[DaveC113]

You mentioned high efficiency speakers.  Many high efficiency speakers have fairly well-controlled radiation patterns, and in that regard at least they'd be a step in the right direction in my opinion.  They also tend to have good liveliness even at low volume levels.  Omega comes to mind - I used to be an Omega dealer, and think very highly of the line. 

Duke

When I moved into a smaller space I went with Omega XRS. I can't compare them to the 3 way floorstanders I used to have in the small space because I never tried them, but they are a great speaker and a great value as well.

Dave

[Ethan Winer]

Duke,

Regarding the imaging being "killed" by reflection-induced frequency response differences at the two ears, I'm not so sure. The ear/brain system derives directional cues primarily from the first .68 milliseconds (corresponding to roughly 8 inches path length) of a sound impulse.  After this, the precedence effect, or Haas effect (after Helum Haas) kicks in, suppressing directional cues from reflections of the original sound.  That being said, a strong, distinct ("specular") early reflection can still skew the apparent direction of a sound source - which is why diffusion or (if necessary) absorption of first reflection energy is desirable.   The Haas effect continues for 40 milliseconds or so (if I recall correctly), after which a reflection is distinctly heard as an echo.  During this interval the ear/brain system is still picking up timbral and loudness cues, but that's a different topic.

What I'm talking about is different from Haas. It is simply due to each ear receiving a very different frequency response. That kills imaging, independent of reflections arriving early and fusing with the original sound. Or you could look at it another way, and say the two are one and the same, which they are to my way of thinking. When a source and a delayed version are combined, the result is comb filtering. This is how equalizers work. So I'm not sure it's even possible to distinguish between delay / combining and the change in frequency response.

Related: I have spent a lot of time listening and comparing absorption and diffusion at reflection points. Absorption won every time, at least in my living room which is 16 feet wide. Perhaps in a wider room, where the side-wall reflections are delayed enough to not be "early" diffusion could be useful. Now, diffusion might be better there than nothing, and even a few feet behind the listening position diffusion (good diffusion) is better than a bare wall.

--Ethan

[bpape]

Agreed.

The off axis response of most speakers (especially from say 3-4k up) is drastically different from on axis.  Even if the ear/brain can 'ignore' the reflection (which I have my doubts about regardless of the research - I trust my ears) it can't ignore the fact that what is being combined is drastically different in the frequency domain. 

Dipoles can help with this to a point by being self cancelling - but normally at low to upper mid frequencies, not in the highs where frequency response is significantly different.

Bryan

[MaxCast]

You have 5K in stereo gear, try 1k in sound absorption...that is of course you can place them with all those windows.

[Duke]

Hi Ethan,

Well I do see what you mean about the different frequency responses being created at each ear by the different reflection patterns, and I don't know of any study that specifically examines this factor.  I think the Haas effect would still suppress the directional cues because small dissimilarities between the direct and reverberant sound don't de-rail it; it still works unless the discrepancy is very large.   This dissimilar-at-each-ear set of reflections would have been present in studies that used loudspeakers for sound sources, but not in studies that used headphones.  They would also be present in live sounds, which "image" pretty well under most conditions (and not under some). 

But I would certainly agree that the liberal use of absorption is conducive to excellent imaging.

Regarding the ideal "balance" between absorption and diffusion, I think that to a certain extent personal preference enters in (imagine that!).   I tend to place a higher priority on getting rich timbre along with a sense of ambience or even envelopment, rather than on sound image localization.  Also, in my experience excess absorption can skew the timbre, as most absorptive materials are far more effective at short wavelengths than at longer ones.  The polar plots published on your site (a very nice feature) show that already there's going to be a relative shortage of high frequency energy in the reverberant field, and in my experience too much absorption can make that situation worse.

What is your opinion on nearfield listening?  It's an effective way to make sure the direct sound dominates the reverberant sound, and I wonder what you have found regarding nearfield listening in a "typical room" (whatever that is) versus farfield listening in an absorptively-treated room.

To bpapa:

The ear/brain system doesn't "ignore" reflections completely, but it does largely suppress them as far as directional cues goes.  This is why we can easily hear the direction of a sound source in a highly reflective environment, where perhaps 90% of the sound power that reaches our ears is reverberant.  But the ear is still hearing loudness and timbral cues from those reflections - singing in the shower is the classic example.  So you are absolutely correct to be concerned about the loudspeaker's narrowing radiation pattern causing problems, because when we talk about radiation pattern we're also talking about the reverberant field.

