Room Acoustics - Large Room and Small Room

[gaspr]

I found it interesting that after all the objective math and analysis,

that one of the authors' main reference points was a great seat in a

concert hall that was "subjectively judged to be excellent".

I don't want to start this "subjective/objective" argument all over

again, but do the authors ellaborate on how this subjective

judging was done?

Also found the absorbtive coefficient charts to be interesting.

Note what a coat of paint does to a concrete block wall. Is this

because the paint prevents air movement through the concrete?

[gaspr]

DrWho

Maybe down the road, one of your independent projects should be

titled "Foellinger Great Hall...Acousticical work of art...or

acoustical nightmare". Of course to complete this project, you

would require funding for a TEF analyzer...heh heh heh.

[mas]

I found it interesting that after all the objective math and analysis, that one of the authors' main reference points was a great seat in a concert hall that was "subjectively judged to be excellent".

I don't want to start this "subjective/objective" argument all over again, but do the authors ellaborate on how this subjective judging was done?

Also found the absorbtive coefficient charts to be interesting. Note what a coat of paint does to a concrete block wall. Is this because the paint prevents air movement through the concrete?

Let me turn this around...

What I find interesting is that there is assumed to be a gulf between models, measurements and the subjective experience.

Regarding time based measurements and their correlation to subjective experience, I suggest you become familiar with Richard Heyser's work (Time Delay Spectrometry, An Anthology, published by the AES).

You will see throughout the work numerous mention of how TEF has enabled the models to be improved and thus allowing for a closer correlation between assumptions, models, the measured results and the subjective experience. In fact, it is TEF that has ultimately confirmed the soon to be presented position that the Large Acoustic Space model is inappropriate for application in Small Acoustic Spaces.(p.179) But I will stop here rather than to get too far ahead.

Painting a surface has the potential to generally change the absorptive characterisitic of any porous surface. You will note that just about every manufacturer of absorptive material issues a performance disclaimer in the event their material is painted. In fact, I am not aware of any that do not. The included chart is a very abbreviated chart compared to others.

Likewise Doc's mention of the potentially dramatic effect of an audience upon a large room. This should not be surprising as you are replacing seats that are often concave hard reflecting surfaces that serve to focus specular reflections with soft bodies that tend to absorb and diffuse acoustic energy.

Also, regarding the hall, it would be a waste of money and effort if a TEF was simply used to identify acoustical anomalies leaving the hall an 'acoustic nightmare'. What is specifically makes possible is the detailed identification of the root causes of the problems and thus it, along with an understanding of the principles underlying acoustic behavior, enables a surgical correction of the problems resulting in a much more attractive acoustical environment.

Also...regarding TEF, one of the first insights it afforded was the detailed examination of the causes and subsequent cure for what is referred to as 'intelligibility'. It was precisely its ability to resolve what would ordinarily be seen as a summed response on an RTA or SPL into the component parts that exist as distinct signals in the time domain that each have a specific phase (arrival time) and an intensity. This ability to resolve a summed response acoustical field into its componant parts in the form of detailed direct signals, specular reflections and reverberant fields is what makes this class of instruments so radically different and so immensely powerful.

What may be missed in the presentation of the material is the significance of the TEF measurements. The construction of the various sound fields and their behavior is no longer a matter of theoretical speculation. the formulas are great, and the history of the process of their discovery is a fascinating exercise in human intellectual exploration. But with TEF and TDS, we no longer have to speculate regarding the nature of the theoretical sound field using an abstract model! We are able to look at the 'thing itself' in astonishing detail.

Thus, when Doc asked about the use of the formulas and their usefulness, one must ask what one desired to do. The TEF allows us to look at an existing space in immense detail. We not longer have to speculate as to what might be going on. Instead we are able to see what is really happening in incredible detail - in deed in much greater detail then our models have heretofore allowed.

Additionally, this insight has also allowed us to improve our models substantially, thus enabling us to increase the effective power of our modelling technology so that our predictive models correlate much more closely with that which they are used to model. But still, TEF is used to verify and refine any such modelled space into a finished product. Therefore, when one has access to, and an ability to directly analyze, the 'thing itself', it is silly to run to an abstraction and to treat it as more accurate. After all, a map is not the territory, not the menu the meal. TEF has allowed our representations to experience a quantum leap forward, but a firsthand examination of the 'thing itself' takes priority!

