Differences between tweeter designs?

[Soniclife]

This is an interesting comment. I've read a few studies testing various kinds of distortion audibility in which it seems to be the case that - perhaps surprisingly - more compressed, artificial and/or repetitive music tends to be more revealing of distortion than high-quality recordings of acoustic instruments/events. I speculate that the repetitiveness may allow listeners to more easily lock onto a specific sound and more easily detect a change in its presentation.

Have you seen the chart in post 1 of this thread...
https://audiosciencereview.com/foru...sic-tracks-for-speaker-and-room-eq-testing.6/

 

[Soniclife]

However, very few 1" domes play well at moderate to loud levels below 2KHz, and those that do tend to be expensive.

I've seen you post this a few times, just what are the limits, and how much can posh tweeters overcome the limits? There are a lot of monitors from the likes for ATC that are meant to play loud, that don't use horns. I'm wondering what crossover slopes and frequencies keep you out of trouble.

 

[andreasmaaan]

Have you seen the chart in post 1 of this thread...
https://audiosciencereview.com/foru...sic-tracks-for-speaker-and-room-eq-testing.6/

Nice, hadn’t seen it

 

[andreasmaaan]

I've seen you post this a few times, just what are the limits, and how much can posh tweeters overcome the limits? There are a lot of monitors from the likes for ATC that are meant to play loud, that don't use horns. I'm wondering what crossover slopes and frequencies keep you out of trouble.

I’m not sure, as it depends on the specific tweeter, crossover, and SPL requirement. AFAIK almost all commercial designs that use direct radiating 1” domes cross over between 2 and 5KHz (often between 2 and 3.5KHz), and the majority use 4th order filters. (I'm not against this at all BTW, so long as they are not crossing over to a large woofer that will be beaming significantly at the crossover point).

Expensive tweeters often do play lower, although when looking at measurements, I'm often scratching my head trying to work out what the benefit is supposed to be of the cost-no-object option vs. the expensive but not crazily-so option within a particular brand's product range. This is all just strictly IME ofc, my observations are far from methodical or scientific and are no doubt somewhat biased.

I’m not aware of a commercial design that crosses a 1” direct radiating dome lower than about 2KHz, but if anyone knows of any, it would be interesting to try to nut out what’s going on with it.

Re: ATC specifically, their two-way monitors use 6" or 6.5" woofers and cross over at 2.1KHz to 2.5KHz (4th order) depending on the model. Max. SPL is listed as 108dB continuous "per pair", which I presume means 102dB per speaker. That seems pretty reasonable to me, i.e. the kind of SPL level that might not sound pleasant but won't permanently damage anything. Their 3-way units cross over at 3.5KHz (4th order) and list the max. SPL as 112 to 115dB continuous (not stated whether this is per pair or per speaker). This maybe gives an indication of the kinds of SPLs that a good direct-radiating dome can produce when crossed over at these frequencies.

 

[Soniclife]

I’m not sure, as it depends on the specific tweeter, crossover, and SPL requirement. AFAIK almost all commercial designs that use direct radiating 1” domes cross over between 2 and 5KHz (often between 2 and 3.5KHz), and the majority use 4th order filters. (I'm not against this at all BTW, so long as they are not crossing over to a large woofer that will be beaming significantly at the crossover point).

Expensive tweeters often do play lower, although when looking at measurements, I'm often scratching my head trying to work out what the benefit is supposed to be of the cost-no-object option vs. the expensive but not crazily-so option within a particular brand's product range. This is all just strictly IME ofc, my observations are far from methodical or scientific and are no doubt somewhat biased.

I’m not aware of a commercial design that crosses a 1” direct radiating dome lower than about 2KHz, but if anyone knows of any, it would be interesting to try to nut out what’s going on with it.

