# An appropriate replacement for RT60s in SAS



## Guest (Jul 15, 2008)

As mentioned elsewhere, CSD/waterfall plots are most useful for the identification and mitigation of LF room modes.

But what do we use to examine the behavior of a small acoustical space above the frequencies dominated by modal behavior where the wavelengths at issue become small relative to the obstacles they encounter?

Unfortunately, there persists the notion of using RT60/30 and their variants in small acoustical spaces. This was a rather common notion 35 years ago, but has since been eclipsed by a greater understanding of acoustical behavior in what is defined as a small acoustical space (as distinct from, yup, you guessed it, the large acoustical space! ;-)

It is time we moved on to understand and to embrace the new acoustical model that has been rigorously verified, for all of our mutual benefit.

In a small acoustical space, the use of RT60s (and any similar variant, regardless of weighting) is completely erroneous, and indicates that we are misapplying a measurement that has no correlation in physical fact.

Fundamental to this is an understanding of the distinction between a large and a small acoustical space.** These terms are not used casually, as they have very specific conditions which define and differentiate the two. And a failure to distinguish between the two will result in some rather unfortunate consequences. 

This distinction is not only the subject of much of Manfred Schroeder’s work, but it is a fundamental concept that underlies all of his and other modern acousticians' work.

To reduce the distinction to its most basic functional charactrisitc, a large acoustical space features a developed statistically random reverberant sound field where reflections at any location are equally probable to radiate from any direction. Conversely, a small acoustical space LACKS a statistically random reverberant sound field where reflections at any location are equally probable to radiate from any direction – and instead is DOMINATED by focused specular reflections which are definitely identifiable as discreet phenomena as energy vectors with both direction, intensity and a discreet time of arrival, while their intensity decay and their distribution in regards to their arrival time can be measured and all of these characteristics easily identified and isolated via such measurements as the envelope time curve (ETC).

The RT60/30, etc. are ONLY suitable to measuring the decay time of a statistically random reverberant sound field the occurs in a Large Acoustical Space. In such a field, not finite atomistically identifiable reflections exist. As such, as they fail to apply to the physical behavior, they have no place in the Small Acoustical Space. 

If one only has a hammer, all of the world begins to look like a nail, and that is _precisely_ what has happened to the mis-application of the RT60 over the years! Instead, the newer proper tools that accurately identify the real phenomenon in the small acoustical space, such as the envelope time curve (ETC), and its variates such as the the TEF PEQ that allows one to quickly and accurately isolate and resolve each significant specular reflection into its 3space coordinates allowing for the easy and precise identification of the reflective points of incidence. These are the tools to which Schultz points below that should be utilized to address issues of: "intelligibility (that) can be degraded by specular reflections that must be isolated and corrected directly, not statistically."

Someone might attempt to use a rock to drive screws, but few would be so bold as to suggest that this methodology is suitable for use in the art of cabinetry. And if you are going to expend the effort and the money to do the job, it is incumbent that we use the proper tools that afford us accurate atomistic insight into the actual phenomena of focused specular reflections, rather than simply using the wrong tool suitable for measuring that which does not exist in a small acoustical space. The small acoustical space is dominated by focused specular reflections. It behooves us to use the tool to view each of the significant specular reflections in a manner that allows us to both address, and verify the effectiveness of any treatment we choose to employ. The days of shotgun application of absorption and overly dead rooms _should _be over. We now have the tools to view and to tailor the room precisely

Understanding this also leads one to use absorption surgically instead of randomly! Being able to see what is actually occurring has a profound impact upon one’s acoustical world view. And as we have had the tools to do exactly this now for over 30 years, it is time that more in the world of acoustics move up and embrace the current paradigms. This capability is precisely what has been afforded by the big toys of the industry such as TEF, EASERA, and SMAART. This is not speculation, this is established fact and but one small manifestation of Dick Heyser's vision presented 41 years ago. After all, even the most stalwart of nay saying classical physicists have begrudgingly admitted that there just might be something to quantum electrodynamics!

Its time to put the idea of using RT60/30/etc. in small acoustic spaces, to bed!

