If you use 100db/octave filters then you use FIR: the one i use are not as steep most of the time and are totaly transparent whatever the frequency range used.
If you took care of acoustical design ( directivity, no mismatch in membrane area, things like that) there is no reasons they would be audible even at 3,5khz which is the peak sensitivity of human beings.
Those artists seems locked in 1982 ( not that it's bad, Vangelis work on Blade Runner is a major breakthrough from early ambiant works like Tangerine Dream or K.Schulze). Maybe it's the style. I'm more used to heavy sub drone with ambient.
And coax are not bad too for this kind of things ( this is what Vangelis used for Blade Runner production). Even more with sub.
If you took care of acoustical design ( directivity, no mismatch in membrane area, things like that) there is no reasons they would be audible even at 3,5khz which is the peak sensitivity of human beings.
Those artists seems locked in 1982 ( not that it's bad, Vangelis work on Blade Runner is a major breakthrough from early ambiant works like Tangerine Dream or K.Schulze). Maybe it's the style. I'm more used to heavy sub drone with ambient.
And coax are not bad too for this kind of things ( this is what Vangelis used for Blade Runner production). Even more with sub.
Hi krivium,
Yes, I am using FIR. I am using such steep filters hoping that it reduces the frequency range where drivers effectively overlap. I think it makes some practical sense. It should also help in my case if the acoustic summation of drivers' outputs are quite different from electrical, and transition bands are messed up. At least I'd have narrower areas of the frequency response messed up, so easier for other DSP S/W to correct them.
Yes, I am using FIR. I am using such steep filters hoping that it reduces the frequency range where drivers effectively overlap. I think it makes some practical sense. It should also help in my case if the acoustic summation of drivers' outputs are quite different from electrical, and transition bands are messed up. At least I'd have narrower areas of the frequency response messed up, so easier for other DSP S/W to correct them.
I fear you overate what dsp can do.
They won't help to solve acoustic design issue, they just can't. Even if they perform 'room correction' *.
Yes they restrict/narrow overlap range but if you have eg a directivity mismatch it won't solve the issue: step in directivity will still be present, transition will be 'shorter' but that is all.
In practice i rarely use higher steepness than 48db/octave, it makes for half an octave overlap for drivers to fade in/out. Steeper slope can be interesting if you need to come close to breakup region or other nasty artefacts but it's mainly interesting in PA or very harsh drivers conditions imho.
* i'm in the camp of users who think dsp don't perform room correction 90% of time, but loudspeaker correction. The only case i think it can effectively correct the room behavior is in low or very low end. Other part of the spectrum it's the loudspeakers/drivers which are corrected. Ymmv but once you'll get into measurements we could dig deeper in the subject imo.
They won't help to solve acoustic design issue, they just can't. Even if they perform 'room correction' *.
Yes they restrict/narrow overlap range but if you have eg a directivity mismatch it won't solve the issue: step in directivity will still be present, transition will be 'shorter' but that is all.
In practice i rarely use higher steepness than 48db/octave, it makes for half an octave overlap for drivers to fade in/out. Steeper slope can be interesting if you need to come close to breakup region or other nasty artefacts but it's mainly interesting in PA or very harsh drivers conditions imho.
* i'm in the camp of users who think dsp don't perform room correction 90% of time, but loudspeaker correction. The only case i think it can effectively correct the room behavior is in low or very low end. Other part of the spectrum it's the loudspeakers/drivers which are corrected. Ymmv but once you'll get into measurements we could dig deeper in the subject imo.
You won't even be sure it's near correct.
In a no measurement type of crossover your first tool will be swapping polarity and listening. This way you might tell whether you are dealing with a null (cancellation). If so you should reverse polarity and not try to fix the null, because 0+0=0 and you'll just create more problems.
A person won't be able to properly describe every problem simply after listening to it, no matter how good they may be. Some people are good at making assumptions in a situation like this, but there will still be limitations in what they can achieve.
Hi krivium,
I don't know why, but this website doesn't allow me to 'quote' your post above. So, a bit inconvenient, but just copy and paste...
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I fear you overate what dsp can do.
They won't help to solve acoustic design issue, they just can't. Even if they perform 'room correction' *.
------
Maybe I do, but I didn't hear serious problems at least in my current setup, and I think I will improve something in the next project.