Two problems arise from speakers that are seriously lacking in radiation pattern uniformity:  First, the timbre doesn't sound natural because the reverberant field is lacking energy in some regions, and has an excess of energy in other regions (usually in the lower treble).  The second problem is more complicated so I'll just give the short version:  When there's a significant discrepancy between the spectral balance of the first-arrival sound and the reverberant sound, listening fatigue is likely to arise.

My own preference is for loudspeakers that have a uniform radiation pattern over as much of the spectrum as is practical, as I believe it's desirable to minimize the discrepancy between direct and reverberant spectral balance.  This is something that live instruments inherently get right, but few speakers do.

Duke

[Ethan Winer]

Well I do see what you mean about the different frequency responses being created at each ear by the different reflection patterns, and I don't know of any study that specifically examines this factor.

Here's one study - mine! - that is meant to address something completely different, but shows this phenomenon very clearly:

www.ethanwiner.com/believe.html

I think the Haas effect would still suppress the directional cues because small dissimilarities between the direct and reverberant sound don't de-rail it; it still works unless the discrepancy is very large. This dissimilar-at-each-ear set of reflections would have been present in studies that used loudspeakers for sound sources, but not in studies that used headphones. They would also be present in live sounds, which "image" pretty well under most conditions (and not under some).

Yes, headphones don't have this problem, but they have other problems instead. Also, live sounds emanate from a 3D source, not a pair of loudspeakers, so they can't be compared directly. Not only are larger instruments like cellos and drum sets large, which means the sound source is spread out and also more omnidirectional, but different frequencies go off in different directions. So there are more reflections off the ceiling than you'd get from loudspeakers, and those reflections might be brighter than what goes forward, versus speakers that lose highs off-axis. That has a lot to do with the "imaging" you'll perceive when hearing a live band or orchestra. Of course, most people have not heard a string quartet live five feet in front of them in their living room either.

Regarding the ideal "balance" between absorption and diffusion, I think that to a certain extent personal preference enters in (imagine that!).

I agree completely but - here comes some arrogance - I think some people's preference is wrong or, let's say, uneducated. Sort of like taking a college course in fine art appreciation where you learn why a painting of big-eyed kids on velvet is not as good as a Monet. I encounter this often in my work, where someone tells me he prefers his too-small room to not be made too dead with acoustic treatment. But small room ambience is always bad ambience, and were people able to hear the difference, and live with a well-treated room for a few weeks, I believe most would come to appreciate the advantage of a room that is more dead than live. At least if their listening room is small.

I tend to place a higher priority on getting rich timbre along with a sense of ambience or even envelopment, rather than on sound image localization.

I'm not sure how you'd define "rich timbre," but to my way of thinking a playback system should aim for flat and neutral, to let the listener hear as closely as possible what the mix engineer intended. Otherwise, we might as well leave the Loudness switch on all the time because that certainly makes things sound richer.

Also, in my experience excess absorption can skew the timbre, as most absorptive materials are far more effective at short wavelengths than at longer ones.

Excellent point, and this is exactly why some acoustic treatment products are better than others. As I often say, what separates the men from the boys with acoustic treatment is how they perform below 100 Hz.

What is your opinion on nearfield listening?  It's an effective way to make sure the direct sound dominates the reverberant sound, and I wonder what you have found regarding nearfield listening in a "typical room" (whatever that is) versus farfield listening in an absorptively-treated room.

Yes, I listen nearfield always. Even in my living room which is 25 feet long. I'm seated behind the halfway point, and my speakers and couch (and first reflection panels) are arranged for an approximately 8-foot triangle.

Good discussion Duke.

--Ethan

[Carlman]

I have a lot of experience dealing with a small room, 11x13.  I basically eliminated the room with absorption.  It's not as lively as some would like it but I loved the accuracy of the soundstage, instrument placement, etc... And the highs were smooth as silk....

I had bass traps from floor-to-ceiling in every corner and still had a big bass peak.  I measured before and after and the room curve got a lot smoother and less peaky but the same profile of the curve existed.  I went from +10db at 100Hz to +6 or so IIRC.  Who knows what else I did to the nodes, comb filtering, etc.. but I liked the sound.

I'm dismantling that system now and moving to a new house/room that's 15x20-something... Not sure yet... been playing with Ethan's calculator to figure out what the back wall needs to be.  I may also get a recommendation from Rives... not sure.

Basically, having a small room drove me to build a new house with a sound room.  So, have fun but you've been warned.

[Duke]

Hello Ethan,

Enjoyed your reply very much.  You got my wheels to turning...

