Reverberant vs Direct field strengths
#1
Posted 05 May 2009 - 09:05 PM
My contention has been that with speakers having solidly wide and smooth dispersion the reverberant field will dictate the spectral balance, or the way a speaker actually "sounds," while the direct field will deal with imaging and soundstaging precision. (I continue to read the Allison and Berkovitz AR-3a/soundfield preprint I posted as agreeing with this stand.) With most classical recordings the two latter qualities are not all that critical, because you rarely get soundstaging precision and pinpoint imaging at live performances unless you are sitting in the front row or conducting. The off-axis response of a speaker will also dictate how well it integrates into a listening room, with wider/smoother dispersion allowing the system to spread out and better envelope the listener.
However, some here continue to believe that the direct field dominates in terms of spectral balance at upper midrange and treble frequencies, and that since it dominates it is mandatory that the direct-field output of the speakers reaching the listener's ears be smooth and free of diffraction, crossover related, and phase-related artifacts. Some have indicated that while the total output of a speaker in all directions is vastly larger than the very narrow angled sounds reaching the listener directly, the amout of damping in a room and such things as arrival angles from reflecting boundaries will allow the direct field to both dominate in the realm of imaging and soundstaging AND dominate in the realm of spectral balance. They acknowledge the spatial impact of wide dispersion, but the spectral-balance perceptions in the midrange and treble will, for them, continue to be dominated by the direct-field output.
Actually, there is no way to solidly prove this contention without going to a lot of trouble and having some very good test gear. Even if one measures the impact of the direct and reverberant fields in relation to each other, we still have the issue of how the strength of the two fields are perceived by the listener. (In some ways, this reminds me of the perennial debate about the so-called sound of amplifiers or wires.) While I see the perception issue with the direct field as it relates to imaging and soundstaging precision, some have indicated that perception also gives dominance to the direct field in the realm of spectral balance.
However, I have made at least one stab at checking the relative strengths of the direct and reverberant fields at normal listening distances. I have posted a curve I drew today to maybe clarify my point of view. The info for the curve was taken from two curves that I ran recently. One measured the on-axis output of a speaker outdoors. The second curve measured the on-axis output of the same speaker system indoors.
I have not posted those original curves, but I have posted the one dealing with the differences. The upper line in the diagram (the lumpy line) shows the difference in dB between an anechoic (outdoor), on-axis measurement and the on-axis measurment in the listening room. The zero line would be the relative level of the direct field, normalized. Both measurements were made at a 10-foot distance, with the microphone centered on the vertical axis between the tweeters in the vertical MTTM array on the front panel of the speaker. A photo of that speaker is included. Forgive me for it not being an AR speaker, but it does make use of Allison/RDL tweeters and good, conventional 4-inch midrange drivers with phase plugs to give them decent dispersion. The idea was to illustrate just how dominant the reverberant field is in a typially reflective and absorptive home-listeing room. The response below 400 Hz was not recorded, since what the controversy deals with involves the direct vs reverberant field dominance in the midrange and treble, especially as it relates to the dispersion qualities of the AR-3a and other AR speakers, as well as the Allison product line.
(Note that I would have preferred to do the measuring with an IC-20 system, but it was impossible for me to lug it outdoors and set it up on the backyard picnic table to get it decently far from house walls and the ground.)
Note that the average difference between the direct and reverberant field strengths at higher frequencies is in the neighborhood of 6 dB, which dramatizes the fact that when you bring a decently wide-dispersing speaker into a typical home-listening room environment from an anechoic environment the overall energy (with the same signal input to the speaker) that reaches the microphone (and by definition the ears) goes up by a factor of four. It is hard to believe that this increase in available, and obviously reverberant-field energy is anything but the dominant factor when it comes to spectral balance. I am quite sure that a super-wide dispersing model like the IC-20 would have had an even greater spread, and I am also sure that a speaker like the AR-3a would have done as well as the model I did use.
