FR vs time domain  

"Time domain issues" could refer to about half a dozen completely different things! You could hardly pick a more general term. You need to get much more specific.

It could refer to the alignment of the drivers within a speaker enclosure, in-room sound reflections of various frequencies and amplitudes, room correction software questions, etc. etc.

The answer is complex, so I suggest you look at a great book on reproduction of sound and acoustics:

Floyd Toole's Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms

Hi Bob. Mathematics tells us that time domain and frequency domain are 100% linked. They are two representations of the same thing. Fix frequency domain and time domain follows. It has to. It has no choice . Here is a quick proof: http://en.wikipedia.org/wiki/Fourier_transform

"The Fourier transform is a mathematical operation with many applications in physics and engineering that expresses a mathematical function of time as a function of frequency, known as its frequency spectrum; Fourier's theorem guarantees that this can always be done."

Nice thing about frequency domain is that it is intuitive. You can see a peak at 30 Hz. But if I showed you a set of digital samples which by definition embodies all frequencies, you would have no easy way to do that.

Kal's reference from Dr. Toole explains and demonstrates why the above is true.

Time is just one of the ways we can look at a signal.

One of the strongest measurement platforms (but rarely used now) is TEF. One way to think of measurement is to make a "TEF CUBE". Take a square block and label each of 3 sides (so that they all touch in a single point) Time Energy Freq.

Buy changing the way you look at sound, you can lok at either Time or Freq or Energy. OR you can look at any 2 on the same graph. Or you can turn it so you can see all 3.

For example the typical "freq response" graph is showing you Energy and Freq-with no regard to time. The Time alone is the impulse response of a system and so forth.

Ads others have stated-saying "time" can many different things to different people. We need to know more specifically what you are talking about.

As a general rule-using an eq to cut a "bump" in the response is not a problem. And very often it will also correct a phase problem.

The problems often start when trying to "boost' a "hole/dip" in the response.

THEN you first have determine what is causing the hole/dip. Is it narturally there in the response of a single driver? If so, then a "little help" from an eq is not always a bad thing.

HOWEVER-if the dip is caused by a time domain artifact (reflection off of a wall-signal arrival (time arrival) of different drivers covering the same freq range-say a mid and high around crossover and other causes), then an eq is not going to "fix" the problem. It might actaully help it out-ONLY IN THE MIC POSITION LOCATION-but will make it WORSE in other areas of the loudspeaker coveage.

When it comes to "fixing dips", there are often many more things that need to be looked at-and most of the time the tool to look at them is the time domain measurement. Or simply move the mic a few feet and see if the exact same problem is still in the response. If it is still there-but has changed freq-then you have a time problem of some sort.

The most a "time problem" (reflection) can boost a signal is 3dB. But it can cut a signal almost to infinity. So you will not see a 6dB "bump" that is a time problem.

And if you are getting a 3dB "bump" (due to comfiltering) you will ALSO see a whole series of deep notches-that you CANNOT fix with eq. And I would be more concerned with all the notches-than a few small "bumps".

This is an enormously complex topic, and I'm certainly not entirely equipped to address it fully.

However, conceptually,...consider this;
EQ'ing minimum phase energy is ok, and EQ'ing the non-minimum phase stuff isn't typically a good idea. It's all about the boundaries, and the size of the wavelengths below the transition (large relative to the dimensions of the room), and the size of the wavelengths above the transition frequency.

We hear a combination of both the direct and reflected sound. So adjusting the amount of energy your speakers produce at a given frequency high enough to propagate above the transition, changes both the direct sound and the reflected sound. This is the problem, because the wavelengths are small enough compared to the room size, that phase issues exist due to the path lengths and complex constructive, and destructive acoustic behavior.

Frequency EQ'ing below the transition frequency is typically acceptable because the energy is minimum phase. Thus changes in frequency EQ'ing are easily accomplished because the wavelengths are so big that direct and reflected energy don't encounter significant phase issues.

Clearly, there are other contributors that possess the technical savvy, and literary chops to do this more justice than I.