Since "loudspeaker designer" is one of the hats I wear (whether as a hobbyist or otherwise), I started looking at what you were saying about the detrimental effect of ambience in small rooms through, shall we say, "loudspeaker-colored lenses".   Hmmm, somehow the words "loudspeaker" and "colored" just want to go together, don't they??  Anyway, if ambient energy is undesirable in a small room, the implication is that narrow-pattern loudspeakers would be preferable.  Hey, that's just the sort of thing I like to learn about!

So you've inspired me to design a couple of test speakers that will differ from one another mainly in radiation pattern, so that I can compare them in a 10.5 foot by 9 foot by 6.5 foot room.   For some time now I've been aware that there's a market niche for a speaker that works really well in a small room, and maybe I'll get a little bit closer to being able to build that speaker.

I read your paper entitled "Why we believe", and, well, you might be right or at least partially right (I still think human hearing perception works very differently from the way we currently measure amplifier distortion, for example - so I give credence to those who prefer amps that "measure" poorly).  When we listen binaurally comb filter effects have very little if any effect on perceived timbre, while in monaural listening we can readily hear comb filter effects (Jens Blauert, "Spatial Hearing:  The Psychophysics of Human Sound Localiization", pages 325-327).  The listening tests you describe are all binaural, so I'm unsure that comb filtering explains the perceived differences. 

On the other hand, I think I found something in Blauert's book that supports your position regarding the detremintal effect of comb filtering on imaging.  On pages 349 through 351 Blauert notes that a lack of correlation in the sound field is "a prequesite for spaciousness", and cites comb filter effects as producing a "spectral incoherence".  He goes on to say that the level of "interaural incoherence" (which would include the differing spectral incoherence at each ear) is a determining factor in the perception of "spaciousness".  Now Blauert takes the position that spaciousness is a good thing, but if (big "if") spaciousness is the opposite of precise imaging, and if precise imaging is your priority, then yes it looks to me like comb filtering is indeed detrimental to such imaging.  And a highly absorptive environment would certainly minimize comb filtering. 

I'm not yet convinced that "small room ambience is always bad ambience" - but maybe it depends on how small is "small", as there may be a threshold below which your statement is true.  I tend to like some "spaciousness" - but I haven't put the time and energy into very small rooms that you obviously have.

It's too bad we live so far apart, as I suspect you could teach me a lot in a few ears-on demonstrations.  Thanks for sharing your work with us through your writings. 

Duke

[Ethan Winer]

if ambient energy is undesirable in a small room, the implication is that narrow-pattern loudspeakers would be preferable.

Perhaps, but all "normal" (box and driver) loudspeakers become omnidirectional below a few hundred Hz. Then again, imaging is more about mid and high frequencies. The usual goal for speakers is to radiate horizontally as uniformly as possible, to avoid lobing which basically gives the same skewed response as comb filtering.

Another problem is the wall behind the listener. In a small room that wall is always close, and that's where the worst of the peaks and nulls originate. The comb filtering off a rear wall that's less than ten feet behind is much worse than comb filtering caused by side-wall and ceiling reflections. So no matter how wide or narrow the loudspeaker's dispersion, the rear wall will still be the main problem unless it's treated with absorption (or diffusion).

I read your paper entitled "Why we believe", and, well, you might be right or at least partially right (I still think human hearing perception works very differently from the way we currently measure amplifier distortion, for example - so I give credence to those who prefer amps that "measure" poorly).

What do you think is different? As I see it, what people like about vinyl and tube amps is the distortion. Recording engineers call this "euphonic distortion" because it damages the quality yet can be a pleasing effect. The pro audio equivalent to audiophile vinyl is analog tape. There's a link in my Believe article to another from Sound On Sound magazine where I explain more about that.

Blauert takes the position that spaciousness is a good thing, but if (big "if") spaciousness is the opposite of precise imaging, and if precise imaging is your priority, then yes it looks to me like comb filtering is indeed detrimental to such imaging.  And a highly absorptive environment would certainly minimize comb filtering.

I don't think spaciousness and good imaging are opposing goals. In fact, I'd argue the opposite. When all early reflections are absorbed the sound stage gets wider, not narrower. At least it does in my living room, with the outside edges of the sound seeming to extend beyond the speakers. When people visit I often have them sit on the couch and listen to some music. Then I have them stand behind the couch, out of the "protected" reflection-free area. This way they can quickly stand up straight and receive the side wall reflections, or lean forward over the couch where those reflections are not present. Leaning into the reflection-free zone always makes the sound wider and more coherent, versus behind the couch where you can more easily hear that the sound is coming from the loudspeakers.

