First order/Time Phase-Coherent speakers discussions


"The game is done! I’ve won! I’ve won!"


I would like to use this thread to talk about this subject which I find rather fascinating and somewhat difficult to get my hands on. I went through a course in electromagnetism in college and I have to say this is even more confusing and you won’t find the answer in calculus, physics, Einstein relativity be damned it’s not in there either and definitely not in quantum physics. Listening to the "experts" from Vandersteens and Stereophile but ultimately it all came down to a missing link sort of argument ... something like this:
"Since if a speaker can produce a step response correctly, therefore it is time-phase coherent, and therefore it must be "good".

It’s like saying humans come from chimps since they share 90% genetic content with us, but we can’t find any missing links or evidence. FYI, we share a lot of gene with the corn plants as well. Another argument I’ve heard from John Atkinson that lacks any supporting evidence and he said that if everything else being equal, time-phase coherence tends to produce a more coherent and superior soundstage, but to the best of my knowledge, nobody has been able to produce some semblance of evidence since there is no way to compare apples to apples. Speaker "A" may have better soundstage simply because it’s a BETTER design, and the claim "time-phase coherent" is just a red herring. There’s no way one can say the "goodness" from "time-phase coherence" because you can’t compare apples to apples. Ultimately it’s a subjective quantification.

I’ve been doing some simulation and I will post some of my findings with graphs, plots, actual simulation runs so that we are discussing on subjective personal opinions. Some of my findings actually shows that intentionally making time-phase may result in inferior phase problem and NOT better! (will be discussed more in detail).

Having said all that, I am actually in favor of first order/time-phase coherent if POSSIBLE. I am not in favor of time-phase coherence just for the sake of it. It’s just that there are a lot of mis-information out there that hopefully this will clear those out. Well hopefully ...

Here my preliminary outline:

1. My "subjective" impression of what is "musicality" and how it’s related to first order filters.
2. Interpretation of step-response. I’ve read a lot of online writing with regard to the interpretations but I think a lot of them are wrong. A proper interpretation is presented with graphs and simulations.
3. A simulation of an 1st order and higher order filters with ideal drivers and why time-phase coherence is only possible with 1st order filter. This part will use ideal drivers. The next part will use real world drivers.
4. A simulation with actual drivers and how to design a 1st order/time phase coherent speaker. Discuss pros and cons. And why time-phase coherence may actually have phase issues.
5. Discuss real world examples of time-phase coherence with Thiel’s and Vandersteens speakers (and why I suspect they may not ultimately be time-phase coherent in the strictest sense).
6. I’ll think of something real to say here ... :-)
andy2

Showing 50 responses by andy2

Who is kenjit?  Is he a mythical hero?  If a mythical hero postings, then by definition all his postings would be a myth?
Hi Tim,

I agree with what you said.  Putting a cap on a tweeter for example does not mean a first order 6db/octave.  The best I can hope for is 6db/octave in a limited frequency range.  I think speakers from Thiel and Vandersteens that "claimed" to be first order, but it's an approximate, but I don't want to say too much here.  And as you said, there are more than time-phase coherence.  There are many ways to design a good pair of speakers.  And I won't argue personal preferences.  I will present an "objective" point of view: here is what first order/time phase coherence.  Whether which one is better is not up to me.

I took me a lot of works and a lot and lot more thinking to put together what I think is a comprehensive and meaningful discussion of first order / time phase coherence approach that I don't think I saw anywhere on the web.  As I said, there are just too many misinformation out there.   Some people ought to pay me lols.  It costs me a good life!

Also I am not really looking to argue with anyone here.  I will present my case, and it's up to you.  I suspect more will end up disagreeing with me than agreeing :-)


Funny ...  I really have no idea if there is such a thing as a "better" speakers.  From personal experiences, designing first order speakers is really hard and it usually takes a long time vs. higher order speakers.  This is not a subjective observation or myth lols, but a matter of fact since since I think I am capable enough to tell the flow of time ... by counting my gray hair :-)

Usual things that are hard tend to be good.  A beautiful hot blond is not going to say "yes" so easily.  Ask me how I know.  Oh well maybe I should stick with higher order speakers ... hahahahaha
High end expensive stuff from companies with sufficient depth to design and program signal processing electronics, i.e. like Harman companies, are doing high end in digital.

That’s not I see in REAL life. Most of the most expensive speakers on the market are analog. I can only speak with real life examples. Sure with imagination anything is possible. There are a few digital stuffs but they are few and far in between and hi-end market does not take them seriously. Like Ferrari or Porsche or Lamborghini, nobody wants to drive an electric supercar.
You can literally be an armchair speaker designer with digital. I've always said that anybody can do it.