Some problems can be solved, but some problems can't be as you pointed out. There is no way directivity of drivers can be corrected by the DSP, or any electronic/electric means. Something has to be done mechanically. However, the problem can be 'mitigated' by DSPs by correcting the response around listeners' ears. I believe that's what 'room correction' does. So, now the term 'room correction' sounds misleading. 🙂. And, it's good enough for me.
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In practice i rarely use higher steepness than 48db/octave, it makes for half an octave overlap for drivers to fade in/out. Steeper slope can be interesting if you need to come close to breakup region or other nasty artefacts but it's mainly interesting in PA or very harsh drivers conditions imho.
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Maybe my steep crossover is more for peace of mind, but you also recognize its possibly limited benefit. According to some people not fond of ATC midranges I am using now, it may be the case that I am putting crossover points(380/3800) quite close to those undesirable regions you mentioned. I don't hear any bad artifact or sign of those, maybe thanks to this steep crossover I am using.
----
* i'm in the camp of users who think dsp don't perform room correction 90% of time, but loudspeaker correction. The only case i think it can effectively correct the room behavior is in low or very low end. Other part of the spectrum it's the loudspeakers/drivers which are corrected. Ymmv but once you'll get into measurements we could dig deeper in the subject imo.
---
This is the point I was wondering about myself I remember Meridian was saying they don't correct room response over fairly low frequency(3kHz, or lower?), and their claim makes some sense. But if the speakers have pretty obvious signature in frequency response, they can be corrected. I used/use my current system in 2 very different spaces, but it sounded quite similar except the bass response, so this appears working quite consistently on the higher side of the frequency range. I also tried my modified surround processor with 2 different speakers(tri-amping ready as prototypes at the time) in someone else's home, and it worked well consistently. So, I seem to have somewhat of conter-examples to your theory, but feel that your theory could have some good amount of truth in it.
I don't know why, but this website doesn't allow me to 'quote' your post above. So, a bit inconvenient, but just copy and paste...
------
I fear you overate what dsp can do.
They won't help to solve acoustic design issue, they just can't. Even if they perform 'room correction' *.
------
Maybe I do, but I didn't hear serious problems at least in my current setup, and I think I will improve something in the next project.
Some problems can be solved, but some problems can't be as you pointed out. There is no way directivity of drivers can be corrected by the DSP, or any electronic/electric means. Something has to be done mechanically. However, the problem can be 'mitigated' by DSPs by correcting the response around listeners' ears. I believe that's what 'room correction' does. So, now the term 'room correction' sounds misleading. 🙂. And, it's good enough for me.
-----
In practice i rarely use higher steepness than 48db/octave, it makes for half an octave overlap for drivers to fade in/out. Steeper slope can be interesting if you need to come close to breakup region or other nasty artefacts but it's mainly interesting in PA or very harsh drivers conditions imho.
-----
Maybe my steep crossover is more for peace of mind, but you also recognize its possibly limited benefit. According to some people not fond of ATC midranges I am using now, it may be the case that I am putting crossover points(380/3800) quite close to those undesirable regions you mentioned. I don't hear any bad artifact or sign of those, maybe thanks to this steep crossover I am using.
----
* i'm in the camp of users who think dsp don't perform room correction 90% of time, but loudspeaker correction. The only case i think it can effectively correct the room behavior is in low or very low end. Other part of the spectrum it's the loudspeakers/drivers which are corrected. Ymmv but once you'll get into measurements we could dig deeper in the subject imo.
---
This is the point I was wondering about myself I remember Meridian was saying they don't correct room response over fairly low frequency(3kHz, or lower?), and their claim makes some sense. But if the speakers have pretty obvious signature in frequency response, they can be corrected. I used/use my current system in 2 very different spaces, but it sounded quite similar except the bass response, so this appears working quite consistently on the higher side of the frequency range. I also tried my modified surround processor with 2 different speakers(tri-amping ready as prototypes at the time) in someone else's home, and it worked well consistently. So, I seem to have somewhat of conter-examples to your theory, but feel that your theory could have some good amount of truth in it.
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You can't quote message just above the one you write, it's a limitation which have been decided to make threads less painful to read.
Can be frustrating at time but it's way more readable as is imho.
You've got ATC mid atm? Those are wonderful drivers but i'm not fond of them ( i spent some years with scm110a as my mains in studio i worked in). In fact ATC design philosophy is to have constant directivity over a wide freq range but it's very 'wide' spread (-6db @ 140° ) which kind of push requirements in room treatments to limit Early Reflections. That's why they are most often used in very 'dead' control room's acoustic : Northward Acoustic's designer T.Jouanjean use ATC monitors but the room is an evolution of Hidley's Zero Environment principle which is as dead as a room can be... only front of the room is reflective the whole rest of the room is a gigantic wideband 'bass trap'. T.Jouanjean implemented diffusors at back wall and above mixing point for the human being into the room not feel too much oprressed...