Re: ATC specifically, their two-way monitors use 6" or 6.5" woofers and cross over at 2.1KHz to 2.5KHz (4th order) depending on the model. Max. SPL is listed as 108dB continuous "per pair", which I presume means 102dB per speaker. That seems pretty reasonable to me, i.e. the kind of SPL level that might not sound pleasant but won't permanently damage anything. Their 3-way units cross over at 3.5KHz (4th order) and list the max. SPL as 112 to 115dB continuous (not stated whether this is per pair or per speaker). This maybe gives an indication of the kinds of SPLs that a good direct-radiating dome can produce when crossed over at these frequencies.

Thanks, things to think about. I wasn't aware most tweeter crossovers were 4th order, I'd assumed in passive designs 2nd was the dominant order.

What do you make of the D&D 8c crossing over at 1.2K?

 

[andreasmaaan]

Thanks, things to think about. I wasn't aware most tweeter crossovers were 4th order, I'd assumed in passive designs 2nd was the dominant order.

What do you make of the D&D 8c crossing over at 1.2K?

The tweeters in the 8C are no doubt an excellent design to begin with, but the distinctive thing (I imagine) is that the horn-loading significantly lowers distortion and raises the max. SPL in that bottom octave or two of their range. That is a deeper, wider horn than on most commercial dome tweeter designs. I don't know a lot about the tweeter specifically though, just what I can see on the spec sheet.

Re: 2nd vs 4th order crossovers, I'd say most are 4th order (at least beyond a certain price point), but many are 2nd order too. Keep in mind also that an electrical 2nd order filter will often result in a 4th order slope, depending on the tweeter and where the crossover point is.

 

[JustIntonation]

Re: 2nd vs 4th order crossovers, I'd say most are 4th order (at least beyond a certain price point), but many are 2nd order too. Keep in mind also that an electrical 2nd order filter will often result in a 4th order slope, depending on the tweeter and where the crossover point is.

I was just thinking about this. And the reality of real world crossovers.
Crossovers are often placed close to where drivers fall off naturally and the two slopes combine as you said. But in less than perfect ways.
If the drivers are not made completely flat in phase before the crossover you'll get in reality that there is no perfect on-axis. For instance if a 12dB crossover is used but the tweeter drops off at another 12dB naturally close to the crossover then that part of the frequency spectrum will be completely out of phase while exactly at the crossover frequency it will be in phase.
I suspect this is what's actually occuring in real life a lot?
I don't know how bad this is if the resulting frequency response is flat enough (though somewhat unpredictable because of this as there can be an addition of freq response of the drivers but also a subtraction depending on phase) and the out of phase parts will be x dB down depending on the crossover slope and distance from the crossover. Less than ideal and a good argument for DSP crossovers where it's easier to make the drivers completely flat in phase before the crossover? Resulting in real world ideal crossover behavior.

 

[andreasmaaan]

For instance if a 12dB crossover is used but the tweeter drops off at another 12dB naturally close to the crossover then that part of the frequency spectrum will be completely out of phase while exactly at the crossover frequency it will be in phase.

I disagree If drivers are functioning more or less linearly, they are minimum phase, meaning a natural driver roll-off should have the same phase characteristics as an electrical roll-off of the same magnitude.

It's important to make sure this is the case, of course.

 

[JustIntonation]

I disagree If drivers are functioning more or less linearly, they are minimum phase, meaning a natural driver roll-off should have the same phase characteristics as an electrical roll-off of the same magnitude.

It's important to make sure this is the case, of course.

Yes I realize this. But what matters is a smooth constant slope crossover as a result. And this is not the case with natural driver dropoff close to the crossover it seems to me. So the real world result is that for instance at exactly the crossover freq the crossover is the electrical 12dB but bit below the crossover the natural let's say additional 12dB dropoff starts of the tweeter so at that point the dropoff is 24dB with its resulting phase shift. So then there will not be a perfect on-axis response all over the full range of the crossover? Or am i missing something?

