We had a discussion about this at AA last year where I showed that the popular JBL 2" drivers(375, 2441 etc.) has an exponential flare in the ballpark of 180Hz and therefore recommended the horn should be made incorporating this part. Also the rest of the horn should have the same flare.
The JBL throats are ca 38 to 49mm dia with 69mm length.
I should have done a more careful measuring of flare angle etc. but it is still in the pipeline
.Did some calculations with Jean-Michels spreadsheet and I got different hornflare depending on T choosen. AFAIR I got 225Hz at T=0,8 but I´m not sure.
Jmmlc said:
OK, same as me. Now, do I have room for a horn like that? Hmmm....
Oh, OK. I see. Yes, it is very handy for that. He is just using it as an RTA. But isn't there a little EQ down at 35Hz to flatten the low end? Maybe from a DCX or something? What is the EQ shown in the measurements? Was that EQ only for measurements?
A little low end boost on a system like this should not hurt. It would extend lower - and I doubt the 416-8A is working very hard!
Hello Panomaniac,
Jean-Paul used to program the DCX2496 with 2 different configurations, so he can switch between them.
One of this configuration is with equalisation below 35Hz (which is not useful IMHO) and the other one without equalisation below 35Hz.
Listening demonstrated that without equalisation was better and this was verified by the pulse mesurement done by the logsweep+ convolution method.
Measurement performed with equalization shows that distortion rises a lot (may be due to too much equalisation: +18dB at 20Hz!).
response with and without equalisation below 35Hz:
http://zepload.com/images/1242489777_estrade D 0cm & cor.jpg
Response + distortion with equalisation:
http://zepload.com/images/1242565743_Disto 0cm estrade cor.jpg
Response + distortion without equalisation:
http://zepload.com/images/1242565693_Disto 0cm estrade sans cor.jpg
Best regards from Paris, France
Jean-Michel Le Cléac'h
Jean-Paul used to program the DCX2496 with 2 different configurations, so he can switch between them.
One of this configuration is with equalisation below 35Hz (which is not useful IMHO) and the other one without equalisation below 35Hz.
Listening demonstrated that without equalisation was better and this was verified by the pulse mesurement done by the logsweep+ convolution method.
Measurement performed with equalization shows that distortion rises a lot (may be due to too much equalisation: +18dB at 20Hz!).
response with and without equalisation below 35Hz:
http://zepload.com/images/1242489777_estrade D 0cm & cor.jpg
Response + distortion with equalisation:
http://zepload.com/images/1242565743_Disto 0cm estrade cor.jpg
Response + distortion without equalisation:
http://zepload.com/images/1242565693_Disto 0cm estrade sans cor.jpg
Best regards from Paris, France
Jean-Michel Le Cléac'h
panomaniac said:
I see! Distortion does rise quite a bit just to get those bottom 10Hz.
Was there a conclusion as to where the distortion is coming from? Horn, amp, 416-8A, DCX? Or is it a combination of all of these?
This is certainly a very interesting bass horn, it would be nice to learn more about it. It certainly raises a lot of questions.
@revintage: I also think the driver throat to horn throat is important, and maybe not taken into account enough. I'm trying to figure that out on my horns, too.
Was there a conclusion as to where the distortion is coming from? Horn, amp, 416-8A, DCX? Or is it a combination of all of these?
This is certainly a very interesting bass horn, it would be nice to learn more about it. It certainly raises a lot of questions.
@revintage: I also think the driver throat to horn throat is important, and maybe not taken into account enough. I'm trying to figure that out on my horns, too.
panomaniac said:
Non-linear distortion limitations of the driver. Anytime you near fs for bass drivers - distortion goes way up. Amplifying below resonance is generally NOT a good idea (..and driver control starts to rely heavily on driver compliance).
Otherwise it's difficult to tell what the spl's are so it's impossible to say that the rest of the system is otherwise good or bad. Still..
As presented 3rd order seems quite low (excepting the behavior near and below resonance.
On the other hand 2nd order appears higher than it should be. A good push-pull configuration could have significantly reduced this problem (and other even order effects). (..a little late now though.
)The thing is though, in a number of areas a good array (large grouping of woofers) can outperform a bass horn for size, usually with lower distortion, less excursion, fewer thermal problems, and much lower extension. Additionally, you actually can "boost" the low end of such a system without dramatic increases in distortion.