Howard Ferstler
#2
Posted 05 May 2009 - 09:49 PM
You still haven't made the connection: If the flat response field as measured in AR's reverberant chamber dominates in real listening spaces, where does the energy above the transition frequency GO, Howard?
In fact, in Allison and Berkovitz, the response in AR's reverberant chamber was BOOSTED well above flat in the midrange and high frequencies by setting the level controls at Max (see Figs. 17a vs. 17b), and the in-room mid and high frequency response STILL rolls off well below flat in every instance measured, progressively more at higher frequencies, as is also clearly indicated in the averaged composite curve. Toole describes the reality as revealed by the research of others: we listen in a transitional zone where what we hear is a combination of the direct and reflective fields; a steady-state reverberant field as may be found in large listening spaces such as concert halls simply does not develop in typical listening rooms....
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#3
Posted 06 May 2009 - 09:39 PM
You have merely demonstrated that the effective solid angle in your listening room is ~180 degrees, and substantiated the dispersion characteristics of your Allison speakers, which I never doubted. 4-Pi --> 2-Pi = + 6 dB; that is not evidence of the in-room reverberant field you posit. You must measure it directly to substantiate that it exists, and I earlier suggested how you might proceed to accomplish that determination.They are not the same as you indicated in your first sentence. The reverberant field (room) curves were 5-6 dB LOUDER on average than the direct-field curves taken outdoors, even though there was no change in signal input level to the speaker.
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#4
Posted 07 May 2009 - 01:24 AM
Interesting measurements and good of you to share them.
I agree that the 4 to 6dB gain is the gain of the reverberent field in your room. At these frequencies the 4pi 2pi argument doesn't apply. The baffle would be an adequate 2pi baffle, indoors or out.
I do find it odd that the response runs up hill 2dB. This isn't an indicator of wide dispersion, but actually implies a rising power response or a room that gets more lively with rising frequency. Both non-typical conditions. It is crucial that the outdoor curve is taken exactly centered between the tweeters. Any misallignment would give cancelation in the direct curve that would translate into additional rise in the difference curve.
I'm afraid your "paragraph 3" still defines my point of view. Here is an experiment (after the ruler test). Assuming the two tweeters are in parallel, my contention is that you should be able to hear interference effects at your listening position as you move up and down across the mid line between the two tweeters. If this were audible, in spite of us both agreeing that the drect sound component is quite low per your measurements, then the direct sound must be impacting the sound more than a simple reverberent field measurement is showing. So how about a little pink noise and some deep knee bends at the listening position?
As always, it is the perceived frequency balance, not the simply measured room curve, that counts. (And they are not the same!)
David
#5
Posted 07 May 2009 - 04:59 AM
Is this definitive evidence of a dominant reverberant field?I agree that the 4 to 6dB gain is the gain of the reverberent field in your room. At these frequencies the 4pi 2pi argument doesn't apply. The baffle would be an adequate 2pi baffle, indoors or out.
How would the first-order early reflections sum with the direct source @ 10 feet?
No, it's not semantics; see Toole 18.2.1.
What were the measured SPLs, Howard? I'm not asking for the curves, merely the overall levels, but if you want to post the curves, that'd be fine, too.
Also, how wide is the baffle, please?
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#6
Posted 07 May 2009 - 10:50 AM
Is this definitive evidence of a dominant reverberant field?
How would the first-order early reflections sum with the direct source @ 10 feet?
No, it's not semantics; see Toole 18.2.1.
Hi Zilch,
I checked the Toole reference and I'm not exactly sure of your point. Are you keying off his naming the third component (reflections after the early bounce arrivals as the reverberent field). In this context I think it is best to notionally divide between the direct sound and all other energy, both early and late. People in acoustics frequently split sound fields into 3 parts (direct, early reflections, and reverberation) but this is an artifice. There is no real distinction between early reflections and reverberation unless it is: reflections I understand and could have predicted vs. reflections I couldn't have predicted and can't really see amongst the clutter
Howard's point is that the gain in the room is 4 to 6 dB hence the reflected/reverberent energy dominates the direct sound. That is the Hopkins Stryker equation again, nicely illustrated by Toole in figure 4.2 (and 4.3 and 4.4).