It's too bad we live so far apart, as I suspect you could teach me a lot in a few ears-on demonstrations.  Thanks for sharing your work with us through your writings.

If you ever make it to my part of the world, let me know.

--Ethan

[Duke]

Hi Ethan,

In my opinion loudspeaker lobing which results in large peaks and valleys in the power response is a major problem, and should be minimized at the loudspeaker design stage rather than waiting until it gets out into the room.  Four of the five loudspeaker lines I carry do so.  Omnidirectionality in the bass region is probably less of an audible issue than lobing in the midrange and treble region, and is difficult to address in a physically small loudspeaker.

What you say about the wall behind the listener makes sense - in a small room, that reflection would arrive well within the first 10 milliseconds (identified by Richard Heyser and others as the interval within which all reflections are detrimental).

Regarding distortion in amplifiers, a recent in-depth blind study conducted by Earl Geddes and Lydia Lee finds that the ear is very tolerant of low-order harmonic distortion (30% second harmonic distortion is barely even detectable and was not judged to be objectionable by any listeners), but intolerant of very small amounts of higher-order distortion.  In particular, the ear is intolerant of distortion at very low volume levels, which implies that an amplifier with rising distortion at very low power levels is undesirable ("masking" plays a very significant role in distortion perception - I can explain what masking is to anyone not familiar with it).  Negative feedback and amplifier crossover distortion are types of distortion the ear finds highly detectable and objectionable.   Geddes and Lee proposed a new distortion metric that correlates well with subjective tests, called the "GedLee Metric", but as far as I know nobody is using it outside of their laboratories.  After analyzing the test data, Earl remarked, "now I know why you and your friends like tube amps so much".   I don't think it's necessarily the tubes themselves; I think it's the more ear-friendly distortion envelope.

My idea that there's a tradeoff relationship between spaciousness and accurate imaging probably originated in the landmark article by Pisha and Bilello on live end/dead end rooms, published as a two-part article in Audio Magazine in the mid-80's.  Blauert clearly states that the presence of reflections adds a sense of spaciousness to the sound (page 329).  If those same reflections at the same time also degrade image localization, then there is a trade-off relationship going on.   By the way, I don't think that soundstage width and spaciousness are the same thing; image width is dependent on localization cues that will be heard more easily in the absence of reflections.  Spaciousness is something else - a sense of being immersed or enveloped in the sound field, like what listeners experience in a good recital hall or concert hall - and it arises primarily from a late-arriving, highly diffuse, well-energized reverberant field.

In the living room the spectral balance of this reverberant field is largely established by the loudspeaker's power resonse, so I place high priority on the radiation pattern.  Of course radiation pattern matters a lot less if we're going to absorb most of the reverberant energy anyway.

Duke

[Ethan Winer]

the ear is ... intolerant of very small amounts of higher-order distortion.

Yes, because higher harmonics are farther away from the fundamental and therefore are not masked as readily.

Negative feedback and amplifier crossover distortion are types of distortion the ear finds highly detectable and objectionable.

Well, negative feedback does not add distortion, it reduces it. I think in the past some amplifier designers used it as a band-aid to cover up poor circuit design, but used properly negative feedback is a Good Thing. I can't imagine any amplifier being acceptable without at least some negative feedback.

--Ethan

[Duke]

Ethan,

Obviously you understand the role of masking in distortion perception - you're right on the money there.

My wording was poor in my post; what I should have said is that one of the things negative feedback does is trade off high percentages of low-order harmonic distortion for low percentages of high-order harmonic distortion.  So you are correct that negative feedback reduces the amount of distortion, and it is my understanding that most (but not all) amplifiers require some global negative feedback for stability.  However, too much negative feedback increases the perceived distortion, as it trades off a relatively benign distortion envelope for a more audible (and objectionable) one.  Unfortunately, the marketing numbers game works against moderation in negative feedback.  Earl commented to me that his study indicates a negative correlation between lower THD percentages and listener preference.

The Geddes and Lee study has some interesting implications about the audibility of diffraction as well, and his own loudspeaker designs go to great lengths to minimize diffraction and diffraction-like artifacts.  Briefly, since diffraction arrives later in time than the original sound, it is not masked because the ear is poor at masking when the two sounds are separated in time.  Further, perception of distortion caused by diffraction and diffraction-like artifacts is level-dependent; we don't perceive it at low volume levels but we do at high volume levels.  This may well be the reason that some horn systems (especially those using a diffaction horn with a sharp-edged mouth) sound harsh at high volume levels - the ear has a non-linear perception of what is actually a linear distortion.

