Distortion, Perception and the Spirit-1s

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Aether Audio

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Distortion, Perception and the Spirit-1s
« on: 27 Aug 2010, 04:22 pm »
Friends,

Below is an analysis of the comments regarding the Spirit-1s from a very kind gentleman that recently spent some time with them.  Again, I would like to thank him for his time and effort, and I am NOT suggesting that his observations are necessarily in error in any way.  My only intent is to use this incident for educational purposes.  We believe that the more you know… the better our products sound.

sfox7076 wrote:

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… they are not as good in the mid-range and the high-end as my SongTower RTs
Conversely, he wrote:

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They accurately portrayed the songs flaws, but were not fatiguing.  It’s hard to explain, but it has the mix that I want in a speaker--detailed and not fatiguing.  I actually liked the Mountain Goats on this set of speakers better than on my current set because I thought they conveyed the feel of the lo-fi sound better and in a way that would let me listen to it for hours without missing the detail of the songs.

These two somewhat conflicting comments really spotlight a very interesting and controversial area of audio system performance – be it speakers or electronics as the subject at issue.  Don't get me wrong… I'm not trying to defend the Spirits or take issue with sfox7076 preference of the Songtowers' performance in the mids and highs.  My only intent is to *possibly* help educate everyone, and his observations make for a good illustration of my point.

OK then…I believe and am convinced that MUCH (if not most) of the endless debate in audio over perceived degrees of system and component performance are rooted in nothing more than the age-old parameter of distortion.  No magic… no pixie dust… nothing special about tubes vs. transistors, linear analog vs. PWM, etc.  There is a difference in materials, with some being better than others for a given application, but in general, one class of technology is not inherently superior to another except for the specific, targeted areas wherein that technology's strengths reside.  For now, tubes are better than solid-state for ultra-sonic amplification in the RF range and SS is better at frequencies near DC.  Nevertheless, for most audio applications products can be built well enough that if ALL (measurable and immeasurable) forms of DISTORTION could be and were held at identical values… they would sound virtually identical regardless of the technology and/or implementation involved in their construction.

Taken that as a "given" (go along just for the ride), then distortion products are what give rise to each component's unique "signature" sound.  Distortion below a certain threshold and composed of certain harmonically related signals can sound pleasant, while distortion comprised of non-harmonically related distortion intervals will tend to sound less pleasant and/or… result in a lower acceptable listening threshold.

Upshot – the path to sonic nirvana is (or should be) based on ABSOLUTE ACCURACY as our point of reference.  Unfortunately, in this material world there are few (if any) examples of the "absolute."  Every component, no matter how refined, adds some form of distortion.  The real question then becomes… "What is the threshold wherein we can tell if the sound of a component is due to an excess of information (distortion) or the absence of true, original information?"  Is it possible that we can be deceived into thinking that a certain component sounds good primarily BECAUSE of the distortion it adds?  Conversely, can we also be deceived into thinking that one component doesn't sound as good as another BECAUSE it doesn't add as much distortion to the final sound we hear?  As you will see, I think both statements are true.

When it comes to the subject of detail and/or resolution in audio components, I submit that what is often perceived as greater accuracy and more "detail" is actually an excess of distortion that resides somewhere below the threshold of our ability to identify it as distortion.  I repeat…pay close attention here… this distortion lies BELOW the threshold wherein we can easily tell that IT IS distortion.  Therefore, the brain misinterprets it as something that is "supposed" to be there, when in actuality it is not, but rather an artificial artifact that just so happens to sound "pleasant."   Our brains are wired to make sense of our experiences and to recognize patterns amongst the chaos.  Given sufficient exposure to a false reality, the brain will begin to interpret it AS reality.  This is where "absolutes" hold their real value as reference points to gauge our perceptions against and help to keep us on track.  Without absolutes, we are lost in a forest of "possibilities."

For audio, un-amplified "live" music should always be our reference.  Either that, or complex test waveforms and appropriate test equipment to analyze them.  Seeing the common audiophile is seldom an audio engineer with access to such equipment, live music is about all he has.  Go to your kid's high school symphony concert when they don't use any PA system… and listen.  You'll be amazed at the lack of bass and high frequencies.  Actually, they are there and if the hall is big enough, the bass goes a lot lower than you probably realize.  All the detail from the cymbals and triangle are there too.  What's missing is the DISTORTION.  In the absence thereof, the resulting sound will seem very "laid back" and not particularly "exceptional" sounding.