To quote from *Sound System Engineering*, 3rd Ed.[/B] Pp 178-9:

_“Small Room Reverberation Times

To quote the late Ted Schultz (formerly of Bolt, Beranek and Newman)
“In a large room, if one has a large sound source whose power output is known, one can determine the total amount of absorption in the room by measuring the average pressure throughout the room. This total absorption can then be used to calculate the reverberation time from the Sabine formula. This methods fails badly in a small room, however where, a large part of the spectrum of interest lies in a frequency range where the resonant modes of the room do not overlap but may be isolated…In this case the microphone, instead of responding as a random sound field (as required for the validity of the theory on which these methods depend), will delineate a transfer function of the room… It does not provide a valid measurement for the reverberation time in the room.”*

What is often overlooked in the attempted measurement of RT60 in small rooms is that the definition of RT60 has two parts, the first of which is commonly overlooked.

1.)	RT60 is the measurement of the decay time of a well-mixed reverberant sound field
Well beyond Dc (the critical distance).
2.)	RT60 is the time in seconds the reverberant sound field to decay 60 dB after the sound source is shut off.

Since in small rooms, there is no Dc (critical distance), no well mixed sound field, hence no reverberation but merely a series of early reflected energy, the measurements of RT60 become meaningless in such environments.

What becomes most meaningful is the control of early reflections because there is no reverberation to mask them.”


What you have instead is a small acoustic space dominated by room modes (which are not reverberation!) and focused spectral reflections – which by definition are anything but a well-mixed reverberant sound field wherein the arrival of reflected signals from every direction is equally probable.

In the small acoustical space, there is no mixing, nor homogeneous, statistical reverberant sound field! In fact, in a small acoustical space, as the lowest frequency that can effectively develop across the largest dimension can easily increase to ~500Hz – compared to a large acoustical space where such frequencies are often below 30Hz!

*In such environments, intelligibility can be degraded by specular reflections that must be isolated and corrected directly, not statistically.* 


*Note, It is equally proven that the fundamental form of Sabine’s expression cannot be modified so as to become correct for large absorption. Per Sabine’s Reverberation Time and Ergodic Auditoriums, Wm. Joyce, Journal of the Acoustics Society of America, Vol. 58, No. 3, pp. 643-655,Sept. 1975. _



Imagined non-existent RT60s, or some fascinating “similar but scaled down analysis” has no basis in fact or physics! And they are of no valid use here. The simple persistence of acoustical energy is of little use in a small acoustic space! 

An RT60 _is_ useful in a large acoustic space as the statistical reverberant field is sufficient to mask specular reflections. But this is NOT the case in a small room where the specular reflections EASILY dominate over the all but nonexistent statistically reverberant sound field (where they exist only at frequencies of interest to UHF engineers, dogs and bats!).

The simple persistence of the acoustical energy fails to provide ANY insight into the specific nature of specific focused specular reflections which are the real issue of concern! Such a measurement fails to reveal the intensity, arrival time, or any information that aids in the identification and behavior of, let alone provides specific information regarding the effectiveness of the surgical treatment of any focused specular reflection – and by their nature such a measurement would be location specific as you are NOT in a statistical reverberant field! And an average over many locations would be completely nonsensical! In fact, such a concentration leads only to the shotgun application of absorption – precisely that which we are trying hard to avoid!

It is the persistence in the belief that completely invalid variations of a technique designed to evaluate that which does not exist in a small room that has held back a real understanding of acoustic behavior in small acoustic spaces! Regardless of how one squints and tilts their head when evaluating such nonsense in a small acoustic space.

I realize that this steps on the toes of a few here. But its time to move on to the new tools and to use the measurement techniques which we have at our disposal to better and more accurately understand the physical phenomena of acoustics and sound for all of our benefits.

-----------------------------------------


As far as where does this misconception arise? I think it is rather simple to source this. There may be others, but a common vector for many is Alton Everest’s *The Master Handbook of Acoustics*.

Now I know that taking issue with this work is tantamount to sacrilege by many, but while applauding his efforts to bring many divergent topics and advances to the masses, he also was guilty of overly simplifying some fundamental issues, partly because they were evolving as he wrote his original drafts, and also because delving into them more fully would have required a substantial rewrite and the additional of several more chapters!

Why do I say this? Witness his section entitled _Reverberation Time Vs. Decay Time _(p. 277 2nd Edition) in the chapter entitled _Acoustics of the Recording Studio_ in *TMHOA*.