Duke

[Ethan Winer]

what I should have said is that one of the things negative feedback does is trade off high percentages of low-order harmonic distortion for low percentages of high-order harmonic distortion.

Yes, but this is true only if the amplifier's open-loop bandwidth (no negative feedback at all) is insufficient at higher audible frequencies. If you look at the open-loop response for a typical op-amp, the gain is highest at DC and very low frequencies, then falls continually as the frequency rises. So if a particular circuit requires 40 dB of gain flat out to 20 KHz, the open-loop gain better be at least 20 dB higher at 20 KHz in order for negative feedback to be effective at lowering distortion.

I put this issue in the "incompetent design" category, because a properly designed amplifier will have enough excess gain to allow negative feedback to do its thing and lower distortion across the entire audible band. There are other reasons negative feedback might fall to unusable levels, or cause problems with higher order harmonics, such as phase shift from stray capacitance on the circuit board. But inadequate gain is probably the main one. Again, in a competent amplifier, negative feedback always lowers all distortion.

Earl commented to me that his study indicates a negative correlation between lower THD percentages and listener preference.

Do you mean some people prefer more distortion? I can believe that, up to a point anyway. Personally, I prefer all of my gear and speakers to be as clean as possible. When I put on my recording engineer's hat I may add distortion intentionally to some tracks or to the entire mix. But I want to control that, and hopefully the listener's system won't add yet more distortion on its own. Likewise, when I'm just listening I want my system as clean as possible to best reproduce what the original mix engineer intended.

--Ethan

[doug s.]

not only do these work in small rooms, but they are amazing, even in big rooms, especially if you have subs.

http://www.proac-loudspeakers.com/tabref8sig.php


doug s.

I have a second system in my home office which is a relatively small square room - 13 x 13.  I have loaded up the room with my best gear but as much as I love my Ellis 1801s they are just too much for this small room.  So they are going back to my large living room (18x30) where they will be much happier.  So thinking about my small room the questions I have are:

1.  what qualities should I look for from a speaker for a small room like mine
2.  what is working for you in a small room
2.  speaker recommendations that will sound great but won't overwhelm a small room

Rest of gear in the room is modded PS Audio amp, Audio Note preamp, modwright Sony cd player, and squeezebox.

[Duke]

Hi Ethan,

You said, "Again, in a competent amplifier, negative feedback always lowers all distortion."

I have to disagree.  Total harmonic distortion is lowered by negative feedback, but the distortion envelope is changed and high-order harmonic distortion is actually increased in level.   

"Do you mean some people prefer more distortion?"

That's makes it sound like the elite among us do not fall for the euphonic distortion that seduces the unwashed masses, which is not what I'm saying.  Yes there is individual variation, but there is also statistical confidence that certain type of distortion are more objectionable than others even if the THD numbers are contradicted. 

What I'm saying is that human hearing is inherently much more tolerant of some types of distortion than it is of others.  If 10% THD with a certain distortion envelope is rated as "imperceptible" by 37 blind listeners, and if .01% THD with another distortion envelope is rated as "intolerable" by those same listeners, then THD utterly fails as a distortion metric if our goal is correlation with human hearing (see Geddes and Lee, references below, where this is exactly what is shown).

Now on the surface it sounds like a great idea to just reduce all distortions to zero, but that simply isn't cost-effective.  It makes much more sense to reduce all distortions to just below the auditory system's detection threshold.  But without knowing what those thresholds are, we cannot judge which tradeoffs to make when balancing one type of distortion against another.  This is why psychoacoustics should be part of competent audio design, rather than just looking at the raw THD numbers.  On the other hand if we are designing for test instruments instead of human ears, then psychoacoustic considerations are irrelevant.

See "Auditory Perception of Nonlinear Distortion - Theory" AES preprint number 5890, and "Auditory Perception of Nonlinear Distortion" AES preprint number 5891, both by Earl Geddes and Lidia Lee.   The industry has been measuring the wrong thing, and these papers explain the problem and offer a solution.

Duke

[Ethan Winer]

Total harmonic distortion is lowered by negative feedback, but the distortion envelope is changed and high-order harmonic distortion is actually increased in level.

I assume "distortion envelope" means the spectrum of artifacts produced?