Well anyone can smoke pot, but it does not mean anyone should do it.
There are mountains of evidence: genetic, fossil, comparative anatomy, homology, and much more.

Carry on...
You really took it seriously did you?  I look more like chimps than apes.  
Real life statistics: what is the percentage of speakers sold here on Audiogon that are digital?  It can't get more real than that.
I was filling in the blanks.
OK, I don't think I should be responsible for someone else's words.  

Are you saying time-phase coherent is possible with higher order filter?  I suppose you could come up with your own definition of time-phase coherent but then anything is possible then.
I think your conclusion w.r.t. filters may be a wrong conclusion based around the type of filters you were using. Different filter types have considerably different step/impulse response, independent of order.
I actually I never said that.  Or maybe you've read my mind but wrongly :-)  I don't even know the meaning of that statement above you wrote there.  Kind of like when the judge asked me "Did you see that girl".  I was like "What girl are you talking about?"
With a digital active cross-over, time/phase alignment becomes relatively easy.
OK, you have just changed the rule of the game. Sure with digital processing, you could, but I was clearly talking about pure analog xover filters.

Digital processing has its own set of problems though which is just another can of worms that I am not sure I want to talk about in this thread.


it has not been mentioned, but remember there is acoustic phasing as you have been discussing
It’s so obvious I didn’t to waste people time like you just did.

Properly done active should always be better
You have no idea. Talk is cheap lols. Want to pack the entire lab into your speakers?

There is still some or even a lot of reading on digital if you want to start pushing the limits / doing custom FIR filters, etc.
Digital is for low end stuffs. High end and expensive stuffs are pure analog. Consider it a lesson.

With digital actives, you just dial it up and listen for yourself...a whole lot easier and faster that way.
When someone claims something is "a whole lot easy", I go like "hello, what has he done?"

Lead, follow or get out of the way :-)
If there's a Ms. Kate Upton involved, I'll do all three lols.
A decent active crossover in knowledgeable hands will crush the performance of a top tier passive crossover.
Haha so much crushing that nobody is bothering doing it except for some cheap eight dollar headphones.  Real life hello?
Anyway, let's put it to rest.  Hi end market doesn't care for your digital amp and digital dsp stuffs stuffing into a speaker with drivers bought from China OK.  Have you never bought any high end stuffs before?  Can't you tell the difference between a $7K amp and some cheap digital make in China amp?

I am not going to use any stinking digital with my high end drivers bought from Seas or ScanSpeak or Accuton.  It's like taking Ms. Kate Upton to McDonalds OK !!!

What am I going to do with my $5K vinyl table?  Ain't no stinking ADC will touch it lols.

How about my $7K McIntosh tube amps?  Ain't none gonna fit into the back of the digital speakers.  The heat alone will burn up your speakers.

So why don't we put all these digital nonsense stuffs to rest.  Maybe there's a "Made in China" forum where you can go to make your case there :-)


a 100Hz tone will modulate a 1KHz tone.
I'd like to know how that feel ... errr I mean how that sounds like.
George Washington is in the car
Is he doing Ms. Washington :-)  That's the whole reason being Mr. George Washington.
I hope that I have expressed this in a way for everyone of any level to understand
As an anecdotal personal experience, for awhile I was learning how to cook, so either I have to take some cooking classes, or being cheap as me, I would look up at a bunch of YouTube vids and learn how they do it.  Natural I would look at vids from the famous chefs like the guy in Kitchen Nightmares and the likes.  But my results were terrible and I hated the tasting.  I then looked at the vids from regular folks figuring out they would be at the same level as I was.  But I eventually found out that most of them basically would watch some other YouTube vids and emulate them and put up their own vids without knowing if their recipes would taste any good.  I think they would just pick some random recipe, went grocery shopping, and made the vid almost like copying and pasting.  I think most of them  just want their face on YouTube and not really caring if their recipes would taste any good.  So I gave up on that too.

So I ended up deciding that I would just follow my own instincts, you know like Luke SkyWalker.  I've nailed down to a few my go-to recipes that I've developed over the years so at least I don't hate my cooking anymore.  Now I have a bunch of healthy recipes that I can use.  I actually enjoy my cookings more now than restaurant foods.  The only problem now is I still can't make my own beers or wines.  Well you can't have everything I guess.  