edit: I mean, the crossover will only be smooth and phase correct for the 2 drivers if they both have the same slope at the same frequency? I get that one can have a varying crossover slopes, for instance 24dB at a certain frequency part of the crossover and for instance 12dB at another frequency part of that same crossover. But the drivers will only remain in phase if the real crossover slope is at those points in frequency the same for both the low pass and high pass parts, which does not seem to be the case in many real world situations? I mean if at some point in frequency the crossover slope is different for the low pass and the high pass then their phase will go out of sync / a change of on-axis angle. So the result would be that there can be different on-axis angles for different frequencies around the crossover.

edit 2: ok I get that if the driver are fully linear and the combined frequency response is made to be 100% flat in frequency response then the result phase is also correct on-axis. So indeed the question is.. how linear are drivers? Any nonlinear frequency response deviations would have to be dealt with by EQ acting on both drivers the same to prevent this from making the phase unequal between drivers?

 

[andreasmaaan]

Yes I realize this. But what matters is a smooth constant slope crossover as a result. And this is not the case with natural driver dropoff close to the crossover it seems to me. So the real world result is that for instance at exactly the crossover freq the crossover is the electrical 12dB but bit below the crossover the natural let's say additional 12dB dropoff starts of the tweeter so at that point the dropoff is 24dB with its resulting phase shift. So then there will not be a perfect on-axis response all over the full range of the crossover? Or am i missing something?

Of course, yes. This can often be the case with passive designs, and is one advantage of using active crossovers. However, the further away from the xover frequency the resultant acoustic roll-off deviates from textbook filter slopes, the less of a problem (if any) it will be. I haven't seen any research into the audibility of this, but it could be simulated using minimum phase filters with additional cascaded filters or EQ to simulate filter deviation due to natural driver roll-off. Given we are much more sensitive to frequency than phase, however, I suspect that so long as there is no audible aberration in the frequency response, the problem will be inaudible.

 

[JustIntonation]

Of course, yes. This can often be the case with passive designs, and is one advantage of using active crossovers. However, the further away from the xover frequency the resultant acoustic roll-off deviates from textbook filter slopes, the less of a problem (if any) it will be. I haven't seen any research into the audibility of this, but it could be simulated using minimum phase filters with additional cascaded filters or EQ to simulate filter deviation due to natural driver roll-off. Given we are much more sensitive to frequency than phase, however, I suspect that so long as there is no audible aberration in the frequency response, the problem will be inaudible.

Made 2 edits in my previous post before I read your post.
It's clear to me now that for all linear frequency deviations there is a corresponding phase deviation, so if the crossover is flat in frequency response on-axis, so is the phase. Though frequency deviations from drivers caused by non linear causes should be EQ-ed out by either minimal phase EQ acting on both drivers at once or by linear phase EQ acting on that driver. I wonder how much of the frequency deviations are by non linear cause?

And if we were to look at real world crossover behavior off axis then we have to take into account the off axis dropoff of the mid driver. This does cause a deviation away from flat around the crossover so with an added phase shift. This may contributes a great deal to the real-world audibility of the crossover under off-axis angles? Makes a case for a smaller mid driver which has less off-axis dropoff around a low crossover point.

Btw here a quick messy drawing showing the relation between mid - tweeter driver distance (their acoustic centers) and crossover frequency. The line represents the point where the cancellation axis is 90 degrees relative to the on-axis (so parallel with the baffle, seems partly by instinct to be a good point).

 

[andreasmaaan]

Nice graph

Woofer off-axis beaming is one reason why I prefer loading the tweeter with a horn/waveguide (think e.g. Revel Ultima, Genelec monitors, D&D 8C, etc). Also because lateral first reflections tend to be beneficial to perceived sound quality when similar in FR to the direct sound.

However, assuming there is a polar response discrepancy between woofer and tweeter, I'm not sure the relatively minor phase aberrations caused by this are likely to be audible, as these reflected waves are not getting to you until after they've bounced off surrounding surfaces; the delay is therefore already orders of magnitude greater than any phase aberrations in the reflected wavefront itself, not to mention swamped by other reflections from all over the room, creating absolutely chaotic frequency and phase relationships. In other words, it's simply the frequency response of these reflections that's of interest IMHO.