Good luck

you have that backwards...
if you attenuate high-gain indirect signals that superpose with the direct signal to produce a comb-filter interference pattern (as measured at the listening position via the frequency response), then you will reduce or eliminate said frequency response anomalies.

high-gain indirect signals and their incident boundaries are determined with respect to the time-domain. knowing the total time of flight of the reflection path with respect to the direct signal allows one to work backwards to identify the actual path and actual incident boundary.


this also is not correct. the frequency response in the specular region details you NO information about the boundaries incident of such high-gain signals that superpose at the listening position with the direct signal to cause anomalies in the frequency response. it is NOT intuitive besides the fact it tells you you are situated in an interference pattern - it does NOT provide you any further information to resolve specular region frequency response anomalies.

the frequency domain does not detail to you any information regarding the arrival time and gain of the indirect signals that cause the frequency response anomalies due to superposition of direct and indirect signals. identify the high-gain signals in the time-domain - attenuate these and the frequency domain follows.

Yes, and it's not really all that complicated. The main "time" issue in rooms is ringing due to resonance fostered by opposing surfaces. Sound from a loudspeaker passes by your head and hits the rear wall behind you, bounces back toward the front wall, then back to the rear again, and so forth. Ringing occurs at frequencies whose wavelengths exactly fit between these walls, and the ringing continues until eventually the sound decays to silence. The result is that some frequencies sustain longer than others, after the original source has ceased. The waterfall plots below show both the response and ringing, where the "mountains" come forward over time. The top graph is an empty bedroom size space, and the lower graph is the same room after adding bass traps to tame the resonances.

Note that this is different from simple reflections colliding with the direct sound and with each other. That's called acoustic interference, and it too is time-based, but the result is a change in frequency response. Acoustic interference can happen at any frequency, as opposed to ringing that happens only at frequencies that fit exactly between boundaries.


An equalizer can only lower the level of the ringing peaks, but it won't reduce the decay times.

--Ethan

if one is interested in the unity of the frequency and the time domains (and how they are different perspectives of the same thing) - you can investigate the Heyser Spiral and domain maps...

and viewing the waterfall for the modal region is not the same as viewing from the PoV of the "time-domain"

It certainly is from the perspective of most HT enthusiasts who ask questions in audio forums.

--Ethan

I could post the domain map showing how all measurements in both the time and frequency domain are related and how all are but various perspectives on the same unified 'thing' - the "Analytic", but the last time I did that Ethan claimed it made his "head hurt". And we certainly don't want that!

So, maybe this will help one see that similar direct and indirect reflected signals that arrive at different times combine (the proper term is: superpose) destructively, resulting in polar lobing and comb filtering.

And that by addressing the later arriving signals in the time domain, that the quality of the frequency response and of the subjective experience can be improved.

But by adjusting the frequency content by EQ, you CANNOT change the time relationship of variously arriving direct and indirect signals! (And EQ ONLY works in the region below about 80 Hz as the particular wavelengths involved are within 1 cycle of each other in time - a condition referred to as 'minimum phase'). This is NOT the case with specular reflections where the signals are non-minimum phase.



Also note, the goal of this post is NOT to suppose that absorption is the only or even the preferred treatment. It is a simplified case illustrating that by the SURGICAL removal of ACTUAL high gain reflections which as a result of superposition are causal to the polar lobing that in the frequency domain appears as comb filtering anomalies, that the result is the elimination of problems exhibited in the derivative frequency domain.

Be careful, as other treatment options such as diffusion that retain energy and which cause the large polar lobing and comb filtering effects to become very small and closely spaced are not shown.

+1 ...address issues in the time-domain and the frequency response will follow!

Yes, stated simply, events in the time domain are "casual", while comb filtering anomalies in the frequency domain due to source-room interaction are derivative.

And the real advancements in acoustics that have occurred in the last ~40 years are directly attributable to our 'new' ability to view the behavior of sound in the time domain.

What "caused" you to put quotes around "casual?"

You can't have something backward when it is two faces of the same thing. And you absolutely can change the time domain response (reduce ringing) by fixing the frequency response. From Dr. Toole's Sound Reproduction:



As the math predicts, using EQ to tame the frequency response had representative (and positive) effect in time domain.


Such a thing is easier said than done at low frequencies given the thickness of the material required. Whereas application of EQ to bring down the peaks (assuming sufficient resolution) works without and generates the desirable effect in time domain as shown above.

If you mean high frequencies, my weapon of choice is getting speakers with good power response than try to eq that with acoustic material. I understand not everyone agrees with this and that's cool.


I realize some people enjoy being human sonars but it is not for me .