Its cool looking, but the net gain really isn't worth the effort/size at lower freq.s.
(..btw, if I remember correctly Bert Doppenberg (BD Design) came to a similar conclusion.)
Hello ScottG,
I guess you never listen to such large basshorns like Jean-Paul's ones:
or as in Marcel Roggero's system:
http://www.melaudia.net/ecouteSud04MR-1.php
http://www.melaudia.net/ecouteRoggero07-0201.php
or at Vincent Brient's place:
http://vincent.brient.free.fr/principale.htm
or Frédéric Lebas's basshorn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1770740&stamp=1236807427
Distortion is non audible even the one mentionned in Jean-paul's basshorns appeared faintly audible after the measurements were done and only in instant comparisons.
He explains this on message:
http://forums.delphiforums.com/HAUTE_FIDELITE/messages?msg=30479.98
The sound of those large basshorns having a very small cut-off frequency are far better than any array I could listen to. I think this is due to the loading which is mainly resistive above 40Hz, something that you'll never obtain with a box loading (closed or bass-reflex). An array sound far less natural than those bass horns,the sound is relaxed, effortless and in the same time rapid and incredibly dynamic. Array sound PA in comparison...
About Doppemberg bass horns we can see at:
http://www.arduman.com/aa/Sayfalar/bert/bert2/visit.htm
http://www.arduman.com/aa/Sayfalar/bert/syst.htm
As you can see the 2 bass horns are probably calculated using planar wavefronts (which they are never) and heavily truncated (in a Le Cleac'h bass horn there is a common vertical curved wall shared by the 2 horns and from this results less truncation and less diffraction at mouth)
.
Best regards from Paris, France
Jean-Michel Le Cléac'h
I guess you never listen to such large basshorns like Jean-Paul's ones:
or as in Marcel Roggero's system:
http://www.melaudia.net/ecouteSud04MR-1.php
http://www.melaudia.net/ecouteRoggero07-0201.php
or at Vincent Brient's place:
http://vincent.brient.free.fr/principale.htm
or Frédéric Lebas's basshorn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1770740&stamp=1236807427
Distortion is non audible even the one mentionned in Jean-paul's basshorns appeared faintly audible after the measurements were done and only in instant comparisons.
He explains this on message:
http://forums.delphiforums.com/HAUTE_FIDELITE/messages?msg=30479.98
The sound of those large basshorns having a very small cut-off frequency are far better than any array I could listen to. I think this is due to the loading which is mainly resistive above 40Hz, something that you'll never obtain with a box loading (closed or bass-reflex). An array sound far less natural than those bass horns,the sound is relaxed, effortless and in the same time rapid and incredibly dynamic. Array sound PA in comparison...
About Doppemberg bass horns we can see at:
http://www.arduman.com/aa/Sayfalar/bert/bert2/visit.htm
http://www.arduman.com/aa/Sayfalar/bert/syst.htm
As you can see the 2 bass horns are probably calculated using planar wavefronts (which they are never) and heavily truncated (in a Le Cleac'h bass horn there is a common vertical curved wall shared by the 2 horns and from this results less truncation and less diffraction at mouth)
.
Best regards from Paris, France
Jean-Michel Le Cléac'h
ScottG said:
As presented 3rd order seems quite low (excepting the behavior near and below resonance.
On the other hand 2nd order appears higher than it should be. A good push-pull configuration could have significantly reduced this problem (and other even order effects). (..a little late now though.
The thing is though, in a number of areas a good array (large grouping of woofers) can outperform a bass horn for size, usually with lower distortion, less excursion, fewer thermal problems, and much lower extension. Additionally, you actually can "boost" the low end of such a system without dramatic increases in distortion.
Its cool looking, but the net gain really isn't worth the effort/size at lower freq.s.
(..btw, if I remember correctly Bert Doppenberg (BD Design) came to a similar conclusion.)
Hello Angelo,
Having listened carefully to Frédéric LeBas's horn system I feel that the integration of the bass horn was really good. Specially the room seems to have less effect than with conventional enclosures.
Though it seem that very few people possess a very high sensitivity to localize the position of the different horns on a vertical and complain that as the sound moves from bass to treble, they feel that the source of sound moves upward.
I am not myself that much sensible to this vertical positionning.
I guess the problem is worst if time alignment between the different horns is not done carefully.