I just got off the phone with my expert friend Bill Eppler, to be sure I'm not overlooking something. Bill confirmed that my understanding is correct - as long as an amplifier is designed well and does not saturate internally, applying negative feedback will lower all distortion within the range of frequencies for which it's designed. And for which it has sufficient extra open-loop gain. However, Bill cautioned that there are a lot of things that can go wrong in something as complex as a good power amplifier - hence my using the words "competently designed" in this discussion.

If you still believe that adding negative feedback can sometimes increase distortion, I'd love to know the specific circumstances.

If 10% THD with a certain distortion envelope is rated as "imperceptible" by 37 blind listeners, and if .01% THD with another distortion envelope is rated as "intolerable" by those same listeners, then THD utterly fails as a distortion metric if our goal is correlation with human hearing (see Geddes and Lee, references below, where this is exactly what is shown).

I agree that THD is not a great metric by itself. IM distortion is usually more objectionable for the same amounts, depending on the frequencies being considered. Though I disagree that 0.01 percent THD is even audible, let alone intolerable, since that puts the artifacts 80 dB below the signal. Nobody can hear that, regardless of the distribution of the added harmonics. I tested this once using a 100 Hz tone and a 3 KHz tone mixed in at various levels. I picked 3 KHz because that's where the ear is most sensitive, and it's very far from 100 Hz so masking doesn't come into play. I don't have my notes handy (I can find them if needed), but I recall at -60 dB I could almost tell as the 3 KHz tone was switched on and off, but at -80 dB it was impossible to hear.

Also, distortion harmonics always fall off in the same way as musical instrument harmonics. No acoustic musical instrument (versus a synthesizer) has more 5th harmonic than 3rd, or more 4th than 2nd. So no "normal" amplifier circuit will have more high-order distortion components than low-order components.

--Ethan

[Duke]

Hello Ethan,

I appreciate your checking up on me with Bill Eppler, and I have indeed made a mistake.  I called an amplifier manufacturer, Ralph Karsten of Atma-Sphere, and he corrected me - I should have been talking about "odd-order harmonics" instead of "higher order harmonics", though it is the higher odd-order harmonics that are most objectionable.  I now think that the even-order harmonics are reduced as you have claimed (lower ones being reduced more than the higher ones), but not the odd-order harmonics.

To the best of my understanding, the mechanism is this:  Odd-order harmonics are an artifact of propagation delay as the feedback signal goes back to the point where it's fed into the signal path again out-of-phase.  Odd-order harmonics are rare and unnatural in nature, and the ear interprets them as loudness cues - so they are much more audible than naturally-occuring harmonic structures. 

The Geddes and Lee papers are well worth reading, and the proposed GedLee metric looks at the shape of the transfer function rather than using traditional THD or IM measurements. 

By way of introduction to the papers, and eventually coming back to the issue of how .01% THD can be not only audible but unacceptable, let me pull a few quotes from Geddes' book, "Audio Transducers":

"Historically, the audio community has viewed distortion in the context of a system's nonlinear response to a sinusoid or sometimes, two or more sinusoids, basically a signal based metric.  A metric is a value which is given to a system to indicate its relative scaling within some predefined context.  For instance, temperature is a metric when the context is human perception.  We can describe the preception of temperature in words like hot, warm, cool, or cold.  Since temperature also has an exact scientific scaling, it is a simple matter to map from the subjective metric to the physical one, although we must remember that the subjective terms are relative and precise mapping is not possible.  Whenever human perception is involved, metrics can only ever be statistically relevant.

"The current metrics of distortion are, Total Harmonic Distortion (THD), Inter-Modulation Distortion (IM), multi-tone intermodulation, etc., all expressed as a percentage - the ratio of the the distortion by-product to the total system output....

"With a reliable metric we could base psychoacoustic studies on it and the same mapping could be done for transducer [or amplifier] distortion as we described for temperature.  But to be useful a metric must be consistent - the same number must mean the same thing in every context and there must be a close correlation between the metric and the subjective response.  This is where the signal-based distortion metrics fail.  It can be shown that .01% THD in an amplifer can be perceived as unacceptable while a 1% THD in a loudspeaker can be perceived as inaudible [in the "Theory" paper, .01% and 10% are the figures given, but "amplifier" and "loudspeaker" are not mentioned].  This simple fact invalidates THD as a viable metric for the discusion of perception.  Furthermore [as you noted!], 1% THD is not at all the same as 1% IM.  Some of the signal-based metrics may be "better" than others, but in our opinion they all fall short of what we are seeking....