#7
Posted 07 May 2009 - 07:13 PM
Yes, and I believe the distinction is significant in many respects.I checked the Toole reference and I'm not exactly sure of your point. Are you keying off his naming the third component (reflections after the early bounce arrivals as the reverberent field)?
Howard (along with Allison & Berkovitz) posits a steady-state isotropic and diffuse reverberant field according to large-space models and asserts that we listen in small spaces in a region where that reverberant field is dominant, and which, implicitly, normalizes all reflections toward the total energy of the source as measured in a highly reverberant chamber, and thus, the answer to Allison and Berkovitz's question is that the spectral balance we hear is better characterized by what is measured in the reverberant chamber than the anechoic response. Here, again, is the question:
Howard argues that the results of the study confirm the existence of a dominant reverberant field in the typical listening rooms studied. They do not. Instead, they clearly indicate that the model fails, and above a relatively low frequency, we listen in a transition zone much as is described by Toole (see Fig. 4.5) in which a reverberant field, if there even is one having the assumed character, is not dominant.But what do listeners hear from the system? Do they perceive the total energy output, or do they perceive as the "frequency response" of the system whatever the direct-radiation output may be at the angle of their location relative to the system?
I have challenged Howard to demonstrate the existence and dominance of an energy-normalizing reverberant field, which I have termed "imaginary" for the interim, and he apparently believes this experiment establishes unequivocally that it is real and that all research suggesting the contrary is obviously wrong. Sorry, but a single first-order lateral reflection having an intensity approaching that of the direct source would alone bump the SPL +3 dB, and the four of them in combination could easily account for the +6 dB differential he measures, i.e., there is no reverberant field in evidence here, and difference is not merely a semantic one; first reflections do not comprise a reverberant field of the nature Howard alleges is dominant in listening rooms....
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#8
Posted 08 May 2009 - 12:57 AM
Yes, and I believe the distinction is significant in many respects.
Howard (along with Allison & Berkovitz) posits a steady-state isotropic and diffuse reverberant field according to large-space models and asserts that we listen in small spaces in a region where that reverberant field is dominant, and which, implicitly, normalizes all reflections toward the total energy of the source as measured in a highly reverberant chamber, and thus, the answer to Allison and Berkovitz's question is that the spectral balance we hear is better characterized by what is measured in the reverberant chamber than the anechoic response. Here, again, is the question:
Howard argues that the results of the study confirm the existence of a dominant reverberant field in the typical listening rooms studied. They do not. Instead, they clearly indicate that the model fails, and above a relatively low frequency, we listen in a transition zone much as is described by Toole (see Fig. 4.5) in which a reverberant field, if there even is one having the assumed character, is not dominant.
I have challenged Howard to demonstrate the existence and dominance of an energy-normalizing reverberant field, which I have termed "imaginary" for the interim, and he apparently believes this experiment establishes unequivocally that it is real and that all research suggesting the contrary is obviously wrong. Sorry, but a single first-order lateral reflection having an intensity approaching that of the direct source would alone bump the SPL +3 dB, and the four of them in combination could easily account for the +6 dB differential he measures, i.e., there is no reverberant field in evidence here, and difference is not merely a semantic one; first reflections do not comprise a reverberant field of the nature Howard alleges is dominant in listening rooms....
It seems to me that the ratio between the direct and reverberant fields in a listening room would be a very easy parameter to measure. First measure the loudness at known distances and angles at various frequencies with a known electrical input level in an anechoic chamber (should fall off at 6 db with doubling of distance) and then repeat the same measurements in a real room. The difference is the reverberant field level at that point for those frequencies with that room arrangement. As I often find, thinking about it, it isn't quite so simple. The field does not transition from anisotropic to isotropic instantly and so very early reflections are closely associated with the direct field. Nevertheless, this should give the right answer....I think.
