## ROOM RATIOS: M.M. LOUDEN ANALYSIS

A primer on room ratios and other matters related to acoustic analysis

### ROOM RATIOS: M.M. LOUDEN ANALYSIS

More will follow

Copyright:  All content here is copyright protected and can not be used (whole or partly) without explicit consent of the Author.
At the bottom of this page you find links to good, to be avoided and not advisable room mode calculators.

click original main topic:  ACCEPTABLE ROOM RATIOS (an overview)

A first remark:
This topic is not meant to discuss or dispute the use and method of Room Ratios in itself, but as an analysis and graphical presentation of the published M.M. Louden  Ratios.

1971: M. M. Louden listed 125 dimension ratios arranged in descending order of room acoustic quality.
Dimension-ratios of Rectangular Rooms With Good Distribution of Eigentones.
Acustica, Volume 24, 1971, pp 101-103/104.

This list does NOT represent 125 acceptable room ratios, but a list resulting from 153 grid points.
From these 153 Matrix points 28 were double having reversed x/y ratios, resulting in the published 125.
To check this logic these doubles are masked by the hatched triangle in the graph.

Some of the published ratios are located in that hatched triangle, and the corresponding ones in the main area lacking.
That seems to justify the assumption that M. M. Louden's publication in 1971 was influenced by much less powerful
and flexible calculation means than available nowadays.

Using this method, unlike ratios of other authors ALL Louden ratios yield standard 1 decimal on the x & y ratios.
With modern means it's possible to extract the acoustic logic from this huge list of ratios ranging from best to really ugly, to be avoided, ratios, reorganize and map them.
Analyzing this graphical presentation one can notice that within the by M. M. Louden published ratios and used method, better ratio points/ranges can be extracted using 2 (rather than 1) decimals are used for the Length/Width values.
Several in-between areas are better than the ones published by M. M. Louden himself.
A graphical approach is easier and user friendlier than huge lists of ratios, giving additional insight in the logic and trends of the original published data.
This results in the following stylized graphical analysis (Copyright ©: Eric  Desart)
The darker the area the better, with the center of the darkest areas being best (note: based on the Louden approach).
The numbered markers are the as 5 best published ratios in order of quality.

Theoretically as per the Louden approach: (scale pragmatically defined by ED)  the perfect ratio should be 0.00
The worst published Louden Ratio interpreted as 1.00.
Hence the lower the number the better.

The best published M. M. Louden Ratio as per this scale = 0.4046
The best ratio the Author calculated over 3321 points = 0.3865. This is included in the darkest green areas (best ranges).
In-between values in this 3321 points grid, likely very small areas can go somewhat  lower to somewhere between 0.385 to 0.386 (only higher resolution analysis will show  these).
These numbers improve towards the center of these darkest green areas, but will likely  go nowhere below this 0.385+ as bottom value.

What you can see is that there is not such a thing as a perfect ratio.  The scale on the graph starts at 0.38
When we search for the 3 best M.M. Louden ratios of the 3 dark green areas representing 3 typical different room shapes then we come to the following 3 best M.M. Louden ratios (ratios calculated by E. Desart, not published ones - Right bottom green areas not included since they are just reversed L/W  ratios)

Some BEST ratios:
• Flattest room (top dark green area):
Ratio: 1:1.50:2.14 - L: 2.14 - W: 1.50 -  Quality: 39.98%  (-/17)
Ratio: 1:1.51:2.14 - L: 2.14 - W: 1.51 -  Quality:< 39.98%  (-/better than 17) (not in Tables, but better than the above)
Closest published M.M. Louden ratios:
Ratio: 1:1.50:2.10 - L: 2.10 - W: 1.50 -  Quality: 41.28%  (3/42)
Ratio: 1:1.50:2.20 - L: 2.20 - W: 1.50 -  Quality: 42.65%  (4/86)

•  Middle flat room (middle dark green area):
Ratio: 1:1.36:1.86 - L: 1.88 - W: 1.36 - Quality: 38.65%  (-/1)
Closest published M.M. Louden ratios:
Ratio: 1:1.40:1.90 - L: 1.90 - W: 1.40 -  Quality: 40.46%  (1/26)
Ratio: 1:1.30:1.90 - L: 1.90 - W: 1.30 -  Quality: 40.80%  (2/31)