About diffraction in horns like Jean-Paul or Frédéric's basshorns
It only happen on the horizontal edge of the top plate of the basshorn. I recommanded myself to the builders of those kind of basshorns to use some Iwata's slots near that edge. But unfortunately until now nobody follows my recommandation.
Where the quasicylindrical waves Le Cléac'h bass horn is better than most other basshorns is the ease for the wave to drag along the walls of the listening room (which can be considered itself as a part of the double horn) and the floor (despite some vertical diffraction).
This is illustrated by the attached graph. We can see on the graph that in the horizontal plane the wavefront can expand a lot before a first reflection occurs.
Best regards from Paris, France
Jean-Michel Le Cléac'h
Having listened carefully to Frédéric LeBas's horn system I feel that the integration of the bass horn was really good. Specially the room seems to have less effect than with conventional enclosures.
Though it seem that very few people possess a very high sensitivity to localize the position of the different horns on a vertical and complain that as the sound moves from bass to treble, they feel that the source of sound moves upward.
I am not myself that much sensible to this vertical positionning.
I guess the problem is worst if time alignment between the different horns is not done carefully.
About diffraction in horns like Jean-Paul or Frédéric's basshorns
It only happen on the horizontal edge of the top plate of the basshorn. I recommanded myself to the builders of those kind of basshorns to use some Iwata's slots near that edge. But unfortunately until now nobody follows my recommandation.
Where the quasicylindrical waves Le Cléac'h bass horn is better than most other basshorns is the ease for the wave to drag along the walls of the listening room (which can be considered itself as a part of the double horn) and the floor (despite some vertical diffraction).
This is illustrated by the attached graph. We can see on the graph that in the horizontal plane the wavefront can expand a lot before a first reflection occurs.
Best regards from Paris, France
Jean-Michel Le Cléac'h
angeloitacare said:
Attachments
hello Jean Michel
i've seen some time ago a paper of yours, where it shows the acoustic radiation of a few orchestral instruments. For certain, most instruments radiate in a vertical range , from the floor to 1,5m - 2m of height . From this starting point, is it not a most accurate reproduction, if a loudspeaker radiates also in a similar vertical range ? For some time, i thought, point source reproduction would be the best. But this doesn't occur at a life event. I got a very good integration of the channels of my system, and it reproduces as a whole single acoustical cloud, giving a nice, lifelike dimensionality, in a vertical range , and loads the room quit evenly.
Angelo
Merci JM.
I have seen that wavefront graph before, but forgetten it. Thanks for reposting. It gives a nice top view of how the horn could be built.
I see from the post on the French forum that Jean-Paul has played with the EQ some and changes it a bit depending on the music and how he feels that day. Makes sense. He also says that the distortion was not noticable.
Of course I ran simulations with your speadsheet and believe that one of these monsters might just fit in my room. Oh dear.... And it will, of course, have the Iwata termination slots. Oh dear again...
I have seen that wavefront graph before, but forgetten it. Thanks for reposting. It gives a nice top view of how the horn could be built.
I see from the post on the French forum that Jean-Paul has played with the EQ some and changes it a bit depending on the music and how he feels that day.
Makes sense. He also says that the distortion was not noticable.Of course I ran simulations with your speadsheet and believe that one of these monsters might just fit in my room. Oh dear.... And it will, of course, have the Iwata termination slots. Oh dear again...
Angelo,
It is impossible to reproduce the radiation pattren of most musical instrument in stereophony. The way loudspeakers are separated on a vertical line will have little or no influence on that.
Human hearing is poor in localizing the height of the sources of sounds but soome people are more sensitive to that and they can perceive a tweeter placed on top of a medium horn itself placed on top of a large bass horn. For them the necessary distance between the axis of the different horns and loudspeakers of the same channel is a problem as they can perceive the tweeter, the medium and the bass as different sources when a "normal" audiophile will pereive it as a single source.
I have a friend who even has the problem when listening to VOT and to a 3 ways Onken System!
On the other hand, in most musical event, the sources of low frequencies are generally positionned at a lower height than the sources of medium frequencies and themselves are positionned at a lower height than the sources of high frequencies so, a set up as those of JeanPaul or Frédéric 's systems reproduce accurately that pattern
Best regards from Paris, France
Jean-Michel Le Cléac'h
It is impossible to reproduce the radiation pattren of most musical instrument in stereophony. The way loudspeakers are separated on a vertical line will have little or no influence on that.
