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
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
@bdp24 probably not effective to put real designers with patents and viable products up against theoretical “ hmmmm” musings... back to the music for me with a great speaker ( since 1977 ) that measures well 2

Satchmo at 45 RPM... sublime


Dont get me wrong I am not a huge fan of single driver speakers, but the lack of crossovers in some speakers is a significant factor in making them viable for some. Also of note is manufacturers which operate certain drivers full range in 2 and 3 way dynamic designs. 

Unfortunately, a full-range driver has yet to be invented! Big ESL’s are close, though. The best we can do for now is use two or three drivers integrated with filters designed to make them behave as one.

Danny Richie has designed loudspeakers in which he used the NEO3, NEO8, and NEO10 drivers in an open baffle frame. All the NEO’s share the same sound characteristics (unlike the drivers in most multi-way dynamic speakers), with each driver covering a different range of frequencies (each driver’s dimensions determining it’s optimal frequency band). He then created filters that combine their individual outputs into a cohesive whole. He mated them with OB/Dipole subs for very full-range music reproduction.

Nelson Pass is a single-driver loudspeaker proponent---watch the You Tube videos made in his listening room to see his. By the way, Nelson has created active analog x/o filters for the OB loudspeaker designs of his good friend Siegfried Linkwitz (R.I.P.), a true master of loudspeaker design. Nelson’s analog x/o’s are used in place of Linkwitz’s stock digital ones.

Yes getting to get the drivers to coalesce using the simplest and most efficient method possible which presupposes using the fewest crossover components. Amplitude and phase are very important but even the best crossovers just minimize the damage. It is impossible to solve amplitude and phase problems when a crossover is present in the design.

As Danny Richie (GR Research) explains in his series of excellent You Tube videos on the subject of loudspeaker design, cross-over design is a matter of getting the individual drivers to coalesce. He uses the waterfall plot as his number one design tool, as it reveals a LOT about what the drivers are doing, both in amplitude and phase, which are inter-related.

The phase responses of the drivers in a speaker is a major component in that speaker’s frequency response. The summed output of two drivers which are out-of-phase at any given frequency cancel, creating a null, and a resulting depression in the frequency response. Listening to Danny discuss a speaker which uses two widely-spaced tweeters to reproduce the same frequency is pretty amusing. ;-)

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.
You can Google and find photos of this crossover. When I look at this thing I dont know if I should laugh or cry. 
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.  
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".  
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. 
Sorry, @andy2 .  My excuse is that I 'was born this way'.  If you haven't run into a 'personality type' of my sort, that's not my problem.

If you'd care to note the time this post has been made, it's a bit early for even my lifestyle to get fried enough to 'drunk post' this early in the day.

As is said, "It takes a lot of souls to fill a freeway."  And, having been born in SoCal (Long Beach) some 68 years ago, I might be able to legitimately claim the effects of smog causing mental dismangement....

But I won't.

As for the way I express myself; if you'd prefer monosyllabic retorts....not very likely from this mortal. 'Short & terse' isn't really my style, here or IRL.

Besides, this is really 'off-topic', you Are the 'OP', so...get back to it.
No apology sought or required.
Have a good week. 
I am with you midnight_rider. You can't proclaim one hypothesis to start the post that defines a holy grail, then claim that something else is too complex and variable to model .... which means no holy grail.
I can see there is no point in going any further. 

Nobody in their right mind would attempt to fully model a physical system when a perfectly good approximation will get you 98+% of the way there with a fraction of the work. Simple harmonic oscillator and rigid rotor are perfect examples of this. Yes, the electron probability density function is infinitely more complicated than our simple model, yer we are still able to predict with stunning accuracy observable properties using these simple models. This extends to many, many practical examples.

Granted, with access to a supercomputer, it can be fun to attempt to add as many perturbations as one can, but that's an entirely different exercise.

I leave you to it, as you are obviously very capable.
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".

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!



EDIT: Woah! I typed this earlier and did not post. The got home and hit "post" and see that it's waaay outdated. This was in response to a definiteion of T/Φ coherence.

Let me preface this by saying that I am not an audio engineer, so I don't know how meaningful anything I say can actually be. 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.

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. Once we establish this, we can discuss things without any subjectivity. 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.

This is my recommended starting point for a meaningful discussion absent the subjectivity or ambiguity that inevitably arises when talking Hi-Fi sound. It’s actually not as daunting as it sounds, and we could easily develop a simple system from first principles.

You have given a terrific definition above, now let’s quantify it! This is a fascinating thread. Thanks for this!
[lurk disengaged} @andy2 ....I won't disagree with you as to the 12:51 pm 11/3 post; all of which is generally acceptable.  As for your personal hearing range, lucky you. *S*

As for how you can discern that I'm drunk or under some sort of influence over and through this medium that we're engaged in....*hmm*
That will take a certain amount of explanation on your part to the viewers of this forum as to how you've arrived at that observation.
I'll leave that issue for you to explain to the viewers here.