•  Least flat room shape (bottom dark green area):
Ratio: 1:1.16:1.44 - L: 1.44 - W: 1.16 - Quality: 41.86%  (-/52)
Closest published M.M. Louden ratios:
Ratio: 1:1.20:1.50 - L: 1.50 - W: 1.20 -  Quality: 42.98%  (5/97)
Ratio: 1:1.10:1.40 - L: 1.40 - W: 1.10 -  Quality: 43.34%  (7/115)
Ratio: 1:1.20:1.40 - L: 1.40 - W: 1.20 -  Quality: 44.58%  (10/158)

As one can notice the difference in rating Length and Width ratios with 2 significant decimals versus the 1 significant decimal in the original M.M. Louden study can shift the sort order in a significant manner.
In very rough terms one could state that only the first 20 room ratios of M.M. Louden can be useful for practical applications, while simultaneously his broad approach of  publishing all 125 (when reorganized and mapped with representative algorithms) gives a good picture of trends and logic in a room.
Hence from a practical point of view only the first 20 are sensible, from a scientific  point of view they all are.
The answer: "BAD", as a scientific result, is equally useful to a result which is:  "GOOD".

Numbers between brackets e.g. (-/17) or (10/158):
1st number: Original M.M. Louden sort order, 2nd number: E. Desart tables sort order.

Note: The Author should need to manually correct the lobbing appearing around the 1/1 length/width ratio (the 1.2:1.2 to 1.8:1.8 45° line), which is caused by too little input data, but practically little matters. The Author doesn't like to rape the used algorithms or numbers just to make it look nicer/more logical there.
Maybe (not sure) will apply some improvements in the future. The solution is entering more in-between data points on this 45° line by 2D regression, preventing the rest of the graph to be negatively influenced, before remapping all data.

The following Tables are synchronized with the detailed M.M. Louden -  E.Desart © Topograph as well for the rating as for the color coding.
The graph presents rating as a value from 0.00 to 1.00, while the Tables present the  same, for pragmatic reasons as a percentage.

Tables 1a & 1b
433 dimension ratios arranged in descending order of room acoustic quality.
This covers all room ratios with a < 0.50 (graph) or 50%  (tables) rating.
These 433 values include the 18 best published M.M. Louden ratios (yellow colored  lines), meaning all others are worse.

Tables 2a & 2b
433 dimension ratios arranged in function of Length and Width ratios.
This covers all room ratios with a < 0.50 (graph) or 50%  (tables) rating.
These 433 values include the 18 best published M.M. Louden ratios (yellow colored  lines), meaning all others are worse.

If a visitor wants to judge a room in function of its ratios,
NEVER use a Room Modes Calculator which DOES NOT take the
Tangential and Oblique modes into account
.
Only taking the Axial modes into account can be alright but can as well lead to WRONG  conclusions.
One just doesn't know!
A more detailed explanation about the reasons for this pertinent advise can be found in the ROOM RATIOS page at:
click here: ACCEPTABLE  ROOM RATIOS (an overview)
Note that about any Author which published acceptable ratios, no matter the manner they obtained them, toke ALL modes into account (axial AND non-axial).

The discussion of the validity of using room mode calculators or not, is an entirely different matter not discussed here.
The more a room will divert from a rectangular shape with statistical symmetrical boundary absorption/reflectivity over the to be investigated frequency range, the less reliable the calculated numbers become.
Either one uses a room mode calculator or not.
If one chooses to use one, then use a good one. There are many public available or accessible for personal use.

An interesting practical and theoretical experiment by:
Art Ludwig: BS - Caltech; MD Mathematics and EE - USC; Ph.D. Engineering - USC
http://www.silcom.com/~aludwig/Room_aco ... calculated.

Some often referred or quality Room Mode calculators:  Please DO respect Copyright of the respective © owners.
TO BE ADVISED: fulfilling the above requirement of  calculating ALL modes (arbitrary sort order):
1. By © HARMAN - Dr. Floyd E. Toole, Vice President Acoustical Engineering, Harman International Industries, Inc.
http://www.harman.com/xls/Room%20Mode%20Calculator.xls
2. By © University of Salford UK - Prof Dr. Trevor Cox (this are lists of rated room modes, no calculators)

These ratios are room size dependent, as such involve possibly/likely a geometric "source to room" relationship (still to check).
Overview:
http://www.acoustics.salford.ac.uk/acou ... ntent=best
Best ratios:
http://www.acoustics.salford.ac.uk/acou ... ratios.xls
Second Bests:
http://www.acoustics.salford.ac.uk/acou ... d_best.zip
3. By © John Griggs: (JAVA program - metric & imperial)
http://forum.studiotips.com/viewtopic.php?p=27336#27336  Only to be downloaded via post (no direct link), registered members only.