#9
Posted 08 May 2009 - 01:17 AM
I proposed the marshmallow experiment over a month ago:It seems to me that the ratio between the direct and reverberant fields in a listening room would be a very easy parameter to measure.
http://www.classicsp...amp;#entry78263
Disconnect the woofer so the low frequencies don't contaminate the result.
I will not speculate as to the likely or potential findings.
[Experimental design analysis welcome....
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#10
Posted 08 May 2009 - 03:12 AM
Reverse the polarity of one channel and play the system in mono.
If it is true that the sound is dominated by the imaginary reverberant field
then there will not be a hole in the middle as the listener moves their head
through the central point between the speakers.
Good designs produce a hole in the middle, especially for a mono source.
#11
Posted 08 May 2009 - 10:25 PM
We are very nearly in agreement here, Howard, because you have used the proper term, though I fully anticipate you will find reason to deny this shortly: "reflected" energy is not evidence of the existence of a normalizing isotropically diffuse reverberant field from which you posit we listen. It is easily seen that, assuming the energy is reflected without adulteration by the relevant surface, its summation with the direct source may be predicted from the anechoic off-axis response at that specific angle, also direct.The zero line in the diagram was the direct output normalized, and what matters is that the reflected energy indoors ramped the sound received by the microphone by an average of 6 dB, even well into the treble, This means that reflected energy bumped up the average, on-axis level by four times.
To the extent that the reflection deviates from the spectral balance of the on-axis sound, whether that is due to anomalies in the off-axis response or non-spectrally uniform reflection by the surface, the summation is also predictable, and it is the early, first-order reflections which most influence the outcome, as they are the strongest.
I will not redefine the direct field to include the first-order reflections, but conceptually, the implication is clear. This is why the Allison & Berkovitz in-room power response above a relatively low transition frequency (in the range of ~200 - 500 Hz) is better described by the anechoic on-axis and off-axis polar measurements than the "total energy" curve as measured in the AR reverberant chamber.
The baffle width defines the frequency below which edge diffraction (baffle step) plays a role in the summation, as well.
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#12
Posted 08 May 2009 - 11:00 PM
Oh really?
I assure you that there are many factories world-wide that have no trouble building a cost-effective 3/4" dome similar profile. However, since the additional treble dispersion has not proven to be of subjective or commercial benefit, it's difficult to justify efficiency, crossover point and power handling tradeoffs.
-k
#13
Posted 08 May 2009 - 11:01 PM
#14
Posted 09 May 2009 - 10:22 PM
Because of the way they were driven and the manner in which the 'dome' moved, they had greater dispersion than a conventional driver of the same dimension. Truly unique designs.
David Moran of the B.A.S. summed it up quite well many years ago when he described the Allison drivers as "strangely unimitated."
To my knowledge, no other manufacturer ever produced anything like them. Just a wild guess on my part, but I'm willing to bet that it was because of a combination of the ease of doing what you had always been doing (faster time-to-market, lower mfg costs, not having to re-train vendors who can be stubborn or slow on the uptick, etc.), and the ever-present, ego-driven 'N.I.H.' syndrome.
Like I said, a wild guess, but there's probably some truth to it.
Steve F.
#15
Posted 09 May 2009 - 11:56 PM
With each bounce, the intensity is diminished not only by the absorptive and diffusive qualities of the surface or object doing the reflecting, but also the increased path length getting to the listener. Draw the ray diagrams for your listening room to analyze this. Your dominant reverberant field is fiction.First reflections may not comprise the "total" reverberant field, but they certainly are part of it. If those and additional reflections (adding up to an increase of 6 dB over the direct-field energy) are not contributing to the reverberant field, just what are they? Any energy not coming directly to the ears or microphone has to be part of the reverberant field energy. As the initial reflections get bounced around more and more the cumulative effect grows stronger still until absorption causes them to fade. Actually, in my particular case some of the energy was absorbed by a side-wall drape, so some of that +6 dB energy was coming from places other than that direction.
