed in the AES journal. There may also be several points that have changed between the RPG and AES paper. Note that both papers are published by AES, but I am using those terms to simplify. I will also refer to data from the University of Salford links as "Salford."

The AES paper describes optimum room ratio determination by using the standard deviation of the room response in dB from the least squares line fit as the quality metric. The room response calculations include the absorption of the walls. The new items since the RPG paper are the inclusion of additional data for wall construction performance and sensitivity analysis for construction variances.

The frequency range used in the analysis is 20 to 200 Hz. As detailed in the RPG paper this was a somewhat arbitrary choice. The Schroeder Frequency or any other upper limit could just as appropriately be used.

The significance of the above point apparent with a bit of thought. On a purely acoustical basis, the lowest mode will reduce in frequency as the room size increases, and the number of modes up to a constant frequency will increase. With the quality criteria being the evenness in response it to be expected that as the room size varies that the optimum ratios would also. Having just written that, the Salford pages detail several ratios that are optimum across the room volumes analyzed. I would suspect that the ratios would also change with the wall absorption.

Practically, I don't see this as significant as it first appears. The ratios of room sizes covered is 4:1. In most case the approximate volume is determined by other factors and then we fine tune the ratios to that size. We would not design a 50m^3 with ratios near 1:2.2:3.1 because of the low ceiling height. Similarly a 200m^3 room near 1:1.2:1.4 because of the "wasted" ceiling height. If designing a "serious" listening room, there are many current standards to follow, and those can fine tuned to improve. If a room is being professionally designed, then the checking and calculating of room ratios would be a matter of course. Also, in most of our area of interest, the room volume is smaller and constrained by already built spaces that are smaller.

Both the Salford and RPG documents reference Walker and (rightly) note that the derived standards are to help avoid bad ratios, as opposed to prescribing optimum ratios. (Walker uses the same modeling criteria, flat room response. but does not include the metric of minimum deviation from least squares fit). The standards include a qualification that the terms should not be integers or within 5% of being integers. Inspecting the 254 optimum ratios for a 50m^3, there are 8 with integer ratios between the height and length, and 84 within 5%. I did not do a detailed study of width to length ratios, but some stood out. For example row 63 1:1.45:1.45 and row 64 1:145:1.46. In other words over a third of the ratios detailed in the optimum ratios spreadsheet do not meet the criteria specified by Walker for avoided bad ratios.

Overall I feel that the RPG and Salford papers are useful for knowledgeable people and are the bleeding, oops leading, edge of listening room acoustics. To make blanket statements with out understanding all of the factors is incredibly misleading.

Any properly spelled words and clear sentences are accidental.
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Postby Savant » Tue Aug 17, 2004 10:30 pm

Andre,

Is there a question? :)

Kidding and volume dependence aside, the practical reality for many amateur studio builders is they have a finite area (and volume) in which to construct their studio. So what's "ideal" in terms of a ratio for their volume is often impractical for their space.

E.g., they have 1600 ft³ to work with, but only an 8' height.

Based on this common limitation, I decided to reread the old papers to see what, exactly, was up. After about 13 months of work (and counting), here's a preview:
Taking the height as the limiting factor, I've used Louden/Bolt and Bonello algorithms and criteria to come up with a short list of room dimensions. IMO, this makes a lot more sense, practically, then ideal ratios.

(Note: I promise to elaborate more on this in the winter... :mrgreen: ...always keep 'em wanting more... :mrgreen: )

FWIW.
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Postby Andrew Steel » Tue Aug 17, 2004 10:39 pm

Hi avare,
I have been reading the same stuff and have the same impression. What I do wonder is does anyone temper the search with information on how audible or problematic modes are to humans as they get lower/ more less densely spread etc. I know one person at Genelec is doing his PhD in this area. In other words, if for example humans can't differentiate between one and two modes in the first octave, why include them in the optimisation etc? You would presume human perception is involved somewhere in making decisions like using std, dev, rather than simple distribution? Are these optimisations based on listening or just more algorithms? If not, how are they arrived at?

just my thoughts
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Postby bert stoltenborg » Tue Aug 17, 2004 11:24 pm

Good one, Jeff.

I thought something like that reading this article about ratio's:
Try to tell somebody with a not to big room, or any room, he has to lower his ceiling because of the room ratio. That could be a hard struggle. :D

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Postby avare » Tue Aug 17, 2004 11:36 pm

Thanks jeff.