He indeed acknowledges the divergent opinions regarding this topic as early as in 1973. And he attempts to present what was then a balanced point of view to both schools. But since then significant advances in this area have been made, principally by the immense contributions to the understanding of acoustical phenomena by Manfred Schroeder, Heyser, Anhert, Davis, Keele, Berger, D'Antonio and SO many other giants in the field. And as such, its time for us to move with the times and the advance of acoustical understanding.

At one time, to suggest the existence of ‘little unseen bugs’ in liquid was enough to get someone ostracized from respectable circles. Now the belief in anything but, accomplishes the same result!
Its time for us to embrace the new acoustical models, for _all_ of our benefits. 

This is_ not_ presented as a debate. I am just the messenger. These principles have _already_ been scrutinized and debated by others of who I respect dearly. This is now the accepted paradigm in acoustics. 

People are free to accept it or not, just as in any facet of life. I suspect some still crawl around on their hands and knees lest they get too close the the edge of the earth and fall off. And they are of course welcome to continue doing so. To each his own. 

The other option is to be open to learning and implementing new concepts that can be of great use. 

But the validity of the principle and its application to real world analysis and problem mitigation is _not_ at issue. 


**May I suggest referring to chapters 7 & 8 of Davis and Patronis' *Sound System Engineering, 3rd Ed.* for an easily accessible explanation of the complete distinction between the behavioral characteristics of Large and Small Acoustical Spaces.


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## thewire (Jun 28, 2007)

mas said:


> In a small acoustical space, the use of RT60s (and any similar variant, regardless of weighting) is completely erroneous, and indicates that we are misapplying a measurement that has no correlation in physical fact



Are you familiar with the revisions to the MHOA?


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## thewire (Jun 28, 2007)

I miss Bryan and Ethan treating rooms back on home theater talk and reading chapters of the book on AVS. :sad:


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## Guest (Jul 15, 2008)

thewire said:


> Are you familiar with the revisions to the MHOA?


Most of what is printed in MHOA is derivative.

At the risk of sounding arrogant, I was literally 'intimate' formally and informally with much of the original research and many of the folks who actually originated and furthered much of the material of which Everest copied and posted in his text as editor. I have had the opportunity to learn from some of the best...and realize how much more there is to learn - especially with the continuing' rapid advance of the science of acoustics.

Hence, much of what some may find to be radically new that I have mentioned has in fact been established as reliable fact literally 20+ years ago.

MHOA is a good compendium of many related topics. But it is _not_ the in depth final reference that delves into each of the individual topics like many treat it. It is a Cliff's Notes edited compendium of assorted acoustical topics. Its a great starting point to wet your appetite and to encourage you to pursue each area in greater depth...It is _not_ an ending point.

For those interested in such topics, may I heartily encourage you to attend a Synergetic Audio Concepts (SynAudCon) seminar led now by Pat Brown - a _most_ excellent instructor. These seminars will provide you with a hands on sip from the fire hydrant of current acoustical thought and methodology.

Additionally, to get a very basic idea of the routine tools that are being employed, and which have become the norm in the pro acoustics industry for over 20 years, investigate TEF and EASERA and their implementations and the derivative capabilites of both TDS and MLS technologies.


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## thewire (Jun 28, 2007)

What is - TEF, EASERA, TDS, MLS?


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## Guest (Jul 16, 2008)

I don't think you realize what you have actually asked.:bigsmile: But in an attempt to point you in a direction where more information is available, Here are a few resources of which many are available in technical papers, texts and on the web.

Its a bit humourous as I have selves of texts, papers, test results, notebooks that cover everything you might ever want to know, but I can't figure out for the life of me how to conveniently jot them down in this spot!

But I hope that this will give you a start. Also, may I suggest getting a copy of *Sound System Engineering*, by Davis and Patronis. Note the 2nd edition (which I suspect you can now get for a discount as the new edition has come out) has MUCH more info on TDS and TEF that is not included in the 3rd Ed. Primarily as the state of the industry has moved from its conceptual introduction to its use.

*TEF* - originally developed by Richard Heyser while at the Cal Tech Jet Propulsion Laboratory, it was due to Don and Carolyn Davis’ energy and efforts and teaching of the technique through SynAudCon, augmented subsequently by Techron-Crown producing the first commercially available unit, which is now developed and manufactured by Goldline. This instrument (TEF - an acronym for time energy & frequency) offers both TDS (time delay spectrometry) and MLS (Maximum Length Sequence analysis) measurement environments with various powerful software analysis tools.