The path of the first reflection from a speaker like AR3a is shown in Toole's Fig. 16.6. Toed-in such that the direct comes from 0° on-axis, and the reflection comes from -73° off-axis outboard. Alternatively, from flat against the front wall, the listener listens from 23° inboard and the reflection comes from 50° outboard. The intensities and spectral content of these off-axis sources are shown in Allison & Berkovitz.
Imagine that if you like, Howard, but it's make believe your talking here. AR3a's directivity is easily calculated from the Allison & Berkovitz data, and flat at Q=2 it's not; far from it, in fact.Again, we are talking about tweeters that radiate nearly as strongly at 90 degrees off axis out to at least 10 kHz as they do on axis. This characteristic is not unusual with the AR-3a .75-inch tweeter, either, and so that system, as well as mine, is nearly as omnidirectional higher up as it is down at lower frequencies. The result is a dominant reverberant field strength that extends from the lower frequencies (where even you admit that it exists) into the fairly high treble.
You're talking to the guy with 100 CD waveguides, and presume he can't do it better? I can build a LST equivalent in approximately 27 seconds here with true, flat, uncontaminated constant directivity to 180° beamwidth and beyond. Yet you suppose nobody else has done this? It's routine in sound reinforcement, actually, and I have suggested how you might try it yourself at home for peanuts.Zilch, you are basing your experience and analysis on speakers that are not very good at widely dispersing energy at higher frequencies.
I do believe Ken got that; he also suggested why it likely failed.I meant the Allison tweeter.
You've been hyping your Allisons for 20 years now; the reverberant field dog don't hunt anymore....
ZilchLab Loudspeaker Recycling Center - Crank up the SIGNAL!
#16
Posted 10 May 2009 - 03:32 AM
Not shown in © are the multitudes of second and higher-order reflections, most of which would arrive at the listener from relatively unproductive incident angles, and , because of their long propagation paths, these reflections will be much reduced in sound level. Any absorbing material on the room walls would further diminish the levels.
As discussed in Chapter 7, interaural cross-correlation coefficient (IACC) is a strong correlate of a perception of ASW [Apparent Source Width], image broadening, spaciousness, and envelopment (Figure 7.4). The more different the sounds are at the two ears, at certain frequencies and delays, the greater the sense of these spatial descriptions. The locations of the ears then determine that sounds arriving from different directions generate different amounts of IACC and perceived ASW (Figure 7.5). Sounds from the sides are most effective, and those from front and back are least effective. It is also know that diffusion in a sound field is a contributing factor, but that diffusion -- or at least directional diversity in many reflections -- is not a requirement for the perception of spaciousness (Figure 8.2).
Even though the data are not exactly comparable, it is tempting to speculate that the direct sounds from the stereo loudspeakers combined with all of the reflections remaining in a room after the first lateral reflections are removed appear to have about the same potential to generate ASW/image-broading [spaciousness] as a single, well-aimed, lateral reflection, as shown in Figure 8.3a. The huge reduction in diffusivity (seen in Figure 8.1 when the early reflections were attenuated) adds credibility to this notion.
Late reflections are rapidly attenuated with distance from the source. Over almost the entire draw-away distance, including the range of listening distances typical of small rooms, listeners are in what can best be described as a prolonged transitional sound field, neither direct nor reverberant. This means that critical distance is not an appropriate concept in these spaces.
Alas, ya need a new horse, too, Howard....