Damn, I thought that I would just cook like the guy in Kitchen Nightmares by just watching his vids lols.

So what's that has to do with time phase coherent?  I am not telling until I am properly wined and dined as one of my dates once told me. :-)  

All drivers moving in perfect unison.... when one driver starts moving outward, all drivers move outward at the same time, when it comes back, all drivers move back at the same time.
Physically is it possible?  For example, the woofer flapping at 70Hz, the tweeter flapping at 7KHz.  For every woofer moving forward and back, the tweeter is moving 700 time back and forth, so it's not possible right?

One reason that a single driver does so many things right is that there are no phase issues.
That's not entirely true.  A driver may have different phase shift at different frequencies.  For example, a driver may have a relative phase of 10deg at 700Hz, but at 7KHz, it may have phase shift of 80 degrees.  Not to mention different parts of the driver may not moving "at the same time".

Anyway, I spent too much time watching cooking vids to have time for time-phase coherent stuffs ... hahahahaha
Andy, you have opinions that you don't understand. I'm happy to stick to your original premise, but slamming others for giving accurate information does not work.
I am still waiting for someone to tell me who can understand time-phase coherent, including all the experts in the world  )-: :-(
OK, if you indeed called me "Timmy boy", you’re probably gay. Then you probably knows wayyyyy more. Then why don’t just spill the beans?

Hey you should pick on someone you're own size :-)  Mines are too big.
Just to mention I am pretty sure Timlub has spent many years building and I think designing, and building speakers.
The only skills I need right is how to get to Ms. Kate Upton.  Now if he can get that done, he's my guy lols.


physical alignment of the voice coils
a good start, but my requirement still not met

minimize or eliminate the use of a Xover
not really likely, consider xover is a necessary evil

driver voice coils are vertically aligned physically

I don't care, but sounds fantastic got my curiosity?

Will 90~180~360 be a minor/major
Too many variables, need more information to fully understand

Will I disappear and stop being an annoyance?
It's your money, your time who am I to say

  (Not f’n likely, but amuse yourselves with that....)

If f'n involved, be my guess be f'n around

I won't argue, but I will say that I've never seen absolute phase alignment between drivers without electronic crossovers.
In my past experiences, most competent engineers will figure our how to "fix" it.  But the difference between a merely good engineer to one who can actually make money is that he understands the consequence of his "fixing".  

Ever heard of stories of a mad genius?  They all know exactly how to "fix" things, but nobody hires him because he'll end up breaking more things than fixing.

Hence I fear ... I fear ... I fear ... the electronic crossovers ... will they turn all my musics into mp3?  Will they cause mad hysteria and drive me to insanity?
Any thoughts?
The Walsh and HHR and full range exotic driver stuffs you mention are a bit out of my depth.

And I am not familiar with some of the references in your post.

I am more into conventional cone drivers and speakers - like the typical Seas of ScanSpeak stuffs.

May be if you have a link that can show some pictures of your prototypes then hopefully I can chime in or maybe learn a few things.  I am more of a visual thinker.  


"Poor Andy...can't take him Anywhere...*long sigh*....
Hey I'll go if you're really hot ... but sigh ... there's the reality :-()-:
The hardest parts of the journey are the beginning and the end.  Still working on the introduction.  Damn it's hard.

Oh God Devil you

Oh duality devil you

He invented taken he

She yang yin less


Want coherence clarity not

Want time frequency not

She makes ruins him

And she he nods


What first second then

What fire ice followed

What desire hate you

What you you last


“Not everything that counts can be counted, and not everything that can be counted counts.”  Einstein 
For those who love to over complicate things, this one for you from Einstein the man himself.  

"Everything should be made simple, but not simpler."  Einstein
And of course keep this in mind for those who love DSP and stuffs.

"Don't get lost in the forest while trying to find your tree"  Kate Upton
Relax and smell the coffee in the morning.


making an efficient pistonic driver is the holy grail.
The only part I care is "holy".  "grail" blasphemy :-()-:
Some of my findings actually shows that intentionally making time-phase may result in inferior phase problem and NOT better 
I think that was also what I said in my original post.  What I said that everything else being equal, then yes, time-phase coherent is a plus.  But I also said that I have seen examples in which the designers tried to make time-phase coherent at the expenses of other parameters such as phase-mismatch or frequency response that may end up creating more problem than it solves.