Human hearing is poor in localizing the height of the sources of sounds but soome people are more sensitive to that and they can perceive a tweeter placed on top of a medium horn itself placed on top of a large bass horn. For them the necessary distance between the axis of the different horns and loudspeakers of the same channel is a problem as they can perceive the tweeter, the medium and the bass as different sources when a "normal" audiophile will pereive it as a single source.
I have a friend who even has the problem when listening to VOT and to a 3 ways Onken System!
On the other hand, in most musical event, the sources of low frequencies are generally positionned at a lower height than the sources of medium frequencies and themselves are positionned at a lower height than the sources of high frequencies so, a set up as those of JeanPaul or Frédéric 's systems reproduce accurately that pattern
Best regards from Paris, France
Jean-Michel Le Cléac'h
angeloitacare said:
Jmmlc said:
True, I haven't.
Note however that I was pretty specific:
"..in a number of areas a good array (large grouping of woofers) can outperform a bass horn for size, usually with lower distortion, less excursion, fewer thermal problems, and much lower extension. Additionally, you actually can "boost" the low end of such a system without dramatic increases in distortion."
I'm not saying that an array will necessarily sound as good *above 40 Hz*, but rather as a bass system that operates near the drivers resonance and below - the an array has a number of advantages (over the bass horn).
Of course some of those horns were also arrays.
The ones that I could see (with more than one woofer) however didn't appear to have push-pull configuration (..though it's entirely possible that the particular drivers used in that instance were already low with respect to 2nd order distortion).
As far as distortion and audibility - at lower freq.s where "hall sound" is more apparent, I have found that this is one of the few exceptions where non-linear distortion actually is audible with music at moderate to high levels.
The loading sound is internal "box" compression (something a bass horn can have depending on the design). A well crafted aperiodic, (or IB built into the home), in combination with a large number of drivers should remove this problem. I'm not saying it will sound precisely the same at all freq.s as a bass horn, but it may have some advantages in sound quality above 40 Hz, and will almost certainly have substantial advantages below (and well below) 40 Hz when compared to an low freq. "eq'ed" system (bass-horn).
Hello ScottG,
As I said before I used to listen to few of those bass horns and you can understand that with those beasts, we were curious to listen at very high SPL. No distortion was audible in the bass and this is probably because, even at high SPL, the cone displacement is very small due to an excellent loading of the driver by the horn.
But distortion is not IMHO what give a more natural sound for those large basshorns. With such bass horn as the Le Cléac'h horn the group delay is constant above 40Hz.
Furthermore as you can use them until 250 to 350Hz there is an excellent pulse response.
Because you simply cannot have a constant group delay below 150Hz -200Hz with conventionnal arrays (even in infinite baffle) their pulse response is quite bad compared to the bass horns. (Aditionally they will be difficult to use until 250Hz or more).
The respect of the relative phase of the harmonic components of a musical note, even in the bass is probably why bass horns sounds more natural...
Best regards from Paris, France
Jean-Michel Le Cléac'h
As I said before I used to listen to few of those bass horns and you can understand that with those beasts, we were curious to listen at very high SPL. No distortion was audible in the bass and this is probably because, even at high SPL, the cone displacement is very small due to an excellent loading of the driver by the horn.
But distortion is not IMHO what give a more natural sound for those large basshorns. With such bass horn as the Le Cléac'h horn the group delay is constant above 40Hz.
Furthermore as you can use them until 250 to 350Hz there is an excellent pulse response.
Because you simply cannot have a constant group delay below 150Hz -200Hz with conventionnal arrays (even in infinite baffle) their pulse response is quite bad compared to the bass horns. (Aditionally they will be difficult to use until 250Hz or more).
The respect of the relative phase of the harmonic components of a musical note, even in the bass is probably why bass horns sounds more natural...
Best regards from Paris, France
Jean-Michel Le Cléac'h
ScottG said:
Jmmlc said:
I'd like to see this (if possible).
Are you saying that there is no phase shifting between the 300-40Hz region?
Or, are you perhaps saying that the phase shift is shifting at a constant rate vs. freq..? (i.e. 25 deg. phase shift between 200-100 Hz and a 25 degree phase shift between 100-50 Hz.)