And indeed once into a room like that the mid shine by it's transparency. But in a domestic environnement where there is low ER control... i don't find the quality to be still shining. It's a pov, yours can be different. But i've heard both implementations and can judge by myself. 😉
The bass respond sounded different for a good reason: a room is a two face thingy with a border defined by something called Schroeder frequency. Above this freq your loudspeakers dominate the rendering in the couple formed by room/loudspeakers. Below this freq the room dominate what happen.
What does it mean in practice?
You can easily solve acoustic issue by physical treatment above Schroeder freq ( acoustic panels, absorbing, reflecting, diffusing/difracting).
Below the room will see modal behavior and this cannot be easily treated by acoustic treatments as the length of waveforms require lot of space/bulkness to perform anything...
In real world domestic room Schroeder freq will vary with room size but expect it to happen between 250hz and 150hz.
There is different ways to approach things but here is my own pov about it: implement an RFZ by treating first point of reflection for 200hz and above with some absorbers panels or by redirecting panels ( but you'll be freq/size limited in that case... for a 1khz wave to be redirected you need an 1m wide panel angled to redirect outside listening point. For 500hz, 2m wide panel, 250hz 4m wide,....).
Below that freq then implement some 'room correction' to compensate for issues. Or implement a multisub approach, or both at the same time...
Have you read Geddes? Have you searched for Mitchba's post on this ( Here and in other sites: look for Mitch Barnett 'accurate audio reproduction' ebook, worth a read... as well as his test of Audiolense and other room correction soft...). Worth a read imho.
Can be frustrating at time but it's way more readable as is imho.
You've got ATC mid atm? Those are wonderful drivers but i'm not fond of them ( i spent some years with scm110a as my mains in studio i worked in). In fact ATC design philosophy is to have constant directivity over a wide freq range but it's very 'wide' spread (-6db @ 140° ) which kind of push requirements in room treatments to limit Early Reflections. That's why they are most often used in very 'dead' control room's acoustic : Northward Acoustic's designer T.Jouanjean use ATC monitors but the room is an evolution of Hidley's Zero Environment principle which is as dead as a room can be... only front of the room is reflective the whole rest of the room is a gigantic wideband 'bass trap'. T.Jouanjean implemented diffusors at back wall and above mixing point for the human being into the room not feel too much oprressed...
And indeed once into a room like that the mid shine by it's transparency. But in a domestic environnement where there is low ER control... i don't find the quality to be still shining. It's a pov, yours can be different. But i've heard both implementations and can judge by myself. 😉
The bass respond sounded different for a good reason: a room is a two face thingy with a border defined by something called Schroeder frequency. Above this freq your loudspeakers dominate the rendering in the couple formed by room/loudspeakers. Below this freq the room dominate what happen.
What does it mean in practice?
You can easily solve acoustic issue by physical treatment above Schroeder freq ( acoustic panels, absorbing, reflecting, diffusing/difracting).
Below the room will see modal behavior and this cannot be easily treated by acoustic treatments as the length of waveforms require lot of space/bulkness to perform anything...
In real world domestic room Schroeder freq will vary with room size but expect it to happen between 250hz and 150hz.
There is different ways to approach things but here is my own pov about it: implement an RFZ by treating first point of reflection for 200hz and above with some absorbers panels or by redirecting panels ( but you'll be freq/size limited in that case... for a 1khz wave to be redirected you need an 1m wide panel angled to redirect outside listening point. For 500hz, 2m wide panel, 250hz 4m wide,....).
Below that freq then implement some 'room correction' to compensate for issues. Or implement a multisub approach, or both at the same time...
Have you read Geddes? Have you searched for Mitchba's post on this ( Here and in other sites: look for Mitch Barnett 'accurate audio reproduction' ebook, worth a read... as well as his test of Audiolense and other room correction soft...). Worth a read imho.