Looking at your graph, it would seem that the kinds of distances/xover points you're aiming for would require a small cone or dome midrange and a tweeter with a smaller than standard (104mm) faceplate; many of these will struggle to play cleanly that low, depending ofc on SPL requirements. But it can be done, especially for very small rooms and systems not expected to reach e.g. THX reference levels. But I could imagine e.g. a tweeter with a 65mm faceplate and a 4" cone midrange (or maybe 3" dome) giving a C2C distance of perhaps 8.5cm, crossed at perhaps 2KHz, playing cleanly enough to do the job in most rooms (all these calculations are very much back-of-the-imaginary-envelope btw).

 

[JustIntonation]

Nice graph

Woofer off-axis beaming is one reason why I prefer loading the tweeter with a horn/waveguide (think e.g. Revel Ultima, Genelec monitors, D&D 8C, etc). Also because lateral first reflections tend to be beneficial to perceived sound quality when similar in FR to the direct sound.

However, assuming there is a polar response discrepancy between woofer and tweeter, I'm not sure the relatively minor phase aberrations caused by this are likely to be audible, as these reflected waves are not getting to you until after they've bounced off surrounding surfaces; the delay is therefore already orders of magnitude greater than any phase aberrations in the reflected wavefront itself, not to mention swamped by other reflections from all over the room, creating absolutely chaotic frequency and phase relationships. In other words, it's simply the frequency response of these reflections that's of interest IMHO.

Looking at your graph, it would seem that the kinds of distances/xover points you're aiming for would require a small cone or dome midrange and a tweeter with a smaller than standard (104mm) faceplate; many of these will struggle to play cleanly that low, depending ofc on SPL requirements. But it can be done, especially for very small rooms and systems not expected to reach e.g. THX reference levels. But I could imagine e.g. a tweeter with a 65mm faceplate and a 4" cone midrange (or maybe 3" dome) giving a C2C distance of perhaps 8.5cm, crossed at perhaps 2KHz, playing cleanly enough to do the job in most rooms (all these calculations are very much back-of-the-imaginary-envelope btw).

Yes that was what I was thinking too, aiming for 2KHz and 8.5cm distance. Seems reasonable.
I'll be listening in my system without ANY direct reflections around the crossover, not even a desk (which I'll make very small and acoustically transparant out of "mesh wire" with a wool carpet on top) and the rest of my room will be anechoic only not in the bass (and only not in the bass directly behind the speakers which will be in phase and should help with bass SPL), and the floor I'm undecided as to wether I'm going to use only a very thick fluffy wool carpet (which I already have) or perhaps even raise it 20 or 30cm or so with glasswool and a metal mesh and on top wool carpet but I think I won't need to do this (and would only have an effect in the upper bass and up, still not for deep bass). So the room will be mostly anechoic except for the bass. Ah it's a strange room I'll explain how it'll all work when finished
I have experience though in listening in a similar room and can tell that without any reflections you will hear every tiny little flaw in the speaker, this is why I'm being so perfectionistic. You hear truly everything. I'm not expecting it to be perfect in the end, but I want to get as close as reasonably possible. (will probably still have to EQ in a final curve that is a little bit warm though, partly to mask errors, partly because almost no music is made to be listened to under such circumstances only far field recordings will sound truly natural and pleasant without any further EQ)
edit: oh and listening distance will be between 1 and 1.5 meter. So very high SPL is not needed and the limiting factor will be the closed 8" bass driver anyway (since it is in halfspace I should get very roughly 95-100dB out of it at 1m or so for 30-40 Hz deep bass somewhat clean?)

Btw, going to make the new crossover simulation audio files now, will share when done

 

[andreasmaaan]

So the room will be mostly anechoic except for the bass. Ah it's a strange room I'll explain how it'll all work when finished

Interesting idea, I'm wondering why you want the room to be so close to anechoic?