Hello ScottG,
You'll find in attached file:
1) the response curve of a Le Cléac'h Basshorn unequalized (the response is a bit limited in LF due to ARTA's FFT window the max length of which depends on the length of the signal window... )
2) the phase curve (the "true" phase curve not a useless "minphase curve")
3) the group delay curve (the "true" group delay not the one calculated from the minphase)
As you can see the group delay is perfectly constant from 40Hz to 800Hz, something very difficult to obtain with a bass-reflex or a closed enclosure...
Best regards from Paris, France
Jean-Michel Le Cléac'h
You'll find in attached file:
1) the response curve of a Le Cléac'h Basshorn unequalized (the response is a bit limited in LF due to ARTA's FFT window the max length of which depends on the length of the signal window... )
2) the phase curve (the "true" phase curve not a useless "minphase curve")
3) the group delay curve (the "true" group delay not the one calculated from the minphase)
As you can see the group delay is perfectly constant from 40Hz to 800Hz, something very difficult to obtain with a bass-reflex or a closed enclosure...
Best regards from Paris, France
Jean-Michel Le Cléac'h
Attachments
Jmmlc said:
Thanks Jean-Michel!
When I look at it though I don't see either phase or time delay ("group" delay) as "constant" or "perfect" from 40Hz up.
Between 80-130 Hz there is significant phase rotation and as a result significant time delay. (..upwards of 40 degrees of rotation and 5ms of delay.) Interestingly, it appears to be the start of horn "ripple" (with 130 Hz as the dominate null beginning upper freq. ripple), and I'm betting it shows up in the impedance.
Are you seeing that as well?
Note that a well designed IB can (for the most part) significantly better this performance. (..at least in these two areas, NOT that it would necessarily sound better in this range.)
I'm not unconvinced that a bass horn as we have here sounds better (40 Hz up) than an array of IB (or Aperiodic or Cardioid/Dipole systems), but I don't think "constant group" delay is the reason for that perceived superiority.
Hello ScottG.
I think as a majority of people you don't know how to read a phase curve.
A rotation of 40° in a large interval of frequency has no meaning by itself.
If the variation of the phase is linear with the frequency then this is a pure delay. A linear variation of the phase is impossible to see on a log frequency scale.
That's why it is much more important to consider the group delay curve which is the derivative of the phase curve (versus puslation)
For Jean-Paul's bass horn the group delay is perfectly constant wiithin 40Hz to 800Hz (with some noise as always with analysis).
This is also very clear on the CSD graph (see attached). The 130Hz accident is due to the driver itself.
Please show me a better group delay curve (not obtained from a min phase curve) and a better CSD for an array, a bass reflex or a closed enclosure ... having the same use for bass reproducing.
Best regards from Paris, France
Jean-Michel Le Cléac'h
I think as a majority of people you don't know how to read a phase curve.
A rotation of 40° in a large interval of frequency has no meaning by itself.
If the variation of the phase is linear with the frequency then this is a pure delay. A linear variation of the phase is impossible to see on a log frequency scale.
That's why it is much more important to consider the group delay curve which is the derivative of the phase curve (versus puslation)
For Jean-Paul's bass horn the group delay is perfectly constant wiithin 40Hz to 800Hz (with some noise as always with analysis).
This is also very clear on the CSD graph (see attached). The 130Hz accident is due to the driver itself.
Please show me a better group delay curve (not obtained from a min phase curve) and a better CSD for an array, a bass reflex or a closed enclosure ... having the same use for bass reproducing.
Best regards from Paris, France
Jean-Michel Le Cléac'h
ScottG said:
Thanks Jean-Michel!
When I look at it though I don't see either phase or time delay ("group" delay) as "constant" or "perfect" from 40Hz up.
Between 80-130 Hz there is significant phase rotation and as a result significant time delay. (..upwards of 40 degrees of rotation and 5ms of delay.) Interestingly, it appears to be the start of horn "ripple" (with 130 Hz as the dominate null beginning upper freq. ripple), and I'm betting it shows up in the impedance.
Are you seeing that as well?
Note that a well designed IB can (for the most part) significantly better this performance. (..at least in these two areas, NOT that it would necessarily sound better in this range.)
I'm not unconvinced that a bass horn as we have here sounds better (40 Hz up) than an array of IB (or Aperiodic or Cardioid/Dipole systems), but I don't think "constant group" delay is the reason for that perceived superiority.