TEF analysis allows or the detailed examination of two port systems – anything with an input and output – in any combination of the fundamental dimensions of TEF – time , energy and frequency.

While there are many ways of measuring each combination of dimensions, many non-TEF systems are generally locked into fixed parameters in time and frequency. The TEF system allows measurements to be made with virtually any combination of time and frequency parameters, allowing great leeway in making measurements under any particular set of conditions.

*TDS* (time delay spectrometry) …Oh boy, and you want this in 25 words or less?!

OK, there are sources for this information, but I will give you the most basic 50,000 foot description…
TDS is a system developed by Richard Heyser that permits a spectrum that has been delayed in time to be measured with the delay compensated for…The unit compensates for the time required for the signal to travel from source to receiver (eg. Speaker to microphone) according to the receive delay that you have set by passing the returning signal through a filter that is sweeping in frequency in sync with, but offset from the test signal. The bandwidth and sweep rate (the speed at which the filter sweeps in hertz per second) of the filter are determined by the setting in the Parameters menu. Totally confused yet? ;-)

TEF: http://www.gold-line.com/tef/tef.htm - pardon their website. I do not know why they have multiple generations 20 year old pictures and plots that make DOS look advanced, instead of current screen shots showing actual current views in a website that looks and functions like it is from the 1950s...! I guess they figure that those using TEF already are familiar with the interface - :wits-end::sweat:

Since TEF, Renkus Heinz has introduced a measurement platform called *EASERA* which natively runs MLS but which also offers an optional add-on TDS environment licensed from Goldline. EASERA expands upon the original capabilities of what was essentially MLSSA in terms of capabilities and refinement.

EASERA: http://www.renkus-heinz.com/easera/index.html

In addition Renkus Heinz also distributes EASE, EARS and AURA, a complete industrial acoustical modeling as well as auralization environment. Note, this tool is not designed optimally for small rooms (although aspects of it can certainly be used for such) and its forte is the most elaborate rooms you can devise.

EASE/EARS/AURA: http://www.renkus-heinz.com/ease/index.html

Additionally, here are a few links to basis descriptions of *MLS* - maximum length sequence analysis. There are many others on the web. Pardon my haste here as i have got to run! ;-)

http://www.purebits.com/mlsteo.html

http://www.silcom.com/~aludwig/Signal_processing/Maximum_length_sequences.htm

http://www.libinst.com/mlsmeas.htm



By perusing the various tools, descriptions and tutorials for the various environments, you can get a basic idea of some of the various tools and techniques and uses that may provide a manner of 'backing into' some of the principles and techniques that are representative of the current approaches. Random generalized environmental treatment is not the current paradigm.

If you need more links or more specific info, PM me.


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## darrellh44 (Aug 18, 2007)

Hi Mark,

Can you tell us what your professional background is? Do you have a website?

Thanks,
Darrell


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## Guest (Jul 17, 2008)

Suffice it to say that I am an over-educated crazy (including among a literal handfull of others, 2 degrees in physics) with a background in the music industry, telecommunications, academia, IT, InfoSec and acoustical design and consulting.

I am a bit hesitant to put too much personal information on a public forum (partly due to other professional policies and security criterion with which I also routinely encounter), but I am _not at all_ averse to speaking personally with anyone and probably talking far too much and attempting to answer any question you might have. ;-)

If you will PM me, I will gladly provide contact info and/or, if you provide a phone number,the latest time one can call(and your time zone)... if you are in continental North America I can call you via telephone for free - otherwise I am available to chat/speak via computer over Skype.

Is that fair?

Acoustics, unlike most other sciences that have been not undergone many radical and disruptive changes in many years and which consist primarily of plugging numbers into well behaved formula established long ago, has undergone the equivalent of an quantum revolution in the past 40 years (and _especially_ the last 30!). The paradigm once dominated by the POV of the frequency domain has shifted with the arrival of the time domain has been radically transformed, with many very exciting new insights and even more fascinating questions being afforded to us. Its truly an exciting time to be thinking about acoustics, yet many segments of the industry have not kept pace with some of the changes simply due to many not being familiar with them. And forums such as this one are a great way for many to share information and to stimulate ideas.