If you used an appropriate midrange driver with an appropriate passband then with your active crossover you could test the truth or not of audiophile beliefs like this. Unfortunately the driver you are currently looking at is not designed to deliver full output at lower midrange frequencies and will generate audible distortion at higher SPLs if asked to do so. Perhaps more importantly it would enable you to hear what different crossover slopes sound like (subject to being able to implement them correctly which without a microphone is going to be difficult) and hence why no high fidelity speakers use steep crossover slopes. The sound effect created with a flat baffle can sound a bit like enhanced detail and may be appropriate for an audiophile speaker (sounds good to me) rather than a high fidelity one (sounds neutral) depending on your objectives. Both objectives are perfectly valid for a hobby but mixing them up can lead to confusion.
It's difficult to offer constructive comments without a speaker design. Are we talking about 2 x 8" cone woofers, 1 x 6.5" cone lower mid, 1 x 2-3" dome upper mid, 1 x dome 3/4" tweeter, a flat baffle tower speaker, active 4 way DSP crossover plus overall DSP room correction. Wide bandwidth for use in a largish room with reasonable acoustics.
If interested, here is simplified test for audibility of crossover frequency: https://audioexperiment.com/pages/crossover-filters-on-headphones/
It's just crossover split and then combined back in electrical domain so it doesn't represent reality in that sense. Point is to test audibility of crossover itself, which to me is inaudible at any frequency and slope (with the complement lowpass setting). Perhaps you guys find some settings more audible than others?
In reality drivers on a loudspeaker are different and at different physical location and summing is in acoustic domain so a lot of things can affect which crossover frequency and slope sounds good. Important point is that crossover frequency and slope in isolation doesn't seem to make much if any difference, but combination of driver performance, system design, room acoustics and how auditory system interprets it all could.
For example, listen outside (~anechoic) at design axis with proper design so that all drivers in their good bandwidth and slopes nice, and I think there should be no difference to ear at which frequency the crossover is at. Listen at small room, fail to design the system properly, fail to position it properly, and it might matter at which frequency the problems are. Although, if there is problems they are likely audible no matter the frequency.
It is very hard to compare as crossover at 500Hz or 800Hz in reality, as it likely means the systems are very different to be "optimal", and there must be a difference due to all kinds of things being different now.
And whether any of this matters is perhaps tied to listening distance (and acoustics), when room early reflections dominate in perception, I think it hardly matters where the crossovers are at, and how well the system is spot on tuned, as it's just mush of sound anyway, phase information stirred up. Many people seem to have their systems setup like that. On the other hand, if one listens relatively close where direct sound dominates perception, then there is a chance crossover has more audible effects to sound. Perhaps here "point source" in mids is important, especially if one moves a lot and not always exactly head at design axis. So, perhaps it is good "ideal" to have vocal range with one driver, but I'm not sure if that is always important.
Personally, I'm not stressing about it myself currently, I'm more stressed about boxy sound of bass, placement, and things like that, how system interacts with room, so overall directivity etc. which all dictate what the system is like, how it must measure in order to work, and crossover are then made to fit the measurements. Crossovers take some work to fine tune, but not sure the frequency as such makes too much difference other than what other problems they bring out or suppress in the system if tuned otherwise. If I wanted to radically change crossover frequency, the whole system must be built again with different components, different design altogether. In this sense, starting system design from crossover frequencies seems backwards to me, because it then dictates directivity and all kinds of things, which are much better optimized from acoustic standpoint in my opinion.
It's just crossover split and then combined back in electrical domain so it doesn't represent reality in that sense. Point is to test audibility of crossover itself, which to me is inaudible at any frequency and slope (with the complement lowpass setting). Perhaps you guys find some settings more audible than others?
In reality drivers on a loudspeaker are different and at different physical location and summing is in acoustic domain so a lot of things can affect which crossover frequency and slope sounds good. Important point is that crossover frequency and slope in isolation doesn't seem to make much if any difference, but combination of driver performance, system design, room acoustics and how auditory system interprets it all could.
For example, listen outside (~anechoic) at design axis with proper design so that all drivers in their good bandwidth and slopes nice, and I think there should be no difference to ear at which frequency the crossover is at. Listen at small room, fail to design the system properly, fail to position it properly, and it might matter at which frequency the problems are. Although, if there is problems they are likely audible no matter the frequency.
It is very hard to compare as crossover at 500Hz or 800Hz in reality, as it likely means the systems are very different to be "optimal", and there must be a difference due to all kinds of things being different now.