So… to evaluate a component, I suggest the following – especially at mid and high frequencies.  Listen for the fundamental notes along the musical scale.  Does each instrument sound like all of the different notes it is generating are there?  What you are listening for is the basic frequency response.  If there are significant peaks or dips in the frequency response, certain notes or sounds will always seem excessive or missing – no matter what instrument is being played in that frequency range.  Extreme high frequencies are very difficult to discern.  Listen to the sound of nothing but brushed (not struck) cymbals.  They should sound metallic and "real" with a soft intimacy.  If the extension is there, that's how they'll sound and you can tell.  If it's not, forget the rest and get a better speaker or other component.

Now after having determined that the frequency response is reasonably flat (and it most certainly is on the Spirits), listen for faint details in the recording that are hard to hear.  Can you hear "between the notes?"  If you can't then everything will tend to sound as if it's blurred together and congested sounding.  An analogy to this would be a photograph that is out of focus to some degree.  Don't listen for the "sound" of a particular instrument (colors in a photograph), but rather the "sounds" of different instruments all playing at the same time (as in the contrast of a photograph).  The sound of an individual instrument is a function of timbre and can vary based on the instrument itself and how it was recorded.  BUT… the "sounds" of all the instruments playing simultaneously is less a function of the recording (unless it is a poor one) and more that of the playback equipment.

So following these guidelines, can you hear instruments distinctly from each other and in their own space, while ALSO being able to hear very low-level background sounds taking place at the same time?  If so, then the component has good resolution and detail. 

Now listen to the timbre of individual instruments.  Actually, the transient speed of plucked strings or drumstick snaps on a snare can be included in this test.  Do they sound real and rich sounding?  Yes… how rich?  Do the transient attacks have "bite" to them to the point that the instrument sounds physically close to you and "intimate?"  Be careful… and don't be deceived by too much of a good thing.  Conversely, does the component "lack" somewhat in this area compared to some other similar component you are familiar with?  If so, go back to the earlier test.  Is the resolution and detail there in the "inferior" component?  Yes?  Hmmm… detail and resolution are there, but the harmonic richness and maybe even the transient "speed" doesn't seem to be as much as the other component.  What gives?

In the above scenario, the component that seems to be lacking something, may very well be… DISTORTION, that is. One of the first signs of a component exhibiting less distortion is that it will seem to lack a certain "euphonic" characteristic.  The words "dry" and "sterile" go too far in describing the effect, but there often seems to be a definite lack of "excitement" and intimacy (often described as "detail") to the reproduction – especially compared to other similar components that do exhibit those characteristics.  Another thing that a highly accurate component will lack is listening fatigue.  You can listen for hours and not get burnt-out.  While excitement and a bit of intimacy may be lacking, naturalness and an ease of presentation will impart a sense of musicality that is somewhat hard to express or "put your finger on."  Another characteristic is that such a component's presentation will vary widely depending on the quality of the recordings.  Nevertheless, only with the very worst recordings should it ever sound harsh or irritating.

Therefore, if a component has high resolution and detail combined with low listening fatigue, while also exhibiting a somewhat less than exciting presentation (especially at first listening), it most likely is producing less distortion than a comparable component that seems to have a richer, more intimate and/or more exciting presentation.  The telling difference between the two is that while the lower distortion component is not as "compelling" at first, it will "grow on you" over time.

On the other hand, he higher distortion component will sound more exciting and intimate in the beginning, but will grow old over time such that you will feel that something needs "fixing."  In fact, were it not for such components many cable companies along with a host of accessory manufacturers would probably not even be in business.

In closing, the final question remains:  Do the Spirit-1s offer less detail than the Salk's…or less distortion?  Without actual test measurements, there's no way to be sure.  It's a moot point regardless though, because in the end the only thing that matters is one's perceptions and preferences.  In that regard, one man's judgment (sfox7076) rules the court and in this one case, the Spirit-1s loose the debate.  Ah… but thank God for lawyers and appeals.  Maybe another judge will have a different opinion and they'll be acquitted!

Take care,  :D
-Bob

PS.  At some point I intend to present some very interesting test data graphs to further illustrate my point.  In particular, spectral analysis comprised of "two-tone" stimulus signals can be EXTREMELY revealing.  You'll see John Atkinson of Stereophile use them in his tests of solid-state components at times.  But… you will NEVER see him perform the same test on loudspeakers.  Why?  Because if he did… you'd probably give up on audio as a hobby altogether!  I'm gonna chance it though. :wink:

sfox7076

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Re: Distortion, Perception and the Spirit-1s
« Reply #1 on: 27 Aug 2010, 07:28 pm »
I have no issue with the comments you made.  I cannot say that I have ever been a person who cared about measurements, I care about how they sound to me.  Maybe your hypothesis is right and I prefer distortion.  I am not sure. 