"The attribute of hearing that overwhelming dominates our perception of distortion is masking... Masking has no analog in linear systems theory and is not very intuitive since it does not occur in common systems other than the ear....

"From our knowledge of masking we may postulate the following two fundamental characteristics:
-  Masking is predominantly upward toward higher frequencies although masking does occur in both directions.
- The masking effect widens - masking occurs farther away from the masker - at a substantial rate with excitation level.

"....We can see that higher order distortion products are not masked as well as lower order ones and that the masking effect is greater at the higher signal level.  Low order distortion at a high signal level is completely masked in this figure [an illustration in the book].  The higher order distortion is never masked, but it would become more audible at lower levels.

"....These statements give rise to our hypothesis for a new approach to quantifying nonlinearity (distortion):
-  Nonlinearity within the specified operating range should be of low order - the importance of the order being weighted by (n-1)squared where n is the order of the nonlinearity (n>1).
-  No order should increase with decreasing input level.

"Consider now our first example of the failure of THD to differentiate between loudspeaker distortion and amplifier distortion.  If the amplifier has crossover distortion then this type of nonlinearity violates both of our principles - it is both very high order and it increases (as a proportion of the linear terms) with decreasing signal level.  One would expect, based on our hypothesis, that this type of distortion would be highly objectionable and it is [I'm pretty sure that amplifier crossover distortion producing a THD reading of .01% is what he was referring to earlier].  Now consider a loudspeaker.  Unless it has some severe design or manufacturing problems, it will have low orders of nonlinearity and the distortion will only rise with level.  Based on our principles, we should expect this type of distortion to be benign, almost inaudible, and in fact this is what we find to be true.....

"So basically our new "metric" is the actual parameters of the nonlinear components themselves, or the frequency response of the orders, weighted by their order and required to only grow with level (again relative to the linear term).  It is not that uncommon to see discussions of the 2nd and 3rd order nonlinearity - we did it ourselves - but it is rare to see a discussion of the higher order nonlinearity.  If increasing order are indeed more audible than lower orders then limiting our discussion to only the lower two orders is seriously flawed.  The ROOT CAUSE of distortion is the underlying nonlinearity of the system or subsystem and the correct way to discuss nonlinearity is with the orders of its nonlinear transfer function.  When one views the distortion problem in this way, signal based distortion metrics (IM, THD, etc.) become irrelevant."  (Taken from pages 236 - 241 of "Audio Transducers" by Earl Geddes.)

I don't offer this as "proof" - rather, I offer it as an attempt to explain the mechanism of distortion perception.  The proof (or at least supporting data) is in the papers, but much of the math is over my head.

Regarding your test of the audibility of a 3 kHz signal in the presence of a 100 Hz signal that's 80 dB louder, I think this is applicable to distortion perception but I am not sure how much so (the 3 kHz signal is another sine wave rather than a distortion, so it might be more tolerable than a distortion would be).  Note also that signal level would play a role - if the 100 Hz signal is at a level of 70 dB, and the 3 kHz signal is 80 dB down, then it's not surprising that the 3 kHz signal would be undetectable.  Finally, correct me if my math is wrong here, but I think that .01% would be four orders of magnitude down in level, or 40 dB down relative to the main signal, instead of 80 dB down.

Thanks,

Duke

[Ethan Winer]

Duke,

We're getting there, but I still see a bit of a road ahead.

it is the higher odd-order harmonics that are most objectionable.

Probably, because all even harmonics are simple octaves, and higher odd harmonics are not even in tune. So higher odd harmonics are more noticeable.

I now think that the even-order harmonics are reduced as you have claimed (lower ones being reduced more than the higher ones), but not the odd-order harmonics.

This cannot be true. If you said distortion-generated harmonics are improved less by negative feedback at higher frequencies, that would be correct. An amplifier's open-loop gain is less as you go higher, so there's less feedback to reduce the higher harmonics. But as stated above, some even harmonics are higher in frequency than some odd harmonics. There's no mechanism I'm aware of that could distinguish which is which, and reduce the evens more than the odds regardless of frequency. Take as an example a 1 KHz test tone. It has harmonics at 2, 3, 4, 5, etc. KHz. In this case negative feedback might not work as well at 5 KHz as at 4, but it will help even more at 3 than at 4. I hope I'm being clear enough.

Odd-order harmonics are rare and unnatural in nature

Hoo boy, try to tell that to someone who plays the trumpet. Or violin. Or indeed pretty much any instrument other than a flute which is one of the few instruments that put out mostly even harmonics. If you'd like I can post spectrum analyzer screen shots for almost any instrument you care to name.