The primary analytical tools employed are TEF with TDS and MLS and the full compliment of software components, while for modeling I use (primarily) EASE/EARS/AURA EASE (primarily) for large acoustical spaces (as it assumes all seating is in the far field where the wavefronts do not vary with distance, unlike the near field where you hear individual component response and the wavefront response varies with distance; also all dimensions are assumed large relative to wavelengths so that room modes are not a fundamental issue. It can be used in certain respects for small acoustical spaces assuming you do not violate basic limitations and attempt to use it for what it is not designed. In other words, you are at least as smart as the tools you use...)

And no, It may surprise some that I am _not_ here to sell anything. While I certainly could, I to not depend on this for a living. I have however been called upon as a hired gun for SR system, large hall, studio and room design and analysis for well over 20 years using TEF (and now also EASERA), and for longer prior to the arrival of the commercial tools. I am available to lend a hand or an ear, or to simply explore options should anyone desire this. The scary aspect of this is that this is what I _like_ to do and what I find myself exploring in my down time as a diversion from my other 'more exotic' obligations.


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## darrellh44 (Aug 18, 2007)

Mark,

No questions in particular. I used to live in Carrollton and frequently go back for visits. I was just wondering if you offered any acoustical products or had any demo facilities. 

Thanks,
Darrell


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## JohnM (Apr 11, 2006)

Could you expand on what kinds of plot you feel are most useful for dealing with small rooms? Discussion of the means by which any particular software derives the impulse response, whether TDS, MLS, log swept sine, PN sequences or firing a cannon are largely irrelevant when operating within the constraints of the particular method, though log swept sine and PN sequences are the most robust. How that impulse response is subequently analysed and how the results are presented to the user are much more to the point, I'm always keen to find helpful ways to present information to the user.


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## Guest (Jul 22, 2008)

I'd be glad to...
But I must beg your indulgence until I can get a few moments to sit down and try to spell it out coherently, as my schedule is 'a bit' chaotic this week - and hopefully present it in a form others can potentially utilize.


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## thewire (Jun 28, 2007)

The Master Handbook of Acoustics fourth edition breifly goes into all of these topics as I can see in the index in the back. I'm not there yet, but close. It has mentioned that RT60 is not a determining factor in common practice but is a part of the sum of test that may be done. It has mentioned that RT60 is not typically a practical application in itself when dealing with small rooms about four or five times so far, and as explained why. That is why I asked if you were familiar with the revisions. I asked about these terms because I am studying to be an acoustician and I thought your explanation would be helpful. Thanks.


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## Guest (Jul 22, 2008)

thewire said:


> The Master Handbook of Acoustics fourth edition briefly goes into all of these topics as I can see in the index in the back. I'm not there yet, but close. It has mentioned that RT60 is not a determining factor in common practice but is a part of the sum of test that may be done. It has mentioned that RT60 is not typically a practical application in itself when dealing with small rooms about four or five times so far, and as explained why. That is why I asked if you were familiar with the revisions. I asked about these terms because I am studying to be an acoustician and I thought your explanation would be helpful. Thanks.


Real quickly... Everest is a very good overview of many technologies, but it is _not_ to be mistaken for an in depth study. It is a great starting point that brings many topics together. But if you are serious and want to apply the concepts, especially as so many 'topics' have progressed far beyond the basics of what he presented, each area should be researched MUCH further. 

The period during which he was collecting and assembling his material - especially during the late 70s, 80s, and early 90s, was a period of incredible change and advances in acoustics. Much of what he reports is of the very early and intermediate changes that were occurring - the significance and implications of which are now much better understood. Note, he did not do any of the research nor was he actively involved in it. He reported about it. Much better source material exists from those who were actively 'doing' the work that can be referenced once you have become aware of the topic(s).

If you are attempting to apply concepts, one fundamental characteristic that you will need to understand is the distinction between a Large Acoustical Space(LAS) and a Small Acoustical Space (SAS). They feature a different set of characteristics and they are_ not_ all interchangeable.

Characteristics of a space determine the tools and approach that you employ. After all, your results will follow from the questions you ask. Ask the wrong questions assuming erroneous characteristics and your answer will be flawed.

May I suggest that your next text be *Sound System Engineering* by Davis and Patronis.
You need to have a thorough understanding of the physics of sound. And if your intent is to practice acoustics, may I _seriously_ suggest attending the Synergetic Acoustic Concepts (SynAudCon) seminars. You will be introduced to the very latest models as well as measuring techniques...most of which are still too new to be written about in books as they are the direct result of ongoing research...not historical overview.