You say it is not correct but then quickly qualify it to be in the specific region? What about the graph in Flyod's book is non-intuitive? What was intuitive about that time domain representation?

just when you think 'forums are so damned boring cause there are no substantive discussion' along comes a beauty!

You have to fix time FIRST, always.

I can't say exactly the cause of the confusions, eg 'science says they are exactly interchangeable', but I suspect we are talking narrow considerations?

I wonder if the graph from toole amir posted is narrow in the sense it could be a single source within the room??? Ok, sure, apply eq and see that corresponding changes in time.

Prob something about min phase systems. THEN yes, what one does in one domain maps into the other (they say, and I fully accept)

But real world experience quickly shows up the complexities. Go on to *any* forum and all that will be discussed is EQ. Understandable BTW, and of course when you have a hammer to fix problems there are only nails, never nuts.

My case is a good example, I have basically four bass sources in the room. You don't have to beleive me natch, but you WILL have varying FR measured with varying time arrivals of the bass impulses (what we'd call time alignment I guess). You CAN apply eq to each of these different responses and end up with the 'same fr at the lp'.

Yet, clearly, it is the varying arrival times that is the cause of these differing FR's, which will not change no matter what eq is applied, even if the response is 'made the same at the lp frequency wise'.

The question then becomes 'are these different time yet same fr situations' audibly distinguishable? They are, there is a clear difference in perceived sound.

There is a lot of discussion around about this question, particularly in the bass. The consensus has always been 'delays in the bass are not audible' which I disagree with, having done it many times myself. (leaving aside the fact that, unless equalised, there are clear differences in FR which alone should be audible).

So, if a dip or peak is caused by non coincident arrival times of the signal it is clearly not appropriate to fix it with as crude a tool as eq (always assuming you have other means to fix it of course, else yeah, eq it it, it's 'all ya got')

This is looking at it from another angle than the room and it's reflections as outlined by others above, so 'time' can encompass many things to different people.


It does not only apply in the bass either. Measure your speakers, then 'move the tweeter back one inch' and re-measure. There will be very clear fr changes, which CAN be eq'd back to the original (using one third say). Yet we know the time has changed no matter the end result fr wise. Again, is it audible? Naturally there are limits to human perception and this example (plucked from thin air) may fall into that category, but yes, differences in time are audible.

It may not appear to you as 'ha, the tweeter is lagging' or anything silly or clear cut as that, but the perception WILL change.

Ok, you can't move the tweeter to observe these things...move one speaker forward an inch. Eq it to the same fr as before (say one third or so). You WON'T hear it as 'the left speaker is early' or whatever, but I can guarantee you you will hear the difference (it does not manifest as we might intuitively think)

(In any case, this type of discussion *usually* revolves around the bass region as that is where we add subs, and where we usually use eq, but rest assured it is relevant in all parts of the spectrum)

Geesh.

You selectively edit a case where Toole is specifically talking about a MINIMUM PHASE modal condition within a context where he specifically decries its use for non-minimum phase conditions - precisely what we are talking about!!!!!!!DUH!!!!!!!!!!!!!!!!

I am glad you quoted that source; but unfortunately you failed to read and understand the REST of what Toole specifically wrote!

You see, Toole calls for "Intelligent Equalization", not the willful ignore-ance of large dominant behaviors such as non-minimum phase specular behavior that occur above the Schroeder transition frequency typically in the range of 200-300 Hz where modes no longer dominate.

Note he also correctly advocates ONLY trying to EQ modal PEAKS in MINIMUM PHASE conditions.

This specifically does NOT apply to the larger condition of which we were referring in regard to specular behavior! Believe it or not, there is more to acoustical behavior in a room than modes!

And Toole specifically denounces trying to use EQ in non-minimum phase conditions! In fact, that is one of the reasons cited for EQ having earned its less than stellar reputation as a result of it having been so commonly and grossly mis-applied.

Its all the more frustrating when folks utterly miss the main point of the very selectively edited article that they erroneously assert as a disproof of the larger case where the limitations are in fact fundamental.

So, here is more selections from the Toole paper Acoustical Design of Home Theaters with some pertinent issues emboldened:

This overview is intended to set a context within which readers can apply the more detailed technical information in the accompanying paper: “Loudspeakers and Rooms - Working Together”. At some point, I plan to improve the relationship between the contents of the two documents, but for now there will be some redundancy, and stylistic differences. Some people come to this topic thinking that, as is some other things, that there must be a simple way to do acoustical design, a kind of cookbook, that anybody can understand. I wish that were so, because it would simplify all of our lives. As it is, achieving truly good sound in rooms requires knowledge of how sound behaves in rooms, and some effort – or more than a little bit of luck.