No question, just a summary of what I have read and understand on that issue. As you and everyone else wrote, practicality is the dominant factor. Echoing what I wrote about limiting factors of existng structures.

Thanks all. The point was get some general discussion about the issues brought up by the paper, as your posts have done.
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Postby avare » Wed Aug 18, 2004 1:24 am

I have been reading the same stuff and have the same impression. What I do wonder is does anyone temper the search with information on how audible or problematic modes are to humans as they get lower/ more less densely spread etc. I know one person at Genelec is doing his PhD in this area. In other words, if for example humans can't differentiate between one and two modes in the first octave, why include them in the optimisation etc?


Thanks Andrew, your queries made me think (that's good :) ) The paper indicates that the criteria for optimum was based upon a number (0.3 I think) that was derived from listening tests.

You would presume human perception is involved somewhere in making decisions like using std, dev, rather than simple distribution?


I don't understand your point here. What are you referring to as "simple distribution?"

Are these optimisations based on listening or just more algorithms? If not, how are they arrived at?


Again, I don't understand your point. All three papers indicate that they are based on theoretical analysis using computers.

What I am curious about, and this may be what you are referring to, is how much difference is there in actual listening rooms built to the "optimum" "second best" and "worst case" rooms. Theoretical analysis and design is fine in and of by itself, but the the only thing that counts is results.
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Postby Brian Dayton » Wed Aug 18, 2004 7:28 am

nice links, fascinating topic, even for someone like me who has only amateur knowledge on the topic, and passed interest.

i think Andrew is just asking "these numbers are great, but do they correlate to percieved quality", perhaps. wondering if all these std. deviations and so forth correlate to audible perception (like the ones in this file: http://www.bbc.co.uk/rd/pubs/reports/1993-08.pdf)

if i interpret his thought wrongly, i am sorry.

anyway, i've little to add, so i'll be gone now :D
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Postby Savant » Wed Aug 18, 2004 2:10 pm

Andrew,

Your point about modal perception is a very good one. It is actually a driving force behind the Bonello criteria. He stated as follows in his 1979 paper in the context of selecting a bandwidth for his criteria:
Bonello wrote:...the finally adopted value has been one-third of octave <sic>. We use a relative bandwidth, not an absolute one, taking into account the logarithmic characteristic of auditive perception and that the ear has become accustomed to musical intervals.

Other papers touch on perception indirectly. In Walker's 1996 paper, he concluded:
Walker wrote:It has been shown that the use of a quality index for the calculation of a single figure, representing the uniformity of low-frequency mode spacings, results in distribution patterns from which rooms of "better" and "worse" quality can be identified.

Unfortunately, his criteria for determining "better" and "worse" quality is never given. One could infer that it's based on quantitative values and qualitative assumptions. Basically, a lower mean square mode spacing sounds good. (He did not actually come out and say it that way. Note that throughout his paper, the subjective words "better" and "worse" are deliberately placed in quotes.)

In short, you are correct about one thing. Which is the same thing that can basically be said across the board about what we know of low frequency behavior in small rooms and the human perception of that behavior: More work needs to be done. (Around here, we call that "job security"! :mrgreen:)
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Postby Brian Dayton » Wed Aug 18, 2004 2:21 pm

More work needs to be done. (Around here, we call that "job security"! ) :mrgreen:


i realize that you jest, but therein lies great truth for many fields. mystery=safety, answers=a step closer to an archaic status.

this ends philosophy from my corner for today.
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Postby Andrew Steel » Wed Aug 18, 2004 9:25 pm

Hi Folks,
Avare, Brian was able to put my query into better words - thanks Brian. I always try to eschew obfuscation :)

I guess what interests me is what these optimisations are driving at i.e. which goal? As is usual in the scientific development of a topic, understanding can change and it seemed to me that the "ideal" has changed in terms of how modes are distributed. I want to know on what basis the "ideal" is/has been based.