And to play devil's advocate, I think in reality you'll have the opposite situation: if your room really is going to be that reflection free, neither the off-axis phase nor the off-axis frequency response is going to be of much concern (other issues that are present in the listening window response will ofc be more audible however).

Just my 2c

 

[andreasmaaan]

Btw, going to make the new crossover simulation audio files now, will share when done

And thanks!

 

[JustIntonation]

Interesting idea, I'm wondering why you want the room to be so close to anechoic?

And to play devil's advocate, I think in reality you'll have the opposite situation: if your room really is going to be that reflection free, neither the off-axis phase nor the off-axis frequency response is going to be of much concern (other issues that are present in the listening window response will ofc be more audible however).

Just my 2c

I want it to be anechoic for 2 reasons. First, it gives the most realistic and detailed soundstage / depth there is with the right music. Truly like being there except you have an additional "magnifying glass" by turning up the volume. It's a very special sound. Like a headphone except many times better in fidelity and not inside your head but instead with perfect head related transfer function so sounds can be heard to be almost against your head to hundreds of meters away. It's really an experience in and of itself, not anything like a speaker in a room and not anything like a headphone.

Second reason is, because you hear everything and the sound is completely flat in frequency response at your ear (or with any curve you choose) it allows to make / mix / master music very well. I've spent the past 12 years doing full time research in music theory (how our brains handle the tonal side of music) and have now finished this. I still have to write a book and publish etc but taking a well deserved break before doing this, and this is my break Still somewhat usefull as I want to produce some music based on some new possibilities given by my reasearch (like correctly harmonized "microtones" like those found in traditional makam music). Want to make it on a high resolution soundsystem and it doesn't get more high resolution than in an anechoic environment.

I had such a room before, but with a few errors. Though we learn from the mistakes.
I thought it wasn't possible to make such a room in my current house. Was fantasizing about building such a room in the future when I got the realization that a version that should work wel is indeed possible in my room. That was a few days before I started this thread

And yes that was my initial though. That in such a room off-axis does not matter. But my experience with several Klein+Hummel monitors in my previous room made me a bit scared. They gave me trouble around the crossover. I then thought the window for truly in phase crossover on-axis is so small you'll have to put your head in a vice grip. So I started thinking about proper crossover behavior and making the listening window wide enough. Perhaps I've gone a bit overboard with this though.. And perhaps more of the trouble I heard before was more due to a ground reflection (which I know was bothering me a lot in my previous room, it was semi anechoic half a meter thick glasswool with space behind everywhere with only the floor not treated, but that was one bad sounding floor it was thick plasterboard with floorheating and it vibrated and gave a strong relfection.. so audible in those listening circumstances).
Still making the crossover sim examples (got distracted a bit) and I'll know after I made them which angle is still acceptable to me. As long as I can move my head in a 20cm vertical window without any SQ loss (I really don't want to hear any phasing in that window at all) I'm actually happy enough perhaps..

 

[andreasmaaan]

I want it to be anechoic for 2 reasons. First, it gives the most realistic and detailed soundstage / depth there is with the right music. Truly like being there except you have an additional "magnifying glass" by turning up the volume. It's a very special sound. Like a headphone except many times better in fidelity and not inside your head but instead with perfect head related transfer function so sounds can be heard to be almost against your head to hundreds of meters away. It's really an experience in and of itself, not anything like a speaker in a room and not anything like a headphone.

Second reason is, because you hear everything and the sound is completely flat in frequency response at your ear (or with any curve you choose) it allows to make / mix / master music very well. I've spent the past 12 years doing full time research in music theory (how our brains handle the tonal side of music) and have now finished this. I still have to write a book and publish etc but taking a well deserved break before doing this, and this is my break Still somewhat usefull as I want to produce some music based on some new possibilities given by my reasearch (like correctly harmonized "microtones" like those found in traditional makam music). Want to make it on a high resolution soundsystem and it doesn't get more high resolution than in an anechoic environment.