Attachments
Jmmlc said:
I'm probably a missing several things here. Any web/free resources to suggest (to better my understanding.. and others)?
I haven't had measurement capability for some time now, nor have I kept previous files. In any event, my recent proposal (base on your 40 Hz up limitation) did NOT suggest that simply an array, bass reflex, or simply a "closed" enclosure could better the group delay and phase character you presented. Please carefully re-read the content and context:
the context:
"The loading sound is internal "box" compression (something a bass horn can have depending on the design). A well crafted aperiodic, (or IB built into the home), in combination with a large number of drivers should remove this problem. I'm not saying it will sound precisely the same at all freq.s as a bass horn, but it may have some advantages in sound quality above 40 Hz.."
and specific statements concerning group delay and phase:
"Note that a well designed IB can (for the most part) significantly better this performance. (..at least in these two areas, NOT that it would necessarily sound better in this range.)
I'm not unconvinced that a bass horn as we have here sounds better (40 Hz up) than an array of IB (or Aperiodic or Cardioid/Dipole systems), but I don't think "constant group" delay is the reason for that perceived superiority."
Again, the above references particular *well-designed* (or "crafted") systems that have little compression from an enclosure (or no "real" enclosure). Simply having an uncompressed system (classic "open baffle") isn't (in itself) enough to meet this requirement. Nor is simply an array of drivers in any configuration enough.
In any event ..getting measurements for what I've proposed, hmm..
Perhaps Gary Pimm has kept measurements of his Dayton IB based push-pull aperiodic system? I'm betting that would conform to what I've recently proposed (better group delay and phase performance 40 Hz up in a much smaller package). You could always try pinging him (..I thought I saw him lurking on the forum here yesterday or the day before). It's not much, but it may lead to what you have requested.
It's entirely possible the subjective impression is a combination of group-delay variation (if excessive and not masked by room standing-waves) and IM distortion.
The major categories of bass reproducers are going to have very different combinations of group-delay vs IM distortion profiles, as follows:
Open-Baffle with (heavy) Equalization: This offers the potential of smooth group delay vs frequency, but the IM distortion will be the highest of all, thanks to equalization. Remember, a closed-box speaker is a constant-acceleration device, which means excursion increases at a rate of 12 dB/octave as frequency is lowered. An open-baffle operating below the baffle peak has another 6 dB/octave term, so the excursion of an equalized OB increases at a rate of 18 dB/octave.
Closed-Box: with the Q set to a moderate value around 0.57, group-delay variation will be low. Unfortunately, closed-boxes trade Q against distortion - the lower-Q alignments have more excursion, and higher-Q alignments have less. These are 2nd-order highpass filters with user-selected Q settings (box volume and suspension compliance control the Q of the highpass filter). As mentioned above, excursion increases at a 12 dB/octave rate in the passband, and below F3, becomes constant. Very deep LF content can intermodulate higher frequencies, even the direct LF is not itself audible, since it is below the passband.
Vented-Box: Excursion sharply drops at the box frequency, which lowers excursion in the octave centered around Fb. The tradeoff is significantly worse group delay, since all vented-box alignments are 4th-order highpass filters, and some of them have additional unwanted group delay near the corner frequency.
There are a couple of unwanted characteristics of vented-boxes: parameter shift under drive, which detunes the rather sensitive 4th-order highpass under dynamic drive conditions (this can be minimized by selecting a Bessel or Gaussian highpass), and an unwanted zero in the response in the vicinity of 1 Hz (this is caused by box leaks, or Ql). This leads to the in-and-out "breathing" under dynamic conditions sometimes seen in vented-box systems.
Below the passband, the vented-box driver is essentially unloaded, and excursion is only limited by the driver compliance. The previous comment about very deep LF content intermodulating higher frequencies applies with greater force to a vented-box system. As a result, additional electronic highpass filtering (raising the system highpass function to 5th or 6th-order) is sometimes needed to protect the driver from damage from extreme LF thumps and pulses.
Bass horns: These have the lowest distortion of all, thanks to resistive horn-loading in the passband. If I recall right, they are constant-velocity instead of constant-acceleration, so excursion only increases at a rate of 6 dB/octave instead of the 12 or 18 dB/octave of the previous devices. With great care in horn design, group-delay can be controlled, as JMMLC's measurements show.