So ultimately, in examining an acoustic space, we take direct measurements of the patient itself, and treat these as preeminent! We do not run to a book describing abstract spaces and try to speculate on the characterisitcs of the patient based upon generalizations!

TEF has replaced the calculators.

[mas]

So...

Let's start talking about the various sound fields, and the nature of their characterisitc components.

May I suggest that we focus on the illustrations on pp. 162, 163, 165, and 210.

It is critical that we understand not only the basic definitions and components of the fields, but just what we expect to see and address in a real space.

Once we understand these, and the assumptions that come with them, we can begin to move at a much more rapid rate until we complicate things with the small acoustic space variations!

[Coytee]

Dang, this is just like college...

First day of class, I walk in, get the book and the teacher is talking about something that is 20 pages AHEAD of the beginning of the book (download).

I'm already behind

[]

[mas]

OK smart aleck, what do you need? [][]

Please let me know! If you would like PM me and tell me how I can help!

[PrestonTom]

"....

I found it interesting that after all the objective math and analysis, that one of the authors' main reference points was a great seat in a concert hall that was "subjectively judged to be excellent "

I don't want to start this "subjective/objective" argument all over again, but do the authors ellaborate on how this subjective judging was done?

...."

You probably got a bit short-changed on the answer to your question. Heyser's work is mentioned, but that is only a portion of what is out there. This has been a popular topic with researchers in Germany and Japan (the later having successfully used cross-correlation models for both description and prediction).

MAS is trying to educate us on a complex topic and I applaud him for that. But regarding your question about the objective and subjective measures, there is a large literature on this and the measures have been both reasonable and systematic. To delve into them, would require another large tutorial and I prefer that this thread be kept focused on the physical, time domain measures.

Good Luck,

-Tom

[mas]

If we don't have a solid grounding and a good understanding of this issue, how can you debate another issue which also is not well understood?

Not to mention the fact that there is a certain amount of irony in studying subjective response. And pyschoacoutics falls into the objective camp.

And I certainly am not going to enter into a debate over what qualifies as being subjective! []

How about one issue at a time![]

[DrWho]

I think gaspr makes a good point though...It's great to be able to see

what's happening, but there comes a point where one must decide what

direction the solutions are going to take. And then the very

experienced individual will be able to and probaby prefer to deviate

from the theoretical "ideal" and actually be a bit artistic (yeah I

know - far be it for an engineer to be artistic) []

But that's not to say that every "ideal" conclusion is completely

subject to subjective criteria. I think most of the variables presented

so far are providing the necessary background information required for

the detection and correction of valid problems that everyone would

agree "sound bad". There's too much crap available for correction to

worry about the things that full under subjectivity.

So all that broad crap mumbo jumbo to say that most of the material

presented so far doesn't need to rely on subjective opinion. The only

variable I think one could play with is the target RT60 for the

room....maybe I want things to be a bit boomier to make that pastor

sound more authoratative [] But anyways, that kind of thinking can only occur after you've gained a firm understanding of the fundamentals - and that's why every engineer will approach things from a different angle (cuz they think certain things are audible more important). It's all about compromise.

So when do we get to the small rooms? I've already seen most of this large room stuff before [A]

(that's not to say I've mastered the material...I'm just familiar with it)

[Coytee]

OK smart aleck, what do you need? [][]

Please let me know! If you would like PM me and tell me how I can help!

You're being MUCH more gracious than my wife usually is [] []

There's nothing you can help me with yet, I should just read the material (which will probably be WAY over my head) and drown from there [ap]

I was going to start reading it today when I got a phone call. Seems one of my clients was killed last month and his wife is now going through the process of getting their financial stuff "straightened out". Unfortunately, that soaked up the rest of my day.

I'll look to read some of this stuff tomorrow (when I get back to work [] )

[mas]

Coytee, you've got mail!

Smile!

Folks, right now we are trying to discuss the objective physics of the acoustical space. And issues of subjectivity are a red herring at this stage of the game. It is rather akin to debating whether or why you like ice cream. But that is not the scope of the thread. Instead we are going to examine the component parts of ice cream, and how these parts interact to become ice cream... the process. And maybe even how to add a few flavors to the ice cream. But I am not trying to tell you what flavor you like or if you should even like it. After you have a strong grounding in the physics, then YOU can decide what you want to do or what combination of attributes you prefer.