Shawn

werd

Re: Distortion, Perception and the Spirit-1s
« Reply #2 on: 27 Aug 2010, 07:45 pm »
Hello

Never much cared for comparisons between two audio components under these circumstances. That being a promo tour. Some one lets you hear their piece and it immediately turns into a comparison right off the bat with a different piece as a theme. The real acid test imo is time with any stereo piece and can't be properly summed up in a couple weeks of exposure when compared to a piece thats been in one's household for maybe a couple of years.

cujobob

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Re: Distortion, Perception and the Spirit-1s
« Reply #3 on: 27 Aug 2010, 09:21 pm »
"We believe that the more you know… the better our products sound."

That really doesn't make sense.  Sometimes what measures best and is technically correct may not sound the best to a particular listener, this happens.  My Gedlee Abbeys are fantastic speakers that measure amazingly well, but the top end won't be for everyone (and no, not because they use a compression driver).  Waveguides present things in a manner people simply aren't used to.  Now, calling the additional detail in the Salk speakers distortion...that's hard to say.  Waveguides will also have additional distortion from the higher order modes created by the waveguide itself.  Couldn't distortion actually hide detail instead of creating more?

bhobba

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Re: Distortion, Perception and the Spirit-1s
« Reply #4 on: 27 Aug 2010, 11:40 pm »
Now, calling the additional detail in the Salk speakers distortion...that's hard to say.  Waveguides will also have additional distortion from the higher order modes created by the waveguide itself.  Couldn't distortion actually hide detail instead of creating more?

Yes it is hard to get your head around.  All I can suggest is you go and listen to some Quad Electrostatics.  In the midrange they are the gold standard.  Bob's and many other speakers obliterate the Quads in bass and are often better in the treble but in the midrange they are simply sublime. Any speaker manufacturer would be very proud if they could get close to them.  Cement that into your memory and then listen to the Salk Speakers and Bob's speakers.  Use material with a strong midrange like Sinatra or Dianna Krall.  You might find it quite interesting. 

BTW Bob is not the only manufacturer with this issue.  I was recently at a demo of another speaker that like Bob's is designed for accuracy and neutrality.  It was being demoed by the maker and the guy commented it lacked air and detail compared to ribbon speakers he heard.  Mike, the manufacturer, explained stuff similar to what Bob said but the guy was unconvinced.  Mike was philosophical about it. He makes speakers according to a certain philosophy of neutrality and accuracy but realizes it is not necessarily everyones cup of tea.  In fact I know of guys that had bought Mike's speakers and had them for years but in the end sold then.  They readily admitted they were dead neutral and accurate but lacked musicality.  No problemo - this hobby accommodates all types.

People on this forum might find a recent interview with Mike interesting since it also touches on many of these issues:
http://www.stereo.net.au/forums/showthread.php/26418-Interview-with-Mike-Lenehan?p=390563

Thanks
Bill

Aether Audio

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Re: Distortion, Perception and the Spirit-1s
« Reply #5 on: 28 Aug 2010, 12:21 am »
cujobob,

Welcome!  :thumb: Thanks for the input.

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Waveguides will also have additional distortion from the higher order modes created by the waveguide itself.  Couldn't distortion actually hide detail instead of creating more?

HOMs, eh?  Woohoo... now it's getting serious.  I'm love'n it! :eyebrows:

A Gedlee customer, are you?  Then you've been well schooled in HOMs.  But then, you don't have a lot of choice in the matter.  Earl's a genius, so if you hang around him for very long you're bound to pick up a few things.  I'm not even in the same league, but this hack has a trick or two up his sleeve as well. :wink:

Now, Earl makes a big deal out of HOMs, but then he has to.  Were he to ignore them, he'd be selling the equivalent of 1940's sports megaphones.  Just take a look at the depth of his OSW.  It would be riddled with HOMs without that foam plug.

Conversely, take look at the depth of the waveguide in the Spirits.  2.25-inches deep from tangency at the front panel... to the tweeter diaphragm.  Then compare that to the ratio of the entrance diamater (1-inch) at the throat to the diameter of the mouth (6-inches).  If you can do the Calculus, find the second derivative.  If you can't, just use your imagination/visulaization abilities (like I do).  Either way... we ain't got no stink'n HOMS!!!