Note all four designs have significantly different combinations of group delay and IM distortion profiles - and these are inherent to the design, not the choice of driver. (If anyone can find a distortionless bass driver, I'd like to know about it.) The reason I mention IM distortion instead of harmonic distortion is the potential for intermodulation with higher frequencies, which will be much more audible than fairly benign 2nd-harmonic. Since excursion at lower frequencies is always greater than at higher frequencies (regardless of alignment), the intermodulation is always in an upward direction - LF dirties the upper-bass frequencies.
In addition, the spectral tilt of the IM distortion is greatest for OB, then CB, then VB, with bass horns having the least tilt of all. This implies a significantly different spectral distribution of distortion that affects the upper octaves of bass - in other words, the loading on the diaphragm controls the resulting distortion spectrum it will create. If the driver was distortionless, we wouldn't care, but drivers are not distortionless, and contaminate the spectrum with IM products that are dispersed upwards in frequency.
The major categories of bass reproducers are going to have very different combinations of group-delay vs IM distortion profiles, as follows:
Open-Baffle with (heavy) Equalization: This offers the potential of smooth group delay vs frequency, but the IM distortion will be the highest of all, thanks to equalization. Remember, a closed-box speaker is a constant-acceleration device, which means excursion increases at a rate of 12 dB/octave as frequency is lowered. An open-baffle operating below the baffle peak has another 6 dB/octave term, so the excursion of an equalized OB increases at a rate of 18 dB/octave.
Closed-Box: with the Q set to a moderate value around 0.57, group-delay variation will be low. Unfortunately, closed-boxes trade Q against distortion - the lower-Q alignments have more excursion, and higher-Q alignments have less. These are 2nd-order highpass filters with user-selected Q settings (box volume and suspension compliance control the Q of the highpass filter). As mentioned above, excursion increases at a 12 dB/octave rate in the passband, and below F3, becomes constant. Very deep LF content can intermodulate higher frequencies, even the direct LF is not itself audible, since it is below the passband.
Vented-Box: Excursion sharply drops at the box frequency, which lowers excursion in the octave centered around Fb. The tradeoff is significantly worse group delay, since all vented-box alignments are 4th-order highpass filters, and some of them have additional unwanted group delay near the corner frequency.
There are a couple of unwanted characteristics of vented-boxes: parameter shift under drive, which detunes the rather sensitive 4th-order highpass under dynamic drive conditions (this can be minimized by selecting a Bessel or Gaussian highpass), and an unwanted zero in the response in the vicinity of 1 Hz (this is caused by box leaks, or Ql). This leads to the in-and-out "breathing" under dynamic conditions sometimes seen in vented-box systems.
Below the passband, the vented-box driver is essentially unloaded, and excursion is only limited by the driver compliance. The previous comment about very deep LF content intermodulating higher frequencies applies with greater force to a vented-box system. As a result, additional electronic highpass filtering (raising the system highpass function to 5th or 6th-order) is sometimes needed to protect the driver from damage from extreme LF thumps and pulses.
Bass horns: These have the lowest distortion of all, thanks to resistive horn-loading in the passband. If I recall right, they are constant-velocity instead of constant-acceleration, so excursion only increases at a rate of 6 dB/octave instead of the 12 or 18 dB/octave of the previous devices. With great care in horn design, group-delay can be controlled, as JMMLC's measurements show.
Note all four designs have significantly different combinations of group delay and IM distortion profiles - and these are inherent to the design, not the choice of driver. (If anyone can find a distortionless bass driver, I'd like to know about it.) The reason I mention IM distortion instead of harmonic distortion is the potential for intermodulation with higher frequencies, which will be much more audible than fairly benign 2nd-harmonic. Since excursion at lower frequencies is always greater than at higher frequencies (regardless of alignment), the intermodulation is always in an upward direction - LF dirties the upper-bass frequencies.
In addition, the spectral tilt of the IM distortion is greatest for OB, then CB, then VB, with bass horns having the least tilt of all. This implies a significantly different spectral distribution of distortion that affects the upper octaves of bass - in other words, the loading on the diaphragm controls the resulting distortion spectrum it will create. If the driver was distortionless, we wouldn't care, but drivers are not distortionless, and contaminate the spectrum with IM products that are dispersed upwards in frequency.