I had such a room before, but with a few errors. Though we learn from the mistakes.
I thought it wasn't possible to make such a room in my current house. Was fantasizing about building such a room in the future when I got the realization that a version that should work wel is indeed possible in my room. That was a few days before I started this thread

And yes that was my initial though. That in such a room off-axis does not matter. But my experience with several Klein+Hummel monitors in my previous room made me a bit scared. They gave me trouble around the crossover. I then thought the window for truly in phase crossover on-axis is so small you'll have to put your head in a vice grip. So I started thinking about proper crossover behavior and making the listening window wide enough. Perhaps I've gone a bit overboard with this though.. And perhaps more of the trouble I heard before was more due to a ground reflection (which I know was bothering me a lot in my previous room, it was semi anechoic half a meter thick glasswool with space behind everywhere with only the floor not treated, but that was one bad sounding floor it was thick plasterboard with floorheating and it vibrated and gave a strong relfection.. so audible in those listening circumstances).
Still making the crossover sim examples (got distracted a bit) and I'll know after I made them which angle is still acceptable to me. As long as I can move my head in a 20cm vertical window without any SQ loss (I really don't want to hear any phasing in that window at all) I'm actually happy enough perhaps..

Sounds really interesting. The research too What angle are you coming at music theory from (pm if it’s too off topic - im really into this stuff).

I’m also building a studio atm for producing/mixing. Slightly different approach as I’ll be absorbing only front wall and back wall up to about 2m from the floor, and also floor reflections via a rock wool filled mixing desk with open back and perforated wood top. Ceiling in this place is 6.5m high concrete with a +/-30cm corrugation, so I’m going to allow some reflections off the ceiling and upper 4.5m of the walls (arrival time >30ms, which I figure should sound quite nice if audible).

Keep us posted on the speaker design...

 

[Thomas savage]

Sounds really interesting. The research too What angle are you coming at music theory from (pm if it’s too off topic - im really into this stuff).

I’m also building a studio atm for producing/mixing. Slightly different approach as I’ll be absorbing only front wall and back wall up to about 2m from the floor, and also floor reflections via a rock wool filled mixing desk with open back and perforated wood top. Ceiling in this place is 6.5m high concrete with a +/-30cm corrugation, so I’m going to allow some reflections off the ceiling and upper 4.5m of the walls (arrival time >30ms, which I figure should sound quite nice if audible).

Keep us posted on the speaker design...

Or make a new thread if you guys think it’s of intrest to the wider membership. Thread drift is fine but sometimes it does a injustice to the invading topic..

 

[JustIntonation]

Sounds really interesting. The research too What angle are you coming at music theory from (pm if it’s too off topic - im really into this stuff).

I’m also building a studio atm for producing/mixing. Slightly different approach as I’ll be absorbing only front wall and back wall up to about 2m from the floor, and also floor reflections via a rock wool filled mixing desk with open back and perforated wood top. Ceiling in this place is 6.5m high concrete with a +/-30cm corrugation, so I’m going to allow some reflections off the ceiling and upper 4.5m of the walls (arrival time >30ms, which I figure should sound quite nice if audible).

Keep us posted on the speaker design...