.....Getting good sound in a room. How is it done?
The science of room acoustics has mainly developed in the context of live performers in concert and recital halls. Relatively little scientific effort has been put into understanding sound in small rooms, especially as it relates to sound reproduction. The irony is that far more music is listened to at home, than in concert halls. Still, there has been significant progress, and we are beginning to understand some of the things we can do to ensure decent sound quality in the semi-infinite range of room sizes, shapes, arrangements, and furnishing variations that exist. It sounds as though it might be difficult. Well, it is not nearly as complicated as “rocket science”, but neither is it a totally straightforward “cookbook” exercise. You will have to do some work, and think a bit.


(pertaining to Room ratios)

So, why did this whole business of special room ratios get started? Actually, it began decades ago, very scientifically, with serious minds trying to optimize the performance of acoustical reverberation chambers, where it was intended to conduct precise measurements of sound power. From there it got picked up and elaborated unrealistically to include rooms, like ours for sound reproduction, where those ideas simply do not apply.

...If the room is not rectangular in shape, or if there are large openings in one or more of the walls, predictive calculations will not work well, or at all. In this case, one must revert to measurements, and trial and error repositioning of subwoofers and listeners. This is not a good situation to be in. Non-rectangular rooms do not eliminate room resonances, they just make it impossible to calculate them simply.

...
Step Four: Improving Bass Performance

It is in these situations, when you have exhausted the acoustical possibilities, that equalization of the right kind can be very helpful. However, it must be done intelligently, since there are some things that equalization can correct very well, and other things that it is a mistake to try to fix.

Not everybody agrees with equalization, accusing it of introducing “phase shift”, and other nasties. Well, there is no doubt that equalization has acquired a bad reputation over the years, but from the perspective of what we know now, it has been absolutely deserved. There are four principal reasons:

1. The popular measuring instruments, 1/3-octave real-time analyzers, do not have enough resolution to describe the problems accurately.

2. The popular equalizers, 1/3-octave “graphic” equalizers, do not have enough resolution to address the problem resonances specifically, without doing a lot of “collateral” damage.

3. Attempting to fill deep frequency response dips caused by acoustic cancellations or nulls is an absolutely futile effort, because no matter how much sound energy one pumps into a room the cancellation persists. All that happens is that amplifiers clip, and woofers distort, or worse, destruct. The only solution to this kind of problem is to relocate the loudspeaker or the listener, whichever is sitting in the null.

4. Equalization is attempted at too high a frequency. Low-frequency room resonances behave like minimum- phase phenomena, and addressing them specifically with parametric filters is a true solution. Above a few hundred Hz, the situation is very different, because we are using steady-state measurements to examine a complicated combination of direct and reflected sounds – time domain phenomena.

The measurements may show “comb filtering” that is alarming to the eyes, but the ears hear only the natural sounds of a room – not necessarily a problem at all. If the reflections are perceived to be too energetic, the solution is not equalization, but rather the addition of some strategically placed sound absorbing or diffusing devices. As stated earlier, if there are obvious sound quality problems at middle and high frequencies, the only true solution is a properly designed, room friendly, loudspeaker.

Intelligent Equalization

So, how do we do “intelligent” equalization? (Note: He is addressing MINIMUM PHASE MODES, Not non-minimum phase specular reflections!)
The first step, is to work with high resolution measurements that can show you what is really going on, the 1/3-octave real-time analyzers simply do not cut it. The ability to average measurements made at several locations within the listening area is a big help, because it will tend to attenuate the interference dips that equalization cannot fix, and help bring into focus the room resonances, that equalization very effectively addresses. Then the task is to decide what to change with equalization. A safe place to start is to use the equalizer to pull down peaks, and to avoid trying to fill holes. A broad, gentle, depression might be filled, but do it in stages, listening to see if something positive is actually happening. It is wise not to add more than a few (say 3 to 6) dB of boost. If you do add boost, remember that each 3 dB doubles the power requirement from the amplifiers, and the loudspeakers. Everything will be working much harder. Preferably, try to find acoustical ways to fill holes, and use the equalizer to smooth out the peaks. If there is a persistent notch, try to identify which mode is involved, and whether the loudspeaker or the listener is in or close to a null. Move the suspected element a foot or so away and see if there is improvement. (Note: Distance effectively equates to time.) The room mode analysis program is a big help in this – assuming you have a rectangular room. If all attempts fail, be content that at least the resonant peaks are gone, and that narrow dips are much more difficult to hear.