Some enjoy that particular thread as they can debate it for days without having to understand anything about the physics. Here it contributes nothing to the understanding of the behavior of sound fields and their component attributes. The fact remains that there are objectively verifiable levels where particular responses are audible - for instance a specular reflection whose intensity that exceeds the logarithmic rate of decay in a true reverberant field. Not only is such behavior able to be objectively measured and correlated, but it also agrees with subjective experience. Likewise the effect of summed reflections in a large space where , after addressing any of the component reflections, the inteligibility is dramatically improved, the result is able to be both objectively measured and subjectively verified. And I don't feel an overwhelming need to debate the subjectivity of one's being able to determine if, for instance, a spoken signal can be understood Besides, such factors can also be correlated with objective measures. And a discussion of how one decides what they like is not pertinent within the intended scope of this discussion.

Thus far what we are dealing with has little to do with subjectivity. And after we cover the material, you are more than welcome to use a blend of the various techniques to create whatever environment you desire. And I will leave you to determine whatever blend of characterisitics you like. As after all, while there are several manners of design that tend to garner the largest consensus of agreement over what sounds best, ultimately you will like what you like. And I have no desire to debate that. What I am trying to present is a 'best practices' approach to the basics of the physics of large and small acoustical spaces.

And while I understand that each person can ultimately decide which manner of final result they want, nevertheless, that environment is now able to be objectively analyzed and quantified! That is not a debateable issue.

The point is simply that we are now able to analyze the sound fields in their component forms. It is possible to have an objective measure of the environment - regardless of what balance of qualities you desire subjectively! And with such an understanding, you are able to propogate and replicate whatever subjective environment you desire!

But it does irk me just a little that even before we have an understanding of the basic physics that there is already a tendency to dismiss everything as the final experience is 'ultimately subjective' in that each person must listen to it! What does not bother me, is that if you have a solid grounding in the physics, you will be able to understand and replicate just such a 'subjective environment' at will, whatever the blend of qualities you ultimately find you desire.

To employ a very lame metaphor, I am not trying to tell you what color to paint your living room. But with an understanding of how the painting function operates, you can then choose the paint and be sure that it will appear on your living room wall in the precise shade you subjectively desire. Thus in the realm of painting, the behavior of paint is well understood. What color of paint you like is an issue you can debate at your leisure. But it has little bearing on a discussion of the physics of the process of painting.

Or, as I cannot resist beating this lame horse to a pulp [] (and trying to have a bit of fun in the process!), I am not interested at this juncture in trying to explain why you like broccoli and not spinach. My concern is simply with trying to explain how to grow broccoli and spinach, and to present several ways that they can be prepared. What suits your taste is an issue beyond the scope of the discussion.

So, in reference to Tom's pointing out that I am short changing the debate, I would disagree! He does not give me near enough credit! [] [] I am trying to ignore it! [] [] []

But it would be nice if here we would try to discuss the physical sound field characterisitics thus far presented without trying to jump to some ultimate conclusion of what you might prefer!

It is my intention after covering the basics of the physics, to present a little more information regarding the LEDE concept. The information regarding how the environment works and how to replicate the environment is not subjective. This is not being done in an attempt to tell you what to like. That is ultimately up to you. Like it or hate it...that is your albatross to carry. And that is another issue.

Rereading this I realize it may subjectively sound a bit terse. I apologize. But then you cannot see my grin. []

And by all means, if you want to discuss this or any topic (and I think that you will find me a rather congenial fellow with quite a healthy sense of humor and of the absurd!), and certainly before you get mad at anything I may say!, PLEASE PM me with a phone number or skype username and a convenient time and I would be glad to discuss any of these issues via voice over skype. Especially since calls to your home phone in the US (I am not sure about Canada) are free, and calls from computer to computer are always free! Most of these issues are easily addressed if we can intereactively focus in on the topic of concern.

Right now our focus is on understanding them within the context of a Large Acoustical Space.

So, does anyone want to discuss the nature of the soundfields and the relationship of their component signals???

Does everyone understand the significance of the ITD/ISD??

Does everyone understand the specific nature of the early specular refelections (Lre)?

Does everyone understand the definition of a true statistical reverberant field? A failure to understand this is going to cause no end to the confusion later in the discussion!

Also, a Large Acoustical Space is defined by Schroeder's room frequency, presented to show the size of the room necessary to support a truely reverberant space. Also, the concept of critical distance, and the measurement of the reverberant space via such tools as RT60 are useful to understand...