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#17
Posted 10 May 2009 - 02:14 PM
The problem with your last sentence is that it opens the door to subjective opinions. In any case, if we are going to talk about the perceived, subjective spectral balance we also have to talk about the perceived widening of the soundstage when wide (really wide) dispersing speakers are involved or if we are comparing the sound in an anechoic space to one that is more typically reverberant. That widening is a real phenomenon, and if the reverberant-field energy impact is not all that big a deal in terms of spectral balance and the direct vs reverberant ratio, the soundstage width (and depth, too, at least from what I have heard) would not be so strongly impacted by speakers that disperse widely. If the soundstage width is notably changed in a typical room space with wide or super-wide dispersing speakers, we have to say that the perceived frequency balance has to be impacted, too.
Howard Ferstler
There are only two ways I can think of for a single loudspeaker driver to have both flat radiated power and flat on axis response at the same time.
1. The driver is a pulsating sphere or part of a sphere which radiates sound in all directions with the same spectral balance.
2. The on axis response and the total energy radiated are one and the same because the driver only radiates on axis such as being mounted at one end of a tube. Energy is radiated only along the axis of the tube.
There are no speakers that exist that meet either of those two criteria I'm aware of although I've heard of some sort of ionic tweeter that uses some sort of flame jet or something (IMF???)
Even that criteria is not sufficient to deliver flat energy to the listener because in a real room the frequency selective nature of absorption/reflection of sound would alter the reflected energy spectral balance making it no longer flat when it reaches the listener.
The hemspherical dome unfocused by being recessed in a surrounding groove that would form a kind of horn is the closest practical approach to a pulsating sphere but it is not nearly equivalent. The dome does not expand and contract, it merely moves air back and forth like any other piston. It's the dome's geometrical shape which is responsible for its radiating pattern by colliding laterally with air molecules it has already launched as it continues to move to alter their trajectory sideways otherwise it would be no less directional than a flat plate of the same diameter. An interesting experiment would be to see if the dispersion pattern is in any way altered by the amplitude of the test signal, the velocity of the cone increasing at any given frequency as it goes through zero phase on each half cycle. Would this change the degree of the way it alters the trajectory of the air molecules it collides with? If so, does the off axis waveform change between the peaks of each half cycle and the zero crossing point? At the peak where the direction of the piston changes, the instantaneous velocity of the dome is zero. Would this cause dynamic compression of the off axis waveform?
#18
Posted 11 May 2009 - 12:32 AM
While the Allison tweeter is not a pulsating sphere, it simulates a pulsating hemisphere better than most. Diagrams of conventional dome (left side) and Allison design (right side), plus photo of the tweeter without its protective screen are attached.
Interestingly, many speaker companies purchase OEM drivers and make them work well by designing good crossover networks and good cabinets. Allison did the crossover and cabinet thing, too, but his company also BUILT its own drivers (even to the point of charging the magnets) to better guarantee the performance characteristics needed. He also did this when he was with AR.
Howard Ferstler
The greatest lateral thrust would seem likely to come from the region between D and E where the stretching alters the movement of the cone from vertical to lateral movement. This side thrust is the wide angular dispersion component. Beyond these points, inward from E the cone is pushed while outward from D it is pulled but both are largely in the direction of the motion of the voice coil. Has the waveform of the lateral component been measured independently? This would best be done by a unidirectional or shotgun mike in an anechoic chamber. It would be interesting to know if this stretching motion causes distortion of the waveform, especially dynamic compression of the peaks.
#19
Posted 11 May 2009 - 11:10 PM
We know what it sounds like; there are no early reflections to generate artificial ASW enhancement. LEV, well that's another issue, now, isn't it?If the reverberant field in normal rooms is a fiction, go outdoors with some of your speakers and discover just what a space without a reverberant field sounds like.
We no more listen in a reverberant field than an anechoic one indoors. Allison & Berkovitz showed us the impact on perceived spectral balance vis-à-vis the "total power" hypothesis; a diffuse, isotropic, integrating reverberant field in typical listening spaces is pure fiction.It is sophomoric to assume that ray analysis can tell us all there is about the sound quality of speakers in enclosed spaces, while at the same time downplaying the significance of the reverberant field and its impact on perceived spectral balance.
http://www.stereophi...hur/index3.htmlLander: You began corresponding with the speaker expert Dick Small when he was working on his PhD thesis in Australia, and maintained that relationship. In fact, you played the first pair of production Model Ones for him. Tell us that story.