Jeff,
I'm glad you are kept occupied doing things that interest you - if you need someone to carry your tape measure let me know :-)

Andrew
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Postby avare » Thu Aug 19, 2004 6:11 am

Andrew wrote:
Avare, Brian was able to put my query into better words - thanks Brian. I always try to eschew obfuscation

I guess what interests me is what these optimizations are driving at i.e. which goal? As is usual in the scientific development of a topic, understanding can change and it seemed to me that the "ideal" has changed in terms of how modes are distributed. I want to know on what basis the "ideal" is/has been based.


and Jeff wrote:
Unfortunately, his criteria for determining "better" and "worse" quality is never given. One could infer that it's based on quantitative values and qualitative assumptions. Basically, a lower mean square mode spacing sounds good. (He did not actually come out and say it that way. Note that throughout his paper, the subjective words "better" and "worse" are deliberately placed in quotes.)


Thanks for clearing up the confusion about "quality index." The quality indexes used are clearly stated, to me, but I have a background in statistics that makes the descriptions of the quality indexes clear to me.

Summing up the similarities and differences in the quality indexes used:

Both RPG and Walker use statistical measures of the spread in a group of data.

- RPG uses the difference of individual values of the room response from the best fit linear regression line.

- Walker uses the spacing between modes.

- RPG uses a constant 20 to 200 Hz frequency range.

- Walker uses the lowest mode frequency up to 120 Hz.


The reason for the first two items is quite obvious if you think about for a second. Walker is a continuation of traditional modal analysis. RPG is breaking new territory by including surface absorption, so the modal spacing is not sufficient.

As far as the difference in frequency range goes, they are arbitrary. RPG even states that in the paper.

A significant point of interpretation is that theoretically (but in reality impossible) a flat spectrum would have with RPG's quality index a value of 0, regardless of the slope of the linear regresion line.

I hope this helps. I know that this discussion has helped me understand the differences better by directing my thoughts to various aspects of the criteria.

Andre

(edit) removed false information about difference in the metrics.
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Postby Savant » Fri Aug 20, 2004 4:16 am

Andre,
avare wrote:- RPG uses the difference of individual values of the room response from the best fit linear regression line.

This is an interesting topic all by itself. I'm not sure how much confidence I have in it. I seemed to notice a lack of testing to verify the response predictions. What do you think?
- RPG uses a constant 20 to 200 Hz frequency range.

Note that their program does go up to 300 Hz.
A significant point of interpretation is that theoretically (but in reality impossible) a flat spectrum would have with RPG's quality index a value of 0, regardless of the slope of the linear regresion line.

Regardless of whether it's possible, is a "flat" response truly what is desired?

Questions begat questions...
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Postby avare » Fri Aug 20, 2004 11:41 pm

Quoting is awkward working of line, so please accept the quoting errors Andre,

- RPG uses the difference of individual values of the room response from the best fit linear regression line.

This is an interesting topic all by itself. I'm not sure how much confidence I have in it. I seemed to notice a lack of testing to verify the response predictions. What do you think?


From the comparison of actual versus predicted results in both RPG and Walker I am confident that the predictions are sufficiently accurate for current technology.

As to what they should be, that is an unknown! As far as the reasoning for using the linear regression instead of the mean, I have a problem with it.

from RPG:
. The deviation from a best fit line rather than the mean is used because it is assumed that slow
variation in the spectrum can be removed by simple equalization, and what is important is to reduce large local variation


This to me is back to the seventies thinking that equalization can correct acoustic issues.



- RPG uses a constant 20 to 200 Hz frequency range.


Note that their program does go up to 300 Hz.


Really! My thoughts right now are that an upper limit of the Davis or Schroeder Frequency would be more appropriate.

Similarly starting at the first mode but identifying it.

A significant point of interpretation is that theoretically (but in reality impossible) a flat spectrum would have with RPG's quality index a value of 0, regardless of the slope of the linear regression line.


Regardless of whether it's possible, is a "flat" response truly what is desired?


Definitely not desired, but a factor to recognize in the interpretation. Perhaps for other people reading this thread I should have written that a flat response would mean no reflections as in outdoors or in an anechoic chamber.

No doubt in the future recommended values for the various indexes will evolve. A certain is that there will end up being more than one to describe the room effectively. As one possibility, a number for smoothness, a number for
low frequency limit, a number for upper frequency of modal behavior.