[mas]

So, in what may prove a vain attempt to get this moving along into the realm of acoustical physics... []

In an enclosed space we will focus first on what constitutes the sound fields in a large acoustic spaces. We will then look at some of the characteristics of a Large Acoustic Space (LAS).

We focus first on the LAS simply because all of the components are present.

First, may I suggest referring to figure 7-15 and the idealized acoustical response relative to level and time.

By examining the various signals in the time domain we are able to make a few convenient distinctions in behavior that characterize the various component sound fields.

Upon the stimulation of an acoustical space, the first arrival of acoustic energy is referred to as that of Direct signal (L_D), the acoustical energy that arrives at the listening position without reflecting off any surfaces. This energy dissipates in intensity consistent with the inverse square law. Thus for every doubling of distance traveled, the signal will be one half as loud.

Immediately following the arrival of the direct signal and prior to the arrival of the reflected sound energy, there is a small gap in time referred to as the Initial Time Delay gap, or more accurately, and Initial Signal Delay gap (ITD/ISD respectively). During this period the listening position experiences a short period of anechoic response. The nature of this gap should be easily grasped as you realize that the paths of the reflected acoustical energy are greater than the direct path, and as such take a correspondingly greater time to arrive. Additionally, the larger the space and the greater the distance of the source from adjacent reflecting surfaces, the greater the ITD/ISD will be.

Following the ITD is the first arrival of the reflected acoustic energy. The early arrival energy is appropriately referred to as early reflections (Lre). These are focused specular reflections characterized by reflections whose incident angles equal their reflective angles and arrive a short time after the direct signals. Typically, the reflections tend to retain much of their initial incident energy as well, following a decrease in intensity corresponding to the inverse square law (thus after traveling twice as far, they will be half as intense). In order to arrive in such close proximity to the direct signal, they necessarily have not traveled a distance that is much greater than the direct signal. They can be further broken down into their order indicating the number of reflective boundaries they have encountered. Hence a first order reflection has encountered one boundary surface prior to arriving at the listening position, where a third order reflection has encountered 3 boundary surfaces.

Note, depending upon the topology of the installation and the close proximity of reflective surfaces, there need not be any significant ITD/ISD before treatment. (An example is the attached sweep.)

Following the period characterized by the early specular reflections (Lre), we encounter reflections that have encountered many boundary surfaces. But this reverberant field has a set of very specific conditions that must be satisfied.

Diffuse (Reverberant) field (Lr) :

In a diffuse of reverberant sound field, the time average of the mean square sound pressure is everywhere the same.

The flow of energy in all directions is equally probable, which requires an enclosed space with essentially no acoustic absorption.

While direct sound experiences no reflections and decays at a rate consistent with the inverse square law (for example, every time the distance traveled doubles, the intensity decreases by one half), a reverberant field remains at a constant intensity level as long as the sound source continues to input a relatively steady source of acoustic energy.

In physical terms, reverberation is a series of multiple reflections, decreasing in intensity with time, so closely spaced in time as to merge into a single continuous sound, eventually being completely absorbed by the inner surfaces of a room.

This reverberant field assumes a statistically well-mixed environment where specular reflections (those whose incident angle is equal the angle of reflection) are no longer distinguishable. Specular reflections in a reverberant space are audible.

Please take a look at the 3D display in figure 7-18D (p. 163) and figure 8-13C (p.183).

A reverberant field can also be characterized by what is called an RT_60. RT₆₀ is the time required for the reverberant field to decay in intensity by 60 dB once the steady state stimulus is removed.

An RT₆₀ of 1.6 sec approximates the decay time expected for a minimum density sound field.

In a truly diffuse reverberant acoustical space, a high RT₆₀ is not harmful to live speech until reverberation times of approximately 5-6 s at 2 kHz are reached. Many times in reverberant spaces, if trouble occurs it is not due to the length of time it takes for the energy to decay, but instead the culprit is a focused (summed) energy. Addressing any of the component pathways of the summed specular energy quickly resolves the issue.

What reverb is not: (p.182)

A significant and valuable observation is that of how many folks ascertain the liveliness of a room. Often one stimulates the room with a vocal stimulus or claps their hands in order to listen to the rooms response, and then mistakenly thinks they are determining how reverberant a space is as they listen for the time delay between the stimulus and the level of the first reflection. This is NOT reverberation! Nor are echoes evidence of a reverberant field.