This is a rather unique program designed by John Griggs, and the ONLY freeware tool,  capable of finding optimum room measures between user set boundaries.
It goes much further than traditional room mode calculators, by allowing the user to set any combination of different published comply/reject methods originating from several authors + one comply/rejection algorithm designed by the software designer himself.
4. By © Bob Golds: One of the best on-line HTML/JAVA Room Mode Calculators  (metric & imperial)
http://www.bobgolds.com/Mode/RoomModes.htm

A very popular one, giving lots of additional info.
5. By © Dr. Jörg Hunecke: A very unique on-line calculator (only metric)
http://www.hunecke.de/en/calculators/ro ... modes.html

This page can interactively show a 3D graph of the calculated modes, even the oblique ones (not so evident and AFAIK unique on-line).
It calculates only the first 20 modes (no matter which type) which are likely the most dominant (but could be a limitation), but does this in a very neat surveyable manner.
The interactive graphical 3D presentation of these modes makes this calculator standout, if only for this feature.
Hence I see this calculator more as a very good and neat educational page than a complete calculator.
Yet it is a handy calculator as long as one is certain that one investigates a problem <= 20th mode frequency.
6. By © Eric Desart, R&D acoustician Antwerp/Belgium (metric & imperial)
http://forum.studiotips.com/large_files ... ulator.zip
7. By © Jeff D. Szymanski, Ex-Chief Acoustical Engineer Auralex (haven't checked  difference between both files yet)
http://forum.studiotips.com/files/MODESv2p.xls
http://rodssoundsolutions.com/files/Roo ... ulator.xls
8. By © Chris Whealy,
http://www.whealy.com/acoustics/ControlRoom.html (note this file does more than modes)
9. By © Mark Wieczorek, (metric and imperial)
http://www.marktaw.com/recording/Acoust ... Calcu.html

Just a listing, but what it gives seems correct.
10. Yet to be completed, as they come to the attention of the  Author.
Yet to be completed.
11. OUT OF CATEGORY; This are NO Room Mode Calculators.

1. By © FRD Consortium, Yavuz Aksan  2002
http://www.pvconsultants.com/audio/reflection/rrc.htm

Room Response Calculator modeling the ambient response of rectangular shaped rooms by recursive reflection.
The user positions the listener and one or two speakers and sizes the room, selects and tunes calculation density and wall reflectivity. The program models frequency response and energy delay timing for closed box systems in mono and stereo and has an excellent approximation for a mono dipole.
Not tested yet, but at a first glance worth investigating.
2. Yet to be completed, as they come to the attention of the  Author.

TO BE AVOIDED for diverse reasons (arbitrary  sort order):
1. By © Mc Squared System Design Group, Inc.
Mode Calculator Metric version:
http://www.mcsquared.com/metricmodes.htm
Mode Calculator Imperial Version:
http://www.mcsquared.com/modecalc.htm

It's a pity: It looks as nice on-line calculators comprising the non-axial modes.
However these non-axial modes are far from complete by the mathematical build-up of these pages.
You get a lot of senseless non-axial modes going unnecessary high in the frequency  range, while most of these being important are lacking.
The author contacted Mc Squared about this some years back, with as sole result that  they altered the accompanying text a bit, more to act as a disclaimer than making the calculators more useful.

For people relying on the presence of these calculated non-axials, these  calculators are badly misleading.
Only experts will automatically recognize this limitation (still not making the  related pages more useful), but that's not the target group such pages are aiming at.
2. By © Sengpiel Audio., Dipl.-Ing. Eberhard Sengpiel (Metric)
http://www.sengpielaudio.com/calculator-roommodes.htm (English)
http://www.sengpielaudio.com/Rechner-raum-moden.htm (German)
I made copy of all related pages, as prove for the correctness of my statements.