I see it evolving like reverb. With a rough time line for other readers:

Identify it as a measurable quantity and quantify it (Sabine in the 1900's)
Apply it to large spaces (Sabine in the 1900's)
Apply the theory to smaller spaces (recording studios in the 20's)
Reduce it in smaller spaces (recording/broadcast studios in the 30's/40's)
Start of different reverb calculation equations (30's)
Develop optimum room ratios (40's to today)
Recognize full frequency absorption significance (40's)
Quantify reverb components like initial reflections, initial decay (Beranek 60's)
Change paradigm to decay rate for heavily damped rooms (70's)
Address early reflections (Chips Davis start with Don Davis 80's)
The explosion of refining the knowledge and use of it due availability of inexpensive computers (90's)



Questions begat questions...


Incredibly true in this case.

One thing that is very apparent to me studying these reports is that they are very transitory. The underlying concepts will not change. What will increase is the speed of computers ,making it feasible to include factors not included now, and to run multiple sizes on smaller (read common) computers.

It reminds me how often just in the last month I have referred to my JAES form the late 70's/early 80's because the papers in them are now being applied. Linkwitz-Riley crossovers, Jeklin disk recording method, Jensen op-amp, hearing acuity for varying amplitude with frequency, Bonello criteria, are from that range of JsAES.

We are very much on the leading edge of revolutionary acoustics.

Thanks Jeff
Andre
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Postby Eric.Desart » Sat Oct 16, 2004 8:43 pm

It's still something I must study more in-depth.

So my thoughts now are only superficial.
I'm busy with some indirect related things and I thought back on this d'Antonio/RPG program thing.

I'm still wondering how the heck there can be a difference in a room when one changes the volume but maintains the same ratios.
The only thing I can imagine is that the relative position of the listening position remains on a constant height, therefore one sits in a deviating modal and interference pattern.

It's a difference like measuring the same room at different height levels.

But indeed, when using a larger room, one can hardly scale a listener with it.
Still I have serious doubts here.  I think this is more a discussion of how this is calculated and excited and the reception position than really a room difference.

I wondered if I was missing anything, in function of angled incidence, or non-axial modes which relate to 2-D and 3D diagonals rather than a linear behavior with the increasing x, y, z axis.
I thought however this shouldn't make any difference whatsoever.
I still am going to do a detailed analysis of such rooms to check if I miss something, and if so: what do I miss?

Being busy with my calculator now (for other things), I just recalculated an arbitrary room where I increased the size as such that the modes shifted with exact 1/3 octave band.
This results in a relative modal distribution which is exactly similar for both room volumes. That includes the tangential and oblique modes which are related the room sizes with quadratic relationships.
This means (for now, if my mind still works OK, will recheck later) that this is also valid for standard boundary interference and whatever other patterns.

Look at both pictures below:  They look as copies of one another (this isn't a graphical manipulation I did, but just a plain naked recalculation based on a deviating volume). Just the scale is shifted with 1/3 octave and the frequencies are adjusted to their respective volumes.
The room sizes are noted on the Room Mode Calculations.
The reason that I chose a volume shift equaling 1/3 octave x axis shift is just that it makes visual comparison much clearer. But the basic principle remains for any volume. With other volumes the markers should shift a fraction or whatever of a 1/3 octave band.

Image
Image

For me this gives the (preleminary) feeling that d'Antonio's conclusions are based on calculations where not all parameters were scaled with the room. (e.g. speaker position, Mic position, mixing height).
In fact D'antonio's conclusions contradict everything all the others ever wrote about it and at a first glance, mathematically I can't see the logic either.
Of course the Schroeder frequency lowers with largers rooms, but that's not related now to the topic at hand.
Maybe more in-depth analysis explains his conclusions (need more dedicated time for that).

This also shows what I described in the Room Ratios Overview topic.
One must be careful with the Bonello approach, because the same ratios, but deviating volume can cause as well rejection as acceptance as per the Bonello approach depending on the resulting position of the modes within the 1/3 octave band scale.

In fact one can see this relative distribution really as a fixed picture, only the x-axis scale shifts and the modes will show other frequencies, but seen relative this whole thing is a constant if ratios are preserved.
Changing the volume of a room, while preserving the ratios will only shift the mode markers as one fixed overall picture, within the scale of the picture.

I have no time to go in detail now, but certainly aren't forgetting it.
In the time between I gladly will read your thoughts about all this.
Image
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Postby avare » Mon Oct 18, 2004 5:51 pm

Thanks Eric.  You reminded me of this thread and a couple of thoughts that have evolved in my head in the passing time..  I'll post a proper post shortly detailing them.

Andre
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