In this scenario, reverberation is the persistence of the sound in a room after the original sound has ceased. For example, reverberation is the sound you hear just after you shout in an empty gymnasium. The sound of your shout persists in the room and gradually decays. It is not an echo!

Rather the reverberant field contributes to the noise floor and effects the signal to noise S/N ratio of the space.

Also significantly mentioned:

The effect of reverberation on intelligibility is far less than single late high-level reflections, inadequate S/N, or comb filters generated by sources within 1 foot or less of the primary source.

Manfred Schroeder defined the large room frequency ( F_L ) as the frequency above which a large number of room modes will be excited to vibrate at the source frequency (p.167):

(and as I have just dicovered, this forum does not support the importation of the Equation Editor... )

V=K²[RT₆₀ / F_L²]

An RT₆₀ of 1.6 sec approximates the decay time expected for a minimum density sound field.

Thus the minimum volume for a large room becomes:

For music exhibiting a response to 30 Hz:

V= (11,885)² (1.6 / 30²) = 251,117 ft³

Or, for music exhibiting a response to 20 Hz, this volume grows to:

V= (11,885)² (1.6 / 20²) = 565,013 ft³

Therefore,

For general purposes a large acoustical space used for music will be one in which the internal volume is: >=250,000 ft³, or for an extra 10 Hz of LF extension to 20 Hz, =>=565,000 ft^{3 !}

I think that most folks will agree that most home listening spaces do not qualify as Large Acoustical Spaces, and thus fall into the small acoustic space category!

Also, in a large acoustical space, one of the most important concepts is referred to as the Critical Distance (p.199). Critical distance, Dc, is the distance at which the reverberant sound field is equal in level to the direct signal from a sound source. I will not go too deeply into its derivation here. But you should understand the concept.

So, in Large Acoustical Spaces, it is also important to address the presence of audible specular reflections within the reverberent space Thus, two fundamental concerns become:

1.) What is the level of the reverberant field?

2.) How uniform is the reverberant sound levels distribution in the space?

[DrWho]

So ITD = ISD?

[mas]

ITD = ISD.

As is stated in the text, several popular labels are actually used as slang, in that we misuse the language and pervert the meaning of the concept in doing so...

Two such labels are "time align(ed)" and "Initial time delay" gap.

We cannot align nor delay time.

We can, however, align or delay signals within the time domain.

[mas]

Regarding a reverberent space, the definition should provide some real insight into the nature of just what we are dealing with...

In a diffuse of reverberant sound field, the time average of the mean square sound pressure is everywhere the same.

The flow of energy in all directions is equally probable, which requires an enclosed space with essentially no acoustic absorption."

Thus the reverberant field cannot be resolved into any particular reflective path. The summed pathways are so random and so distributed that you cannot identify any particular reflective pathway that will diminish the field.

It is what is commonly referred to as "well-mixed".

The developed field also is maintained at a relatively constant level, relatively independent of any momentary transients.

It is also sufficient in intensity to allow for the signal to decay 60dB with respect to time once the stimulus is removed.

[mas]

Small Room Acoustics Pt 1 of 3

[mas]

SSE Small Room Acoustics Pt 2 of 3

[mas]

SSE Small Room Acoustics Pt 2 of 3

[mas]

Well, so much for a discussion of the material... Doc has asked a few questions and we have also encountered the dreaded "how do we know what we like" issue.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

If anyone has taken a look at the small room material, the most significant thing you should have noted is that almost everything you spent reading about the reverberant field is moot.

A small room does not support a true reverberant field. The room is actually a mixed environment. While it may potentially at higher frequencies exhibit a small component of diffuse reflections, it is comprised predominantly of focused specular reflections that are audible. The Lre early reflections predominate. Thus, the room is primarily a mixture of room modes (at the frequencies blow ~300 Hz) and specular reflections (above 300 Hz)

Thus there is no critical distance and there is no meaningful RT60 measurement, as the well mixed diffuse sound field does not persist long enough in time. So, while the definitions provide an ideal by which to compare the real, the ideal does not exist in a small acoustical space.