Personally, I've been called worse.  How far you care to sink is your call.

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.  
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.  

I recently came across a pair of vintage DCM TimeWindow 3 speakers. Phase and time aligned, by designer Steve Eberbach.

TO MY EARS, they sound great.  The usual superlatives: can hear more details, voices are more real, brushes on a drum more realistic.

I had to sell off my modest system a few years back: C22, MC275, Vandertseen 3A signatures.  Heck, I thought I was in heaven, then.


Well, I now hear at least the same detail and more, especially on the upper end from these TimeWindow 3 speakers.  (Guessing the 3As were "laid back"?) 

I pulled out my old Carver (don't laugh!) TFM-35x from the 90s.

Carver C-23 pre-amp.  Same old Rega Planet CD player! 

I did A-B testing years ago between the Carver and McIntosh amps. Very little difference.  Bass tighter with the Carver. Possibly a tiny bit better midrange with the MC275.  But one beer equalized everything!  lol!

So, if you look around what's the most traded, bought and sold  audio components?  Yeah, SPEAKERS!   Everyone looking for nirvana, since all our ears are the same, but they are all DIFFERENT, like fingerprints!  

FOR ME, I believe I am sensitive to more correct phase and time alignment factors, whatever they are, however you explain them!

If you can listen to speakers for about 4-5 hours without fatigue, they work for YOU!! 

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

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!


Nice thread read. Never to old to learn stuff.   Now, get those ears tested and maybe you'll figure out why you prefer certain speakers over others! 

My wife can't hear the difference. She thinks I'm an idiot.

trust me you don't have to be 'ocd' to fall into that camp.
"...thinking of something Real to say here..."
*mmm*
Well, if you haven’t illustrated succinctly the issues and complexity of any attempts to resolve the time/phase-coherence Gordian Knot as it relates to any speaker array, I think I’ll have to be patient to read it....
...and I will thank you for that. *S*
"...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.."
Volumes in 2 sentences...;) So, in my ’unconventional approach’ to my ’quest’, I may have to default to @cousinbillyl ’s comment:
"A Linkwitz Riley 2nd order series crossover, with drivers acoustical centers aligned, is phase perfect."
The line that follow that is also interesting....at least, to me. ;)

What I distill from your post is that if one designs to correct All that one can correct, what one May end up with...you won’t like to hear...Perhaps.

You Might get lucky.

The odds are towering against you.

Now....that’s Quixotic in the extreme.

...from @ivan_nosnibor , awhile back...
But, with active digital crossovers, there’s no need to spend all that time reading all the tea leaves (white papers, testimonials, reams of MLSSA charts, searching for who could be the most unimpeachable source of info on it, etc) in an attempt to get a handle on comparing them all from afar and then try to divine which might be best. With digital actives, you just dial it up and listen for yourself...a whole lot easier and faster that way.
I’ve got one of those...active eq as well (been doing that for decades now, like to play ’flat’ into the space as much as is practical). I think I’ll just wander off with all of this in mind and at hand...

...and see (well, hear) what I can conjure up. *S*

@andy2 ....I think that a digital Xover..."...is our only hope!" ;) *smirk*

Good variable factors, Obi Wan.
And thanks....to you, and all the posters quoted and read.
I may not have a road map, but I may have a destination to target.

[lurk mode engaged]
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.


Andy2: "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 "

Please follow through on posting these data. Why simulations and not real data from speakers.


"Money changes everything.... C. Lauper
Same subject, different song, SOS...*L*
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.
@andy2 , I used to carry a thermos with a biohazard sticker on it.
It didn't stop those from asking for a 'hit' if the night previously had some sort of 'adventure'. ;)
As for 'simple'>'not simpler', just enough of the 'right things'.  Where one draws the line is the issue... I opt for 'minimalist', just enough.

@kenjit , yeah, but many will argue...excuse, 'discuss' the experienced results just the same. *G*  It's the interpretation 'twixt the ears that appears to be the crux of it...

My fav 'case in point': White people.

Look @ your hands.  That is Not 'white', in the classical sense.
Beige/pink/l. brown-yellow in varying amounts.  Not even 'even'.
I always thought the goal was having 20to20 arriving at your ears, at the same time and in phase
They do. Theres no evidence they dont. 
“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.


@danvignau234, I liked 'Domestic Motor'. *G* So...'householdy'...;)
@kenjit, a myth, and into the mystic. Smoke, mirrors, obtuse formula....
@viking62....what era for the Mirage?  The Infinity I noted had a 3' typical cone tweeter on the back as well.  The intent of the unit was to have a more 'airy, holographic' quality...