And whether any of this matters is perhaps tied to listening distance (and acoustics), when room early reflections dominate in perception, I think it hardly matters where the crossovers are at, and how well the system is spot on tuned, as it's just mush of sound anyway, phase information stirred up. Many people seem to have their systems setup like that. On the other hand, if one listens relatively close where direct sound dominates perception, then there is a chance crossover has more audible effects to sound. Perhaps here "point source" in mids is important, especially if one moves a lot and not always exactly head at design axis. So, perhaps it is good "ideal" to have vocal range with one driver, but I'm not sure if that is always important.
Personally, I'm not stressing about it myself currently, I'm more stressed about boxy sound of bass, placement, and things like that, how system interacts with room, so overall directivity etc. which all dictate what the system is like, how it must measure in order to work, and crossover are then made to fit the measurements. Crossovers take some work to fine tune, but not sure the frequency as such makes too much difference other than what other problems they bring out or suppress in the system if tuned otherwise. If I wanted to radically change crossover frequency, the whole system must be built again with different components, different design altogether. In this sense, starting system design from crossover frequencies seems backwards to me, because it then dictates directivity and all kinds of things, which are much better optimized from acoustic standpoint in my opinion.
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I agree with Andy, it is difficult at this early stage, but hey you have a bunch of guys all interested and trying to help, so even before you reach 1st base it proves the DIY forum is a good thing!
The "heated debates are actually really good as it pushes everyone to focus on the most important points they are trying to make, then you/the OP/ guys asking the questions, can sit back read the "debate" and then cherry pick what you like... As Sir Winston Churchill once said in his defense of democracy and freedom of speech challenging those who wanted to appease Hitler, "Although I will disagree with you until my dying breath, I will also defend your right to challenge me" . Long live open debate!
I have never seen that before, and I find its funny cause up until recently I was cutting and pasting exactly the same as jheoaustin!
As you say without a binaural signal, simulated driver radiation pattern, simulated cabinet diffraction and simulated room this headphone test includes little that is relevant to the audibility of crossovers. With it (and implemented reasonably well) it would be an excellent test because the effects of the speaker baffle and room could be varied to see how they interact with the crossover slopes.
We must wait that capability for a while still. Tried https://www.treble.tech/ some time ago and it wasn't realistic enough for this kind of tests. Perhaps in few years, if they have interest to develop it, I left some feedback and request to do so. But, assuming it's not lucrative as architectural acoustics I fear it's not gonna happen. Perhaps DIY folk could do one, with AI assisting proramming and math. Original ideas needed though, and processing power, ability to optimize / generalize as well as listen to evaluate when it's accurate enough. Quite a task.
Until then, best to build real things and try to develop listening skill and knowledge in general, to gravitate toward better sound, what ever that is for each 🙂
Until then, best to build real things and try to develop listening skill and knowledge in general, to gravitate toward better sound, what ever that is for each 🙂
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Thanks for posting this Krivium, I think this is very important point. A very simple but effective way to eliminate most directivity/radiation errors is to avoid "mismatch in membrane area". These 4 little words are very important!
Assuming a DSP active 4 way, my "my top tips" (dare I say that without Jim throwing his plasma conduits out the air lock?🤣) are:
Subs, 18 inch to 12 inch - Never use above 80 Hz so directivity is pretty much a non issue regardless of what you are crossing over to.
Dedicated mid bass:
Using a 15 inch covering 80 Hz to 300 Hz is the best IMO. https://www.beyma.com/speakers/Fich...ers-data-sheet-low-mid-frequency-15P80FeN.pdf
Also a superb 12 inch midbass option is cover 80 Hz to 800 Hz. https://www.beyma.com/speakers/Fich...rs-data-sheet-low-mid-frequency-12P80FeV2.pdf
A fantastic option is a 10 inch covering 80 Hz to around 1,200 Hz, maybe 1,400Hz, https://www.precision-devices.com/w...PD-103NR1-Technical-Specifications-051021.pdf 9 Just look at that frequency response...!
An 8 inch mid bass can cover 80 Hz up to 1,600 Hz. https://www.eighteensound.it/en/products/lf-driver/8-0/8/8NMB420
Midrange:
Using 10 inch - 200 Hz to 1,200 Hz. Again this PD driver is great: https://www.precision-devices.com/w...PD-103NR1-Technical-Specifications-051021.pdf
8 inch mid - 300 Hz to 1,600 Hz. https://www.phlaudio.com/fileadmin/user_upload/phl_audio/2520_SpecSheet.pdf
6.5 inch 300 Hz to 2 KHz. https://www.phlaudio.com/fileadmin/user_upload/phl_audio/1752NdU_SpecSheet.pdf
I have never used smaller dedicated midrange drivers so I will leave it up others to advise on those.