You are therefore left with a room that is characterized predominately by room modes below 300Hz and with focused specular reflections above 300Hz. You might think of the room as the ultimate Mission Impossible nightmare (sans Tom Cruse- he just makes the nightmare exponentially worse- and no amount of nifty techniques will solve that problem!), where you have a room to penetrate that has thousands of times more laser sensors just waiting to foil your listening pleasure.

Thus, to overly simplify, our need is to control the early reflections and create an effective ITD/ISD gap, and then to create an environment where the early reflections Lre are well behaves and not intrusive, as well as to diffuse the remaining Lre specular reflections into a pseudo reverberant field.

We also need to understand much more about the characteristics of absorption and diffusion, as their actual behavior is much different than most assume.

For instance, and absorber is only partially an absorber! It is partially absorbent in a frequency dependent passband. But perhaps more significantly, it is also seen as a hard reflecting surface as well. This should stimulate a few questions.

Diffusion is also a complex issue, as we have heard mention many styles of diffusion that likewise treats the entire audio spectrum as if it were 'one thing'. But diffusers are also frequency dependent. And many of the recommended techniques, such as the poly-cylinders, while not technically wrong, are actually "scatterers' - simply breaking a focused specular reflection into multiple specular reflections, albeit with a lower component energy. But they are nevertheless still focused reflections and not diffuse, and as such, they have the potential to reman audible.

Thus we must find more effective ways to control the early reflections in order to adequately define a satisfactory ITD/ISD; and we must discover more effective ways to diffuse the specular reflections into a sound field more closely resembling a 'well-mixed' and diffuse field - albeit with a shorter decay period than a true reverberant field.

Sound simple? The concept is actually rather simple. However, the manner to accomplish this has proven more complex than originally envisioned. The reason for this is that while we need to control a few early reflections, but we still need the acoustical energy to provide for the establishment of a pseudo-reverberant' field. Plus the fact that the absorbers are not completely absorbent, but act as the very thing we are trying to control and minimize - 'hard' reflective surfaces!

But there are a few current techniques that seem to present an relatively effective method. and a yet few may not be what many of you have assumed. So you might want to read ahead, especially if you thought the solution was a simple as scattering lots of absorptive material around and simply scattering a few of the specular reflections. The potential problem here is that of creating a relatively dead space while at the same time increasing the ratio of 'later' arriving specular reflections that still exhibit sufficient energy about the well-behaved exponential decay rate - hence potentially remaining audible.

Why can't things be simple!? <?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /> []

Luckily we now have tools that allow us to see exactly what is going on in the room, and to break an extremely complex system into its component parts.

But while it is possible to take the complex system apart, it is not quite enough to simply look at the pile of disassembled parts lying about on the floor and think that we have sufficient information to reassemble them into a desirable and functional relationship.

And hence the need to become familiar not only with the pieces and parts which have not heretofore been individually identifiable, but we need to understand optimal effective goals before we can employ methods of effectively manipulating them within the total context of a complex interactive system, where changing one element effects many other attributes, in order to effectively accomplish the desired goal.

[PrestonTom]

MAS,

Maybe I can start off with some of the questions.

From the first article: Large-Room Acoustics:

The first equation Pg 167 of Large-Room Acoustics) is rather sobering (computing Volume or computing FL). The room would need to be very large indeed. I played with the numbers and here are my comments and questions.

1. Why is the RT60 of 1.6 secs used. I have have seen this elsewhere also. Is it a target value for some applications?

2. I assume the RT60 of 1.6 sec is actually frequency dependent. My thinking is that with a high frequency (small wavelength) the sound would not diffract around a multitude of objects and obstacles in a room. Also many surfaces will easily absorb if not diffuse the small wavelengths. It is difficult to imagine that the high frequencies will "bounce" around for as long of a time. Your comments, or is this addressed later.

3. Last question on RT60. When reading Toole, he conveys that this is properly a measure of the room, and that the source should really be omni-directional. Yet our endeavors are to describe the speaker/room as a system or interface. As such an RT60 can be inlfuenced by the directional charateristics of our source (in my case the speakers). Your thoughts about RT60 in general re: speakers in a living room?

4. I played with the numbers from the first equation. Using the typical size of a biggish living room and even setting the RT60 to 0.4 sec (1/4 the prescribed value of 1.6 sec). FL frequency would barely be low enough to hit the voicing fundamental of a female voice (about 200-250 Hz). Again, emphasizing your point that living rooms are not "Large Rooms"

I'll try and be more timely in my reading,

-Tom