Regarding the RT60, it is by definition the measurement of the decay time in seconds of a well-mixed reverberant sound field well beyond Dc (the critical distance) to decay 60 dB after the source source is shut off.

Modal decay rates are _not_ reverberation! A modeal decay rate is the dB/s rate of decay for a modal frequency. And they are certainly not beyond the critical distance(Dc)!

Likewise, focused specular reflections are _not_ reverberation. 

Thus SAS decay behavior is dealt with differently...and we will try to explore that further in the reply suggested above.

Let's start by reading the appropriate chapters in _*Sound System Engineering*_. Thereafter there is _much_ information by Schroeder, Anhert, D'Antonio, Keele and _many_ others - depending upon the amount of math you like....:bigsmile:


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## thewire (Jun 28, 2007)

:unbelievable:


mas said:


> May I suggest that your next text be *Sound System Engineering* by Davis and Patronis.
> You need to have a thorough understanding of the physics of sound. And if your intent is to practice acoustics, may I _seriously_ suggest attending the Synergetic Acoustic Concepts (SynAudCon) seminars. You will be introduced to the very latest models as well as measuring techniques...most of which are still too new to be written about in books as they are the direct result of ongoing research...not historical overview.


Yes. The book you mention looks good without any doubt.


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## NLP (Oct 26, 2008)

Interesting quick review of some obsolete and/or too costly systems:

_Measurement systems

MLSSA board and software from DRA Laboratories: measurement and processing of impulse responses with the MLS method. Very old system (1988, DOS-based, ISA board) - this was the history (in 1989 I was the owner of the first MLSSA board imported to Italy, and I really need to thank here Douglas Rife for developing it - Aurora is "son" of his work!), but nowadays the MLSSA system is completely obsolete, and still very expensive.
Gold Line TEF analyzer: measurement and processing of impulse responses with the TDS (linear sweep) method or with MLS. Expensive and obsolete. Severe hardware limitations.
CLIO board from Audiomatica: the same as MLSSA, but cheaper, two channels and 16 bit converters instead of 12 bit. Another good Italian work, made by Mauro Bigi. Also this system is "son" of MLSSA... And I am also the happy owner of a couple of CLIO boards...
WINMLS software for measuring impulse responses and computing acoustical parameters with the MLS method. Powerful, but expensive.
ETF software for measuring single-channel impulse responses with the MLS method. Cheap and easy to use, although limited capabilities.
DIRAC program from Acoustics Engineering (now sold by Bruel & Kjaer)- measurement of room's impulse responses and computation of acoustical parameters. Nice, but very expensive.
Sample Champion - software for MLS measurement for room acoustics and loudspeaker evaluation. Good competitor of Dirac, WinMLS and Clio, cheaper and more versatile.
JBL's Smaart Pro : real-time room acoustics measurements and reverberation time computation with a standard sound card_

Author is dr. Angelo Farina.


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## SAC (Dec 3, 2009)

Along with Clio is SysID, both popular back in the late 1980's and early 1990's. But largely eclipsed today, along with the various MLS platforms twhose capabilities have been incorporated and vastey expended in platforms such as ARTA, TEF, and Easera.

ARTA incorporates MLS stimuli (along with many more configurable options) for 79 Euros and goes far beyond MLSSA and WinMLS.

Easera, in large measure resulted from the lack of development in the MLSSA platform and likewise is a substantial advancement over MLS only systems.

Both are current actively supported systems.

BTW, Smaart has traveled a long convoluted road since Sam Berkow brought forth that baby in conjunction with JBL! Moving the the black hole that was EAW, to further incompetency with Loud, and now to Rational Acoustics. Useful but primarily oriented toward live sound applications - for which I would also suggest one look (instead) at SysTune.


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## NLP (Oct 26, 2008)

Exactly.
And ARTA is shareware, you can use it for free fully functional only that you can not import and saving files, you can save screenshots etc.


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## NLP (Oct 26, 2008)

mas said:


> I'd be glad to...
> But I must beg your indulgence until I can get a few moments to sit down and try to spell it out coherently, as my schedule is 'a bit' chaotic this week - and hopefully present it in a form others can potentially utilize.


A "few weeks" are waaay back... so?!


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