It was an interesting go at it....basically a 5 speaker, '4 way'. It could be done better these days...
I always thought the goal was having 20to20 arriving at your ears, at the same time and in phase. Many ways to do this. Wasn't Mirage one of the first to put an out of phase tweeter on the rear ?
Phase alignment is certainly measurable.  
its all a myth. Most important thing is frequency response. 
...much like real life...

What’s in the YT video is the basis of what I’ve been pursuing; a 2-way column, close proximity of the drivers, height to take advantage of the ’angle of radiation’, spare construction. Appearance in the long run will be a simple ’lipstick’ fabric column of fabric.
Not ’cat-proof’ to begin with...don’t have any at this time... ;)
Form following function...
I have followed B&W since the company was founded.  You can measure time phase differences.  When B&W began, all the profits went into laser and computers.  They measured the electrical signal and compared it with what the laser showed came out of the speaker.  The they bought some KEF three way speakers, and designed a better crossover, marketing the product as a  Domestic Motor.  This speaker used the same drivers as KEF, their oblong woofer, a Celestion upper midrange/tweeter, and a Coles super tweeter.  The woofer was designed to be narrow for tax reasons, because the British Value Added Tax wa based on speaker width. Their second speaker only changed to a round woofer.  The DM 4 ported the same box, instead of the lot, and turned this speaker upside down, which it should have been from the beginning, because it was a bit large to put on it side on a shelf.  Further research, with evolving better equipment showed that phase alignment created a more coherent sound stage, begatting the DM6, affectionately known as The Pregnant penguin.  The DM 7 and DM14 were next, with the position of the exposed tweeter of the 17 drawing a lot more attention than using electronic time delay, which also a had the issue of only working in a frequency dependent way.  The rest is history, but includes better and better measuring equipment, materials, beveled cabinet edges (explaining why the wood Advents sounded better than the vinyl ones), then the sound deadening of the Matrix cabinets.

Phase alignment is certainly measurable.  
@atdavid...yup, there's the points where the driven surface has to slow down, stop, and accelerate in the opposite direction.  'X' x per second, constantly varying....
I'd get distorted too, which occurs with far simpler motions.*L*
There's various 'this 'n that' applied to compensate, but none make it 'go away' completely.
The above is why a Walsh radiator appeals to me.  Pistonic motion is primarily converted into a radial radiation at the voice coil/cone interface.
It doesn't 'go pistonic' until the waveforms descend further down the cone, where the diameter of the cone is less likely to radial excitation of the surrounding air...
Think of a bell...stuck, it vibrates radially.  In this instance, the cone needs to be light but physically stiff to endure the induced waveforms. That requires a driver that is under a considerable amount of resistance.  Which translates into heat...which will fry most voice coils.
I've lost a couple that way...a finger on the magnets' backside gets hot to the touch.
That's one thing that I've worked to address, as well as the cone materials, cone interior reflections, surround material selection, et all...
Even the choice of structural material is not typical; stiff, yet absorptive.

There are those that consider omni's 'non-starters', but consider the nature of 'live music'.  It doesn't exist as a sound from a plane; it's omni by nature, as you are.  You hear from all around you, reflections and all.
Crossovers don't exist either...*s*
Yes, omni's are a bitch to set up in a given space. *shrug*  But, given that many spend big $ to 'condition' their listening environment, what's the diff?
I'm a fan of Linkwitzs' comment: "Ignore the room."
Which is why I approach the issue by 'going 5.1', a surround array with a sub.
Direct overrules reflections when you're in the midst...;)
Even if you have perfect pistonic motion, you still have intermodulation distortion with a pistonic driver. It is unavoidable.
...and @andy2 has a 'poetic interlude'....*G*

Lets' drift 'off topic' for a moment....*S*  Good for the soul, tics everyone else off...*L*
Walshs' are Not Normal....

I've been accused of that...but it works for me.  Thinking 'outside the box' is easy when you don't believe the box really exists... ;)
@bdp24 , Thankx, I'll go stare @ that....and ignore what I don't think applies. *L*

I do that.... ;)
For excellent tutorials on loudspeaker design, watch the You Tube videos on the subject made by Danny Richie (GR Research) in conjunction with Ron of New Record Day fame.
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


making an efficient pistonic driver is the holy grail.
The only part I care is "holy".  "grail" blasphemy :-()-:
"Poor Andy...can't take him Anywhere...*long sigh*....
Hey I'll go if you're really hot ... but sigh ... there's the reality :-()-:
@tomic601 ...and why I'm trying to avoid 'pistonic' as much as practical..given frequencies, and how they're recreated...

A sub for major air movements...anything above is fair game. *G*
The problem with your perfect single driver is that it ain’t, in fact very very very few purpose built narrow bandwidth drivers are pistonic. Most paper cone single driver speakers are out of phase a LOT
see the Vandersteen video of the German laser scanning machine of the 7 midrange vs another highly regarded midrange....
making an efficient pistonic driver is the holy grail.
getting cheap high trash output out of a single driver w big motor not so difficult