Allison: He and his colleague Neville Thiele were making a speaking tour of the United States and had dinner with Nancy and me and our children. So after dinner we sat them down and played some music for them on Model Ones. Their response was very polite but unenthusiastic. It turned out that they were used to hearing speakers, characteristic of the Commonwealth, that had very precise, pinpoint imaging. The imaging of Model Ones was satisfactory to almost everyone who heard them, but not to people as enthusiastic as they were about the concept.
What's to wonder? "Almost everyone" was wrong.Allison: Sales picked up gradually, but we weren't growing as fast as I thought we should have to become really viable in the long run.
Sorry, Howard, I have far more productive pursuits on deck here. The truth is for you to discover, but you are obviously unwilling to do so, for fear your outmoded frame of reference might collapse....The only way you could prove that you could mimic the RP of the LST in 27 seconds (what, not 26 or 28?) would be to have a pair on hand and do the A/B work. Otherwise, you are just grandstanding.
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#20
Posted 11 May 2009 - 11:36 PM
Allison claimed low distortion for his drivers. One of the two-way versions was obtained by a representative of SEAS some time ago and they indicated to me that it did have some distortion in the 3 kHz range at high output levels. The three-way tweeter's network did not allow that driver reach down that far (the crossover point to the midrange driver was at 3750 Hz) and the two-way version, with its normal 2 kHz crossover point to the woofer/midrange, could probably be excused, since it was used in lower-cost systems and would not ordinarily be played loud in a large room.
In the actual tweeter unit the outer rim of the surround (which is made of paper) was separated from the mounting plate by a thin foam separator that dampened some of the possible artifacts. After Allison left the company the new owners may have cut corners and left the foam ring out. I say this, because while the units that Consumer Reports tested over the years when Roy was with the company always had that tweeter output being very smooth in their response-curve measurements, a later system built after Allison left showed the tweeter response to not be nearly as good. Allison told me that leaving the separator out would simplify construction, but also cause the diaphragm to ring.
Attached are three curves. One is of the three-way version of the tweeter's crossover-controlled output at 15 degree intervals out to 90 degrees off axis. The second is of the two-way version of the tweeter, also crossover controllled and also out to 90 degrees off. The differences between the two designs is that the three-way job used silicone grease as a coil coolant and the two-way version used Ferrofluid. The three way could handle more average power, but silicone grease would spatter if the driver were pushed down another octave below the three-way transition point. The third curve is of the midrange driver used with the three-way systems, also out to 90 degrees.
Also attached is a blurb from an early catalog that tells how the driver curves were done. The blurb notes that the 90-degree plot fits between the 60-degree and 75-degree plots, which is probably related to the design artifacts you mention. Later versions of the drivers had protective screens over the domes.
Howard Ferstler
It seems to me that once you've accepted that a multi-tweeter arrangement is acceptable for improving dispersion, it would be simpler and more cost effective to just use more of them than to design one from scratch that is so novel and where the possibilities of new problems would emerge. That's what Allisoon did in LST. Hard to understand why he didn't stick with that notion in his own speaker line. One thing wide dispersion assures that listeners with narrow dispersion speakers can't appreciate, you can enjoy the stereophonic effect over a much wider area of your listening room. This means several people can enjoy it at the same time and you are not constrained to sit in one specific spot. I've been listening to my speakers with an ear towards the apparent width of the soundstage, something I rarely pay attention to and it can be remarkably wide. Of course my speakers don't merely radiate flat to 90 degrees and more, they compensate for the hf absorption of the walls so that the reflections are almost flat too. It's an added benefit I hadn't considered. As I've said, I don't find it particularly important personally.
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