THIS IS PLAIN BREACH OF COPYRIGHT AND/OR LACK OF RESPECT FOR SOURCES.
This Dipl.-Ing. is Lecturer at the Universität der Künste Berlin - UdK - Fakultät Musik
All comments related to the above Mc Squared Room mode calculators apply here since the related mathematical source code is just plain copied. (I followed these sites since ca 2000).
But additionally, and unlike Mc Squared, rather than at least explaining what that room mode calculator does (did E. Sengpiel understood/saw himself?), allowing experts to see where these limitations come from or relate to, this text wasn't copied.
In fact you need another good calculator to see that this one lacks important modes and as such worthless and very risky.
Hence this 'room mode calculator' is a perfect example of what a calculator and educational/scientific attitude should NOT be.
This makes me enormous frustrated. I'm getting, as a matter of speech, almost used on the net that all too often commercial companies and private persons don't bother about Copyright and respect for sources. Giving rightful and/or legal credit seems all too often more a sin than a virtue.
But if even a lecturer in higher education, who's job it is to teach people, setting standards, being supposed to have a model role giving the example, then educational scientific attitude is going down.  This attitude suggests that there must be more comparable stuff on the owners extensive site.
For the same attitude, a teacher is supposed/expected to warn or sack his own students.
Special software is developed and used nowadays designated to search the net for plagiarism, too often shown by students.
Being a lecturer for Higher Music Education E. Sengpiel should be ashamed of himself.
3. By KlipschCorner.com, Damon Payne (On-Line calculator - Imperial only)
http://www.klipschcorner.com/Tools/ModeCalc.aspx

It's a pity: It looks as a nice on-line calculator comprising the non-axial modes.
This calculator however seems to calculate wrongly, including either a principle error, or a poetic license.
I can't figure out the principle involved, nor how exactly the mode strength is defined.
This calculator seems to calculate non-existing oblique modes. Hence I checked no further if other anomalies are involved or not.
4. Yet to be completed, as they come to the attention of the  Author.

NOT TO BE ADVISED due to LACKING NON-AXIALS (arbitrary sort order):
1. By © REALTRAPS - Ethan Winer, (metric & imperial)
recent Windows version:
http://www.realtraps.com/modecalc.zip
original DOS version:
http://www.ethanwiner.com/MODECALC.EXE

This is most likely the most linked and referred Room Mode Calculator (caused by the huge net and commercial penetration of © owner).
However, here one can clearly state that net penetration is no synonym for acoustic quality.
The author uses as (pseudo) argument user-friendliness, which, as per many  professionals is a false argument.
User-friendliness obtained by simplification causing potential wrong decisions/conclusions is not user-friendly at all.

This calculator is a contradiction in itself by advising ratios, which by their respective Authors (not referred to, or given credit by the designer of this tool) are based on "ALL modes" calculations, while the calculator isn't capable to reproduce them, showing why they are officially published advised ratios.
Several of them should be very clearly rejected on the "axials ALONE" approach,  looking quite ugly as modal distribution.
This shortcoming is extensively discussed on several occasions over the years with RealTraps' owner Ethan Winer.

Make things as simple as possible, but not one bit simpler.
The above quote of Albert Einstein applies.  Why? -  because they become potentially wrong or misleading.

User-friendliness must be provided by the design of software, not by skipping useful or necessary data.
As per the worldwide respected "Scientific Method" an "axials alone" calculator, to judge room measures/ratios, is to be rejected.  click: Scientific Method
2. Yet to be completed.
There are many others on the net, reason being that, making an ALL-MODES calculator graphical enough to preserve user-friendliness isn't easy.
Hence lots of them are more simplified listings, which are executed in relative simple manners.
In a future stage  (additional to current explanation on main ROOM RATIOS  page), more detailed comparisons will be made to prove the limpness  and risks of calculators only taking axials into account.
The above room calculator lists do not pursue to be complete (impossible  task).
The author will gladly add additional calculators in this list as they are brought to his attention and represent some significant impact on the acoustic community on the net, or distinct themselves by their proper approach or quality.  Hence this list is dynamic.

Items can be added or removed, trying to preserve oversight of these items which are most important.  The Author knows that this is as well pragmatic as subjective, and is therefore open to related suggestions.

Have Fun with this stuff....
(for me an enormous amount of work was involved, hence you must have fun with it, as return on investment)

Eric Desart
R&D Acoustician
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