OK. maybe not "none," bit virtually none.  The flare rate is so fast that there isn't enough time for any to develop.  Sure, there will always be some, but they're at extremely high frequencies and their magnitude is very low because the boundry area is changing so rapidly.

You may not take my word for it, but I'm telling ya... whatever folks hear from our speakers - good or bad - HOMs have little if any to do with it.

Take care,
-Bob


Charles Xavier

Re: Distortion, Perception and the Spirit-1s
« Reply #6 on: 28 Aug 2010, 12:27 am »

cujobob

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Re: Distortion, Perception and the Spirit-1s
« Reply #7 on: 29 Aug 2010, 02:03 am »
My understanding is that the earliest reflections are those that matter most and while a shallow waveguide should have less HOMs than a deeper one, that doesn't tell the whole story.

gedlee

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Distortion, Perception and the Spirit-1s
« Reply #8 on: 29 Aug 2010, 03:57 am »
Some misinformation in this thread about distortion and HOMs.

About ten years ago I was convinced, just like Bob, that distortion was the key (when I say distortion here I mean nonlinear distortion not linear distortion - understanding the difference is key).  I was at the time a consultant to B&C helping to improve the sound quality of their horns and compression drivers.  We set out a very detailed study of distortion and how it influences the perceived sound quality of the components.  Some two or three years later we had to conclude that nonlinear distotion was not even a small factor in sound quality (for what we were looking at).  This work has all been published in the JAES if the details interest you.

It is no coincidence that Toole, Olive, Fincham and the like all agree that nonlinear distortion is a very small factor in loudspeaker sound quality.

After I stopped working for B&C I was still very curious what it was that I didn't hear in a good waveguide that was ever present in a bad one - I've listened to horns and waveguides for some forty years, so I had a lot of experince with a wide range of them.

After another long investigation I found that the HOM (which I need to remind you ARE NOT nonlinear, they are a form of difraction which is a linear phenomina) are indeed a big part of the sound quality because elliminating or minimizing them is the key to a good sounding device.

Now it is completely untrue that the size of the device has any efect on the amount of HOM that it generates.  The size of the waveguide dominates how well it controls the pattern at its lower frequency edge and hence has a lot to do with how low you can take the crossover point and how low you can control the directivity.  But size has nothing to do with the generation of HOM.  The exact same shape, but smaller, will generate the exact same HOM, but at a frequency that is scaled up as size goes down.  It's the contour that matters, not the size.  A larger waveguide with a larger mouth will also have less problems with the edge diffraction that all terminated waveguides have.

HOM can also be generated by the driver, and most likely are to a large extent, or by the driver to waveguide interface and that too has nothing to do with the size.

An OS waveguide can be shown to generate the least HOM of any shape - no matter what size, but none-the-less HOM are still generated, they are just lower in level than any other shape, and then there are the HOM from the driver itself.  Hence, even though an OSWG is the optimum, there are still some residual HOM and always will be.  The foam takes care of this.

It is often stated that I "require" the foam to get rid of the HOM that are generated - this was implied above - but this is not the case at all.  Even without the foam my OSWG will still be exceedingly low in HOM, its just that the foam makes it even better.  Now others will say that "they don't need it", but the fact is that it would make there designs better, but "they can't use it" because it is patented.

Those are the facts.

Aether Audio

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Re: Distortion, Perception and the Spirit-1s
« Reply #9 on: 29 Aug 2010, 04:25 pm »
Dear Earl,

Thank you so much for chiming in.  I am honored that someone of your credentials would even grace our little forum here with his presence.  Just so we are clear, I want to emphasize the fact that I DID NOT refer to your work with the intent of disparaging it in the least.  Anybody remotely associated with the subject of waveguides or even professional audio in general would be well aware of the many contributions you've made to the field and in particular, your leading edge research in the field of waveguides.  In fact, it was your AES paper on the OSWG back in the '90s that helped me to clarify and more deeply understand the results of my own research, and for that alone I owe you a sincere "thanks."  :thumb:

Nevertheless, we all know that there is more than one way to "skin a cat" and depending on the given design criteria and objectives, different solutions to waveguide design may be called for. In that, while the OSWG is, in fact, the ideal solution for CD performance, such was never the primary objective in my designs.