It seems that Thiel (an I am being VERY careful not to appear to make any false accusation) has claimed that the company's speakers have very small excess phase, which means that the phase shift of the entire frequency range (from 50Hz - 20KHz) has very minimal phase shift, and based from Tom, within a few degrees.  Now that is EXTREMELY difficult (trust me) and I do not even think it's doable or even REAL.  I tried to model one of my speakers like that and I could only achieve about +/- 25 degree but I had to bend over backward to get that done at the expense of freq. response and proper driver integration.  Therefore I really did not like the design and I think I am better off with a more conventional approach.  But having said that, there may be about 2 or 3 speakers in the world that can have +/25 degree excess phase.  John Atkinson had said that you can count will all the fingers in your hands the number of speakers he measured that can get a proper step response which is pretty hard in itself.  But having a proper step response AND having 0 excess phase is like winning the lottery every single week.

For reference, if you use 4th order (24db/octave), you automatically get an excess phase of at least 360 degree.  If you do a regular 1st order but with one of the driver inverted, you probably get about 180 degree of excess phase.  To have zero excess phase (or close to zero as claimed by some) is like hitting a bull's eyes from 7Km away.  I think you can count with five fingers the number of speakers in the history that can achieve 0 excess phase.

When you look at the step response from John Atkinson measurements, it's easy to spot if a speaker has too much excess phase.  Even if a speaker can achieve a proper step response, if the initial spike is too "spikey" vs. the rest, then it probably has too much excess phase.  I've seen various measurements of Vandersteens from Stereophile, I doubt they are qualified as "time-phase coherent" across the entire freq. spectrum.  Maybe from 50Hz to up about 7Khz but not all the way to 20KHz.  And I also posted the CS3.7 measurement and showed it to Tom and I said I doubt about the claim as well.  

I have quite a few real world data and simulations but I am waiting for better Confirmation before posting the data since I don't want to be accused of not have REAL or FAKE data.  I've heard of a lot of people including all the experts in the world talking about it but at the end you get even more confused!  Maybe it's a secret and once you know it, you don't want to share.


Where one draws the line is the issue...
Those who have more juice .... errr I mean money get to draw the lines.  Always have been the case.

It's the interpretation 'twixt the ears that appears to be the crux of it...
Read two or three line above.

My fav 'case in point': White people.
Read four or five line above.

Look @ your hands. That is Not 'white', in the classical sense.
Beige/pink/l. brown-yellow in varying amounts. Not even 'even'.
Read seven or eight line above.

Conclusion: More juice more win.
Hey, people I got a little secret want to let you in.
assvjerry posts were all done while drunk lols.

I may not have a road map, but I may have a destination to target.
Oh good lord.  See what I meant.  A drunk with no road map.  

For the record, my ears can't hear past 13K. (going on 64 years old)

That's true.  I can't hear past 15KHz.  But I am pretty sensitive to speakers with high frequency issues.  Why? (Read below)

If you get yours tested, you'd be surprised how little you can hear on the upper end. Not to mention most guys don't have a flat response curve!
But not to worry.  Most of meaningful music lies much below that.  My speaker has a rising freq. from about 7KHz.  At 15KHz it's 5db above the rest! and I swear it doesn't sound bright at all.  And I am listening almost on-axis with toe-in.  

But IF that 5db was around 3KHz, you'll or I'll be running for cover.

Treble starts at much lower frequencies than people think.

People hearing is very sensitive around 1KHz - 3KHz.  A slight bump in this freq. range will be very audible.  It's like running fingers on chalk board.

In general, 6KHz - 8KHz is sibilance if the speaker is excessive at this freq range.  A bit high will make the  neutral ssssshhhhh to ssssssshhh.  If too high will be like sssssssssh.  When you hear actual people talk, you don't hear sibilance unless they talk straight into your ear.  

8KHz or above, we call "air" or whatever that is.  After 10KHz, unless it's very excessive, most people probably can't hear.  I guess young people could.  And I am sure some people are more sensitive than others, but in general, most people especially old are not very sensitive above 10K.  

Some tweeters are designed intentionally to have a bit lift above around 13Khz to artificially give an extra "air" to the sound.  I actually hate that they do that.  I prefer a more neutral freq. response.  If I need more air, I can do that myself thank you.  
Personally, I've been called worse. How far you care to sink is your call.
It depends on the level of weirdness of your posts.  If there are more than three run-on sentences and more than three random thoughts randomly put together into a sentence, then that would be qualified as being "drunk posting".