Highs:
I cant stand small dome tweeters.
Also I have no experience with compression drivers / horns (but would love to try one day).
Over 25 years ago I heard the Manger driver and was hooked... Then BMR and even better the Rapid Energy Decay (RED) drivers, now its only Beyma TPL 200 for me!
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yes…..Maggie’s ……the LRS in particular do very well with symmetrical placement in free space as indicated by your drawing. I have mine set up this way at our country house supported by 4 10” sealed subs in a chalet shaped family room…….with all humility, this little installation trumps everything I’ve built and placed to date…….it’s the system working with the room that makes all the difference. Sadly I cannot recreate anything close in our main home…..living gets in the way. The Maggie install has encouraged me to visit more often than before…..I get out there at least once a month now, even in the winter.
With all the above being said, I won’t extol some heavenly hifi gobbly goop on the Maggie’s…….there are some issues….or ‘non hifi’ things inherent with them…..but damn are they fun to listen to. Combined with the subs, live Led Zeppelin sounds like inside MSG in this room.
More precisely audibility of the group delay, caused by the crossover. But the reality is much more complex than that, because in the case of multi-way speakers, every driver or combinations of them have very specific polar response, distortion profile and the crossover between them affects the combined polar pattern and distortion profile, not just the group delay, but I think you know this.
Anyway, it's good to see probably not the group delay that we hear as difference from different crossovers.
Edit.: after all, the polar polar responses is also a kind of distortion beause there is no perfect polar response that we could talk about.
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YSDR thank you giving me an opportunity to link my prefered white paper! 🙂
https://www.xlrtechs.com/dbkeele.co...ear Phase Digital Crossover Flters Part 1.pdf
https://www.xlrtechs.com/dbkeele.co...ear Phase Digital Crossover Flters Part 2.pdf
Part one is a bit difficult to grasp if you are not a math nerd, second one is easier to get imho.
It's all about what YSDR just talked about: 'every driver or group of them have very specific polar response'.
In this papers they study what happen in vertical directivity with vertically aligned spaced pair of drivers, develop a specific FIR filter profile to allow 'shaping' of overall response in vertical coverage.
Fig 6 of second part is a visual illustration of how you can play with what YSDR talked about.
It works mainly because FIR makes group delay moot. And it show limit of what dsp can do as once past 3x critical frequency (for the 'last' pair+tweeter) you would have to rely on other means ( waveguide) to extend coverage way up. Can be visually seen in the last graph of part 2 ( fig 17,18,19).
There is a lot of useful info hidden into the graph presented: Fig3 of second part is worth spending time looking at and think about imo. Especially on left side of the range of importance of their study... it will make some thumbrule often given obvious ( 1/4 wavelength for Centre To Centre spacing of 2 drivers - and not nescesseraly a pair vertically aligned).
https://www.xlrtechs.com/dbkeele.co...ear Phase Digital Crossover Flters Part 1.pdf
https://www.xlrtechs.com/dbkeele.co...ear Phase Digital Crossover Flters Part 2.pdf
Part one is a bit difficult to grasp if you are not a math nerd, second one is easier to get imho.
It's all about what YSDR just talked about: 'every driver or group of them have very specific polar response'.
In this papers they study what happen in vertical directivity with vertically aligned spaced pair of drivers, develop a specific FIR filter profile to allow 'shaping' of overall response in vertical coverage.
Fig 6 of second part is a visual illustration of how you can play with what YSDR talked about.
It works mainly because FIR makes group delay moot. And it show limit of what dsp can do as once past 3x critical frequency (for the 'last' pair+tweeter) you would have to rely on other means ( waveguide) to extend coverage way up. Can be visually seen in the last graph of part 2 ( fig 17,18,19).
There is a lot of useful info hidden into the graph presented: Fig3 of second part is worth spending time looking at and think about imo. Especially on left side of the range of importance of their study... it will make some thumbrule often given obvious ( 1/4 wavelength for Centre To Centre spacing of 2 drivers - and not nescesseraly a pair vertically aligned).
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Hmm. Depending on the release i think i have a start of answer why Led Zep could sound so good on your Magnepan:
https://www.barrydiamentaudio.com/credits.htm
https://www.barrydiamentaudio.com/studio.htm
https://www.barrydiamentaudio.com/loudness.htm
😉
Bob Marley's mastering he did are very good too!
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