There is virtually no debate that if space permits, CD control to the lowest possible frequency is a highly desirable objective.  But there's the rub… optimization of that one parameter requires significant size for the device and commensurate physical space for its location in the environment.  For near and mid-field applications, I question the value of striving to optimize the CD parameter at the expense of the required space and other parameters.  As an example, were I designing sound reinforcement loudspeakers, my hat would be off to you and I would be forced to admit that the OSWG is the ideal device.  Little argument can be made that constant coverage over a wide seating area in a large venue is one of a handful of paramount objectives.

Home audio and studio applications though usually imply a restricted listening area in the first place, so I contend that other parameters rise to a higher order of importance.  Even still, if folks do have the space, a reassessment of that opinion would then be in order such that optimization of the CD parameter would once again rise higher on the list of objectives.  Therefore, I am targeting the niche wherein it is assumed space is at a premium and other parameters rise to the fore.

In that, I would take issue with the following statements:

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…we had to conclude that nonlinear distotion was not even a small factor in sound quality (for what we were looking at).  This work has all been published in the JAES if the details interest you.

It is no coincidence that Toole, Olive, Fincham and the like all agree that nonlinear distortion is a very small factor in loudspeaker sound quality.

For me and the customers that my products are targeting, ultimate fidelity and the highest possible levels of playback resolution are the goal.  In that, every and ALL forms of distortion are the bane of this objective.  It is my experience that once a certain level of fidelity is achieved, lower levels of distortion do, in fact, become audible.  It must be emphasized though that such residual levels do not manifest as obvious "distortion" per se, but rather they impart alterations to perceived timbre, imaging and soundstage, and reduced audibility of micro-dynamic details.  Therefore, the quest to reduce all forms of distortion never ceases as we asymptotically approach absolute "0."  A lofty and possibly naïve goal, to be sure… but that's were the fun is.

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After another long investigation I found that the HOM (which I need to remind you ARE NOT nonlinear, they are a form of difraction which is a linear phenomina) are indeed a big part of the sound quality because elliminating or minimizing them is the key to a good sounding device.

Yes… we know.  In fact, it was originally my quest to eliminate diffraction that led me to the waveguide solution in the first place.  Before your seminal AES paper on the OSWG, do you remember a paper written by some guys from Kenwood?  They were fooling around with these very shallow devices and produced some interesting results in reducing diffraction.  It was that paper the stimulated my thinking, only to later on have your paper validate other observations that I made along the way.  As you know, diffraction in all forms can be (within reasonable limits) seen in the acoustic impedance of any device.  Horns and waveguides both depend (in a sense) on a form of diffraction for their very operation, and this can be seen in the acoustic impedance peaks and troughs that they manifest.  To my understanding, it is the reduction of the minima and maxima of these impedance variations that underlies the design of a superior waveguide, but there is a limit to which any device can achieve this objective.

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Now it is completely untrue that the size of the device has any efect on the amount of HOM that it generates.

Yes… but I believe you are referring to magnitude.  What about the distribution thereof and the frequency range, or more succinctly the lower frequency extension, in which/to which they manifest?

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The exact same shape, but smaller, will generate the exact same HOM, but at a frequency that is scaled up as size goes down.

EXACTLY my point.

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It's the contour that matters, not the size.

Hence… the reason for having pointed out the dimensions of my device in the previous posting.

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An OS waveguide can be shown to generate the least HOM of any shape - no matter what size, but none-the-less HOM are still generated, they are just lower in level than any other shape…

I must defer to your research on this fact and have no doubt you are correct.  Once again though, design objectives dictate compromise.  A properly designed OSWG with the mouth diameter of the size we use (6-inches for the Spirit Series) would require greater device depth.  That then "pushes" the distribution density (not necessarily the magnitude) of HOMs down to a lower frequency range.  While the magnitude thereof may be less, density in the critical Fletcher-Munson sensitivity range will increase.  No?  Simultaneously, due to its throat profile/loading characteristics, the OSWG will not achieve the LF gain (efficiency) we require that permits a crossover of 500Hz.

So, what is the point of such a low crossover?  I contend that the HOMs generated by the cone break-up of, AND the HOMs plus the non-linear IM resulting from the excursion-induced compression of, most any woofer... far exceeds those produced by all but the worst horn/waveguide designs.  As long as the tweeter's operation remains well within its excursion limits (and that's the trick), there's not a woofer made that can exhibit such low residuals of distortion.  Therefore, (all things being equal) "pushing" the crossover as low as possible in a given design yields significant over-all system performance gains.  Well, that's my story anyway and I'm sticking to it.