Here is an example, taken from the hands-on workshop held after this course at the 1998 CEDIA convention. The room we were given to work with was clearly going to be a problem (which we liked), because it had rigid masonry walls (good strong, high-Q resonances), and dimensions that were in simple ratios to each other (8 x 12 x 24 feet). With a TV at the end wall, a good viewing distance of 12 feet put the prime listening location close to the mid-point of the room. This puts the listener near a null for the first-order length mode (1130 / 2 x 24 = 23.5 Hz). It is difficult to get very concerned about this, because there is almost no useful information at this low a frequency, but we might try to ensure that the listener’s ears are just ahead of or just behind the half-way point of the room. However, at the second-order modal frequency, 47 Hz, there is an abundance of audio information, and here the listener is sitting in a broad pressure peak.
Figure 2 shows what we measured for the subwoofer, by itself and, as predicted, there was a prominent peak right around 47 Hz. When we listened, the bass was flabby and boomy, with a “one-note” quality. Even movie explosions sounded fake. To address this problem we dialed in a single parametric filter, set to 47 Hz, with the appropriate bandwidth, or Q, and simply turned the resonance down. Room resonances at low frequencies behave as “minimum phase” phenomena, and so, if the amplitude vs. frequency characteristic is corrected, so also will the phase vs. frequency characteristic. If both amplitude and phase responses are fixed, then it must be true that the transient response must be fixed – i.e. the ringing, or overhang, must be eliminated. (The definition of a minimum phase condition!) Figure 3 shows that this is so. Equalization of the right kind can work. Notice that we completely ignored the acoustical cancellation dip at about 73 Hz.


(Figures have been omitted)

The evidence of this series of measurements is quite clear. The 1/3 -octave measurements lulled us into a sense of security by presenting data that did not look all that bad. Certainly there was no evidence of the sharp peak and dip that was obvious in the high-resolution measurement. If we thought we could tweak the performance a little by using a 1/3-octave graphic equalizer, we did not succeed. It can be seen that, just as the 1/3-octave measurement failed to show any evidence of the high-Q resonance at 47 Hz, the 1/3-octave equalization failed to get rid of it. The annoying ringing, or bass “boom” was almost as strong after, as before, the equalization. It is no wonder that equalization has acquired its bad reputation. We threw away some good bass energy, and left the annoying boom. (The result of trying to EQ a combination of minimum and non-minimum phase conditions - which effectively renders the condition non-minimum phase.)



And since some do not understand the distinction between minimum phase modal behavior and non-minimum phase specular behavior, let’s quote Toole further from Loudspeakers and Rooms for Sound Reproduction :

7.2 Below the Transition Frequency

…At frequencies below the transition zone, investigating what is heard must involve measurements made within the room, with the loudspeaker at its intended location and measuring at the intended listening location. All else is of academic interest. Also because of standing waves, different listening locations will experience different low frequency responses. At very low frequencies, wavelengths are long compared to room dimensions and periods are long compared to transit times within it, so what is heard is like listening through a complex filter. At subwoofer frequencies, at least, the behavior of room resonances is essentially minimum phase [63]–[65], especially for those with amplitudes rising above the average spectrum level. This suggests that what we hear can substantially be predicted by steady-state frequency-response measurements. It also means that both time- and frequency-domain correction is possible with minimum phase parametric filters.

9.2.1 Above the Transition Frequency (The specular regions)

• Steady-state in-room measurements may be indicative of certain problems that are audible, but they are of little use in assigning corrective measures. One cannot separate problems in loudspeakers from problems in rooms, and each requires different solutions. For example, a dip in a room curve could be caused by destructive interference from a strong reflection or standing wave, a dip in the frequency response of the loudspeaker, or a reduction in the dispersion of the loudspeaker. Some of these problems require acoustical or electro-acoustical treatment, and others can be corrected by equalization. Equalization schemes based only on room curves involve a risk that the wrong corrective measure will be applied to a problem.