Did someone earlier call Jim Thiel a genius and then reference his 5 model crossover? Look at this crossover and tell me this isnt actually the work of a designer concerned with only one aspect ignoring all else. All I can say is that this crossover is an affront.
Do you happen to have a link?  I am very very very curious to see how they did it.  I agree that Thiel may have concentrated on the "time-phase coherence" part too much but may have ignored other parts of speaker Desgin which are equally important.  Their xovers have been accused to being "too complicated" but I've never got to see the actual "xover".  
What I AM is a fully trained physical chemist, specializing in quantum mechanics and neutron crystallography. I have a tremendous amount of training in wave mechanics and the theoretical mathematics behind it.
I am pretty sure that you're pretty intelligent and capable but this time-phase coherent thing is a lot more complicated than quantum physics and I am not kidding.  

If we are concerned with the time/frequency domain, we must first agree on a mathematical definition of how to represent a sound wave propagating through atmospheric medium.
The problem is not about the mathematics.  As a matter of fact, the mathematics are rather simple.  

Once we establish this, we can discuss things without any subjectivity.
I agree in general but the problem is how to identify which part is objective and which part will always be subjective and you just have to deal with it.  For example, it's difficult to say which is better sounding since it's also dependent personal tastes.  No mathematical modeling can sort that out.

Of course, we will also need data to use with our expressions, and as we are dealing with wave functions, we will likely want a periodic eigenfunction of some sort, a la sine or cosine or perhaps e^(x), which gives a better representation, but is less well-defined when deriving or integrating with it.

Again, the problem is not the mathematics on the objectivity side of thing.  In term of measurements, simulations and so on, all these are fairly well established.  The problem is that our hearing is very complicated and no amount of mathematics can figure it out.  I don't mean to obfuscate the issue.  It's really true that nobody has been able to model our "hearing".  Not even close.

It's actually not as daunting as it sounds, and we could easily develop a simple system from first principles.
Already you have under-estimated the complexity of our hearing.  "A simple system" will not do it! 

let's quantify it!
Amen .....

While I can't say which is better, whether time-phase coherent matters or not, I can give a clear definition of what is time-phase coherent is.  Soon I hope!



Before posting any real data, simulations, plots and what not ... let's put down some basic definitions of what is time-phase coherence.  

I can see three basic types - from easiest to most difficult.  Let's start with the easy first.

1. First order/No Time-Phase coherence: this speaker will use first electrical order, but there is no time-phase coherence.  It will not be able to produce a proper step response.  It's more or less conventional with the exception that it uses first order filters.

2. First order/Time-Phase Coherence, BUT NO "Time coincidence"
    (which will be explained in #3).
  This speaker will be able to produce a proper step response, BUT and an important BUT.  It may not be able to produce an excess phase of 0 degree from say 50Hz to 20KHz.  This means that the speaker, for example, may have a phase shift of 50 degree or more or could be a full 360 degree at 15KHz, but only 5 deg at 500Hz.  That is its excess phase will vary especially at higher frequencies as the tweeter approaching 20KHz.  John Atkinson would agree this speaker meets his definition of "Time-Phase Coherence" since it could produce a proper step response.  My guess is most speakers that were measured by John Atkinson would fall into this category.  I've seen some measurements done on Vandersteens speakers and I was like ... hmmm... I am not quite sure.   But the most stringent definition is reserved for #3.

3. First order/Time-Phase Coherence AND Time-coincident: this is the most difficult definition for any speaker to meet.  That is it has to be able to produce a proper step response like in #2, BUT it also has to be able to have a 0 degree of excess phase from DC - 20KHz.  In reality, no speaker will have absolutely 0 degree, but the variations should be very small.  I believe Thiel claims that their speakers excess phase shift is only a few degrees (less than ten).  To be honest, I am not sure many speakers in the entire history can meet this definition.

So to summarize, you have three distinct possibilities from easiest to hardest:
1. First order/No Time-Phase coherence
2. First order/Time-Phase coherence BUT NO "Time coincident"
3. First order/Time-Phase coherence AND "Time coincident"

As for terminology, I guess you can call anything you want, but as far as the measurements, those are the three categories. 

With real data, graphs, plots, simulations those three cases can be clearly demonstrated.  Just talking about it making things more confusing.  
You can Google and find photos of this crossover
OK, just did.  Actually they don't look that bad.  It all depends.  


When I look at this thing I dont know if I should laugh or cry.
Ultimately it all ends up in "cry" like the "Crying Game".  But I give that it helps to laugh every now and then.
The hardest parts are the beginning and the end. I probably got the beginning all wrapped up, but the end ...