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It is often stated that I "require" the foam to get rid of the HOM that are generated - this was implied above - but this is not the case at all.  Even without the foam my OSWG will still be exceedingly low in HOM, its just that the foam makes it even better.

I apologize.  I unintentionally overstepped my meaning to illustrate a point.  Again, I have no doubt whatsoever that you are quite correct.  After all, you are the "Master" and I humbly bow to your far greater knowledge and experience.  Nevertheless, I suspect the HOM distribution density yields audible artifacts in the critical Fletcher-Munson band, or otherwise it is unlikely an audible improvement would have been realized by using the foam.  In the end (particularly with the foam included), I suspect your OSWG is, in fact, a superior solution to mine in applications where space is not a limitation AND a lower crossover frequency is not desired.  Beyond that, I submit that we have worked out an acceptable compromise that yields very similar performance (sans the CD performance) for the niche market of near to mid-field applications we are targeting.  Now… if somebody approached me to design a system for a large room or hall… I'll definitely be giving you a call.  In those apps, my little waveguides just won't cut the mustard - particularly if optimized CD performace is called for/requested.  :shake:

In closing, thanks so much again for stopping by.  For those of you that have deep interest in all things audio, pay close attention to what Mr. Earl Geddes has to say, as he's one of my personal hero's and a living legend in the field.  Do your research and you'll see… I ain't pumping sunshine up anybody's butt.  If he were a politician, he'd be the equivalent of uh, er… never mind.  Duh… I guess THAT's not a very good analogy. :duh:  There I go again insulting you - sorry Earl! :rotflmao:

Take care,  :D
-Bob

EDIT:  PS.  To summarize for the average reader, I would characterize our waveguide as an optimized compromise and "hybrid" design that bridges the performance of a typical, flat-baffle mounted tweeter on the lower end of the performance scale... and a true OSWG at the top end of the scale.  Such a hybrid reduces space requirements and optimizes distortion performance in the critical midrange and Fletcher-Munson sensitivity range of human hearing, and in so doing somewhat "sacrafices" true CD performance to the otherwise lowest possible frequency...in order to achieve that goal.  Nevertheless, it (the 6-inch version) does offer good CD performance from about 2kHz on up.
« Last Edit: 29 Aug 2010, 05:58 pm by Aether Audio »

gedlee

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Re: Distortion, Perception and the Spirit-1s
« Reply #10 on: 30 Aug 2010, 12:54 am »
I would agree that cabinet size limits many factors and my speakers tend to be bigger than most.  The problem is that people have been told for years that the smaller speakers that were being sold "will sound as good as a full size set."  Thats just not true when the two sets are optimized.  Bigger is always better.

As to the "density" of the HOM, you misunderstood my comment, and thats because I wasn't very clear.  The "size" that ditates the frequency locations of the HOM is strictly the throat size.  For a given throat size and wall angle the HOM will be the same regardless of length or mouth size.  A wider wall angle will bring the frequency range of the HOM lower and a shallower one will make it higher.  So assuming that you waveguides are 1" as mine are and your wall angles are the same, the HOM content will be the same, but the larger waveguide will control lower and have a smaller diffraction hole on axis.  Now if your throat is 1" and your waveguide is wider, then the HOM will be lower in frequency than mine, regardless of the length/size.

Your opinions of the perception of distortion go against all the existing data that I know of and most all of the current researchers in the area.  I guess that you are free to believe that " every and ALL forms of distortion are the bane of this objective", but I would contend that only "audible" forms are important.  Most high quality loudspeaker fall below this threshold, IMO (and that of the poeple that I listed).  Views in this area have changed a lot in the last ten years as people, like myself, have sought to quantify the effects.

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  diffraction in all forms can be (within reasonable limits) seen in the acoustic impedance of any device ... and this can be seen in the acoustic impedance peaks and troughs that they manifest.  To my understanding, it is the reduction of the minima and maxima of these impedance variations that underlies the design of a superior waveguide, but there is a limit to which any device can achieve this objective.

This isn't actually true.  Standing waves show up in the impedance curve, but not necessarily diffraction.  Diffraction can cause standing waves, which then appear in the impedance, but diffraction does not always do this.  I would agree that any device that shows ripples in its acoustic impedance is bad, but the converse is not necessarily true.  Low impedance ripple is a necessary, but not sufficient condition for good performance.  Remember that there always has to be two peaks in the electrical impedance - from the driver - any more than this is bad.