In simple terms: EQ is ONLY effective in minimum phase conditions! Non-minimum phase systems must be deal with their constituent interacting components in the time domain,

And a note about treatment that many would do well to read several times:

• Any device inserted into a reflected sound path—reflector, absorber, or diffuser—should perform uniformly well at all frequencies above the transition frequency region, say, 200–300 Hz. This is in order to preserve the spectral balance of the loudspeakers, to uniformly attenuate the full spectrum of reflections, and to ensure that the precedence effect is maximally effective.

9.2.2 Below the Transition Frequency

• Equalization is the final touch, and, properly done, it works because low-frequency room resonances behave as minimum-phase systems.

Hmmm. Your editor seemed to have missed bolding/highlighting some sentences, so I though I'd take the liberty to correct it.

cheers,

AJ

p.s would you mind forwarding this to that Winer guy? LocalHost and his little wallmount JBLs is too much of a lost cause. Thanks.

what do you contribute other than yet another plug for your business?

people want to lean something you both know nothing about nor are interested in.

bugger off

I have cornered the market on properly designed room friendly loudspeakers?? Sweet! Who knew? Thought they were widely available to all above knuckle dragging IQ.


Should we show them what a world class/as good as anything on the planet/ properly designed by DEQX/room friendly to the point of gauze-bandaids stuck all over, speaker looks like? Would that help?

cheers,

AJ

First of all, I did not respond to you. I was responding to locahost. And to the specific comment that frequency correction does not result in time correction. So I showed him example of that being the case. I assume you agree with that visualization yet I didn't see you be up in arm over accuracy of his statement.


No I didn't. Thanks for the insult anyway. Is there a discussion thread where people are professional here? If you keep this insulting tone going, you will need to find someone else to exchange posts with.

Addressing your point anyway, I provided a proof point that time domain did follow frequency domain. That is the point that was disputed by localhost.


There was nothing in my post about "willful application of EQ." Nor did I suggest to use EQ above transition frequency. You are fabricating an argument for me and then arguing about it not being correct.


That's right. He also scuffs at screwing around with the high frequency response of the speaker and instead recommends getting speakers with good power response.

Precisely what I stated as I responded to localhost.

I do believe it. But when OP asks for a simple explanation, I am not going to write a book as you just wrote in your post. Why not ask OP if he understood what you have explained?


That's right. As I noted, he recommends getting speakers with proper power response.


I have spent considerable amount of time with Floyd and I have complete understanding of his point of view. There is nothing you quoted from Floyd that is new to me or I disagree with. All you had to do was ask me if I meant what you think I did above and I would have answered and saved you your frustration.

Hope you feel better now .

absolutely nothing to do with my point. Good to see the misdirection and dancing beginning already.

as I said in another post about you, just watch his words and apply the concept hypocrite. Dance one two, deflect.



red herring, one of your favorite expressions no? Again, think of the term hypocrite.

you have nothing to contribute other than your usual venom.

go away.

You've ever had one?


Nope, pertains very specifically to gauze/bandaids...and the root cause...world class/good as any on planet/non-delusional objectivist and all

cheers,

AJ

LOL! Then instead of asserting it, implement it.

What part of localhost's specific reference to "high-gain indirect signals " in the "specular region" directly related to behavior indicated in the ETC response lends itself to a non sequitur reference to special case minimum phase modal behavior?

Time domain does not always follow the frequency domain. Simple point. This is local and dragon's point. Amir, your statement was too general. You got a book in response pointing that out. A book wasn't necessary, but they are none-the-less correct; time only follows frequency for low frequency minimum phase stuff. I'm sure you misspoke. Would be easier to just say that.

Terry, per the above, you are wrong. When dealing with low frequency minimum phase phenomenon, which bass in residential rooms absolutely is, time certainly does follow frequency. Your anecdotes do not convince me that the considerable body of empirical measurements and theoretical analyses are incorrect.

Actually frequency 'follows' time in both the modal and specular realm.

Time domain behavior is causal in both realms. It results directly in the in phase reinforcement causing modal reinforcement just as the non-minimum phase time relationships cause the destructive polar lobing in the specular regions.

It is simply due to the special case of very long wavelengths in small bounded spaces that make the time offset less than 1 cycle that renders the low frequencies in this setting as minimum phase.

Modal behavior is a special case due to the time relationships of long wavelengths in a relatively small bounded conditions.

Sure. That's why I never said otherwise.