Aah cool. And sounds like a good ceiling yes! (and it'll surely be audible)
Be mindful though of first reflections in the bass (not even talking room modes). There's basically no absorbing them enough. I had 50cm of the optimal flow resistance glasswool for that thickness and the deep bass still went through by far enough to matter (killed the resonant modes though). In my experience speakers need to be either 6meter of so from front wall or less than a meter with thick absorption for the upper bass and up otherwise the direct reflection will cause interence enough to throw things off in a nasty way.
Room reflections >30ms I have a mixed feeling about personally. I've heard them work really well and sound great, but in my own rooms it never worked out well.. But however nice the reflections may work they will give a different listening experience, room reverb/reflections in my experience can give dry music a sense of space and good sound, but it interferes with recordings where there is a good space in the recording itself. Sadly can't have both at the same time. But for commercial music what you're building probably indeed works better. Diffused direct reflections can be great for this too. Btw if your ceiling doesn't work out thick velour or wool curtains can be a fix if not overdone, removes the most audible hf part (but when overdone can make a room too unbalanced of course).
Strange thing is, best room I ever heard was big, about 8m walls and ceiling, almost completely cubic in form which is usually regarded as bad. Had front and back wall very diffuse, and side walls and ceiling no diffusion at all, was all marble and glass that room and basically no absorption. And strangely it sounded great.. all music put into that room got a huge soundstage in a way that was really intelligible.
Rooms are strange.. hard to tell what'll end up working. What I can tell though is that I've never heard a room with plaster walls work. In my opinion always put absorption on plasterwalls.

As for the music theory research it's too long a story to converse about casually sadly. Really need to write a thick book in the future
What I can tell though is a controversial thing.. I've found that the brain quantizes the interval space into perfect octaves (2/1) and perfect fifths (3/2), corresponding to the western notation system actually. This can in it's pure / just form be described as an extended Pythagorean tuning (and I find what is classically though of as "just intonation" with 5/4 major thirds etc is incorrect, extended Pythagorean is the true "just intonation". We further find that especially in polyphonic music musical context is more important that actual tuning, for instance if a chord behaves as for instance a dominant 7th we can tune that minor seventh as an augmented sixth as if it is a German sixth chord (which is a Pythagorean comma higher when tuned just) but we will only hear it as a slightly out of tune minor seventh in this instance. In traditional monophonic music we are more free to hear the interval as tuned, in Turkish/Arab/Persian music often more complex intervals are used (we used to have them in the west as well before polyphony set in), for instance Turkish rast is G-A-Cb-C-D-E-Gb-G instead of western major G-A-B-C-D-E-F#-G. It gets too complex to explain here how to harmonize these more remote intervals in a musical way, as I wrote earlier with the German sixth vs dominant seventh chord we can't just harmonize this by replacing a major third in a major or minor triad with an augmented fourth as we'll still hear it as an out of tune major third. Long story to explain my harmonic theory for harmonizing such intervals correctly.
And now to get slightly back on topic If we tune (correctly spelled, simple western well understood) music to extended Pythagorean tuning, we actually get an increase in soundquality! 12-tone equal temperament "floats" which gives an overal phasy haze to the music which hides fines details and hinders tranparancy with polyphonic music. Extended Pythagorean tuning is transparent (though this will also show clear any errors in timbre etc, it's a double edged sword. But if your music is otherwise very high quality a simple change of tuning can lift it to a higher level.)

 

[JustIntonation]

Uploaded the crossover simulation files on wetransfer:
https://we.tl/t-qagYM37ZMt

Maybe I overdid it a little 1.4 gig lol.
Only did the 2000 Hz crossovers. All Linkwitz-Riley from LR2 (12dB/oct) to LR16 (96dB/oct).
Further labeled them according to the axis where A0 is on-axis and A100 is the cancellation axis below on-axis (if the tweeter is on top). The other points are A54, A27, A18 and A9. They got to be these angles because then I could use exact an exact sample delay instead of a decimal sample delay which uses internal resampling (not that it would be audible but still..)
Took care I did it all correctly. And was surprised that the difference between an actual delayed cancellation axis is much less severe than simply switching the polarity of an on-axis tweeter (which is how I did my quick test before). So this is good news, crossovers are bad but not as bad as I initially thought.. (edit: nope that wasn't it, just checked. I think it was the different crossover freq that made the difference.. Think I had it set to 1.6kHz before when I tested various slopes. I'll check later to see if that made that much of a difference. Maybe make a new batch with different crossover frequencies to see how much the freq affects it, perhaps the mids are indeed much more sensitive.)