For want of small
I lost self control
For want of beauty
I loss almost everything

Though small comes big
But I’ve been small
And I’ve tasted small
Now I want big

How will it end
Fire or Ice
I’m no Robert Frost
So I want both
Experience the insane imaging of a Vandersteen Model 7 and you will become a believer in time and phase coherence.

Although I am an proponent of time-phase coherence, I can't conclusively say that the reason the Vandersteen and the Thiel are so good because mainly because of time-phase coherence.  I guess I am not fully convinced until I know for sure.  From a theoretical stand point, time-phase coherence is better, but a speaker has so many variables that it's hard to pin down which is the most responsible for the "goodness".

I am sure a lot of people would be impressed by the various Wilson high-end models but they are not time-phase coherent.  

IMHO.
Yeah it’s Friday. And tomorrow’s Saturday and the next day is Sunday...I for one, don’t especially care how long it will take you, or how old you will turn out to be, before someone ’Finally’ leads you by the hand and delivers you (and the rest of us) from your own stupidity.

You can’t be so desperate, can you? Are you saying "stupidity" is what you’re waiting to save you? If that’s the case, can you jump off a building somewhere lols? If "stupidity" is what you’re waiting for, well just go and say "Hi" to whoever closest to you.  That should give you a quick "stupidity" fix.  

I got more poetry for you. More "stupidity" for you every week. Chew on that brother.
So desperate!  I figured since you're probably a high school drop-off, I'll start with "stupidity" first lols.  Then maybe go somewhere from there.  After that I'll work with you to make you feel less pathetic.  I feel ashamed for you, I really do.  
I think I'm out
Yeah, why don't you're out of this universe if you know what I mean.  Some how I doubt it.  I'll probably have to deal with your shenanigans sooner or later.  


He started it. I think he intentionally tried to piss me off so I’d give him some bread :-) Hey self defense and gun ownership are still alive and well.
Ivan Ivan come out where ever you are lols.  Are you hiding in my closet lols.
man who can’t think his way back down to earth long enough to answer his own question...ya got me there I guess.
aaahhh ... so I guess that’s your problem all along. Come clean and you’ll be forgiven brother.

Why go around the neighbor dog? Just come and knock on the front door. You look kind of stupid now, don’t you!

I know enough not to sprout around someone else nonsense.  
Hi Richard,

It seems interesting that you posted with regard to the "Infinite Slope" in a time-phase coherent thread.  It's quite a different philosophical design vs. time-phase coherent with respect to phase shift.  I would assume Infinite Slope filter would have higher phase shift using very steep roll-off slope filters. vs. a time-phase coherent design that uses first order filter which has the least amount of phase shift.  "Infinite Slope" advantage is minimal over-lap in frequency response between different drivers, whereas time-phase coherent is the complete opposite being having a large overlap.  I suppose the disadvantage of "Infinite Slope" is the excess in phase shift?  

I was wondering if you could share your opinions on "time-phase coherent" as to the extend it may affect on sound quality.  Time-Phase Coherent insists that the phase of the system response (the overall response of a speaker) should be as close to 0 deg. phase shift as much as possible from 1Hz to 20KHz.  Thiel design has claimed to achieve +/- 10 deg difference.

With "Infinite Slope", I would assume it would violate the criteria of 0 deg. phase shift.  Would you share the amount of phase shift a typical "Infinite Slope" speaker.  For example, what is the typical phase shift at 17KHz vs. to something like at 270Hz?  For a time-phase coherent design, the phase shift should be very close to 0 degree.

Thanks.
Why would you assume that?
I was hoping you would enlighten me?  Since your post above implies you know the answer?
Hahaha .....  I miss the good old days.  A gigantic flag ship pair of speakers only costs $25K.  Something like this today would be $80K.  Nice square step response!  
Hi Richard,

Thank you for your posts and your unique perspective. For now, I would like to take a rain check as for a proper response from me since it may require a bit more thinking from me.

The only thing I want to say now is that, after listening to different types of speakers with different design philosophies, some being optimized for freq. domain and some being optimized for time domain, I think a well designed speaker all sound very good regardless of the underlying design philosophy.

Some one once told me all women are beautiful. If she doesn’t look beautiful, it just means that she does not know how to put on make up. Same with speakers. If a speaker does not sound good, it probably because it was not well optimized for its purpose - however different in design philosophy.

I would like to stop for now, but without trying to sound too general, I think ultimately, either you gain in frequency domain or time domain but at least for now, I don't know of a way to have both.  God does not seem to give us human any free lunch.