By way of introduction to the papers, and eventually coming back to the issue of how .01% THD can be not only audible but unacceptable, let me pull a few quotes from Geddes' book, "Audio Transducers":

I see where he says, "It can be shown that .01% THD in an amplifer can be perceived as unacceptable" but that doesn't make it so. As I said before, I have demonstrated this to my own satisfaction, and I encourage you to do the same using any basic audio editor program.

"If the amplifier has crossover distortion then this type of nonlinearity violates both of our principles - it is both very high order and it increases (as a proportion of the linear terms) with decreasing signal level.  One would expect, based on our hypothesis, that this type of distortion would be highly objectionable and it is"

What this misses is that a distortion percentage means less unless the SPL is also taken into account. For a given power amplifier, let's say the crossover distortion is fixed at a constant SPL of 20 dB. That corresponds to 0.01 percent referred to a hypothetical maximum output level of 100 dB SPL. But the noise floor in most domestic rooms is well above 20 dB. So this distortion will be inaudible at any listening level - whether the distortion products are 0.01 percent or 80 percent!

"So basically our new "metric" is the actual parameters of the nonlinear components themselves, or the frequency response of the orders, weighted by their order and required to only grow with level (again relative to the linear term).  It is not that uncommon to see discussions of the 2nd and 3rd order nonlinearity - we did it ourselves - but it is rare to see a discussion of the higher order nonlinearity.  If increasing order are indeed more audible than lower orders then limiting our discussion to only the lower two orders is seriously flawed.  The ROOT CAUSE of distortion is the underlying nonlinearity of the system or subsystem and the correct way to discuss nonlinearity is with the orders of its nonlinear transfer function.  When one views the distortion problem in this way, signal based distortion metrics (IM, THD, etc.) become irrelevant."  (Taken from pages 236 - 241 of "Audio Transducers" by Earl Geddes.)

I agree in theory. But again, harmonics always go down in level as they go higher in frequency. You will never see an amplifier that has more 7th harmonic than 3rd unless it is very badly designed.

Regarding your test of the audibility of a 3 kHz signal in the presence of a 100 Hz signal that's 80 dB louder, I think this is applicable to distortion perception but I am not sure how much so (the 3 kHz signal is another sine wave rather than a distortion, so it might be more tolerable than a distortion would be).

I think you're missing something fundamental here. Each individual distortion component an amplifier creates is a sine wave! You put in 100 Hz, and the amp puts out a sine wave at 100 Hz, another sine wave at 200 Hz, another at 300 Hz, and so forth.

Note also that signal level would play a role - if the 100 Hz signal is at a level of 70 dB, and the 3 kHz signal is 80 dB down, then it's not surprising that the 3 kHz signal would be undetectable.

You got it! This is exactly the point I made above about the audibility of crossover distortion. In my test I listened at a pretty loud level, though I didn't use my SPL meter. I should have! Next time I do a test like this I will.

Finally, correct me if my math is wrong here, but I think that .01% would be four orders of magnitude down in level, or 40 dB down relative to the main signal, instead of 80 dB down.

No, one order of magnitude is 20 dB.

--Ethan

[macrojack]

I love the way you audio nuts are always recommending padded rooms to each other.

[Duke]

Hi Ethan,

Thanks for your in-depth reply.

It is true that odd-order harmonics are generated by many instruments; I wasn't including man-made instrumental sounds when I used the word "nature".  Those instruments with a lot of odd-order harmonic content (trumpet, cymbals) tend to be piercing due to the way the ear/brain system reacts to those sounds.  As our ear/brain system evolved, odd-order harmonic content was associated with "alarm" sounds - crashes, breaking sticks, lightening, etc.  So we react to odd-order harmonic content with heightened perception.

Regarding the audibility of a nasty distortion that would have a THD measurement of only .01%, I agree that saying it doesn't make it so (and specifically tried to make that clear).  That's why I refer to the published study. 

I'm not sure that amplifier crossover distortion is a sine wave phenomenon; rather, I think it's a discontinuity in the transfer function.  But maybe it can be deconvoluted into sine waves.

Still working on understanding the relationship between THD and decibel levels.  I'm more used to talking about loudspeakers, and one order of magnitude (a ten-fold) increase in amplifier power output will give a 10 dB increase in loudspeaker sound pressure level (ignoring power compression for the sake of simplicity) - rather than a 20 dB increase.  I don't yet understand the reason for the discrepancy.

Duke

p.s. - To Macrojack... it takes one to know one, my friend!