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.