Subwoofers: a need for lower distortion?

[RCAguy]

Very low frequency distortion is perceived “inflated,” based on Fletcher-Munson as updated in ISO226:2003. For example in the chart (transposed as Equal-SPL contours), at 30Hz a typical mid-quality SW measuring 3% THD sounds like 25%; like 10% at 60Hz. The harmonic artifacts generated, mostly by the SW driver, are post crossover, so are not filtered by it, causing auditory confusion with the main speakers’ “soundstage.”

 

[fineMen]

A very nice question, indeed. It boils down to: "When measuring x, is the human hearing, with all its characteristics, part of the device under test?"

(I raised this question here: https://www.audiosciencereview.com/...es-down-to-0-01-thd.47414/page-2#post-1699731)

Your proposal leads to another qualification criteria, namely distortion weighted with audibility, e/g "perceived dirt" which, as the above mentioned headphone example makes clear, may be a very individual one. WIth bass distortion it would also be dependent of listening distance and the effective frequency response in-room.

And not the least it depends on the program's content, because the musical harmonics of synthetic or mechanical instruments mask, at a certain point, all of those evil distortions.

In short, the weighting would ask for a deep dive into understanding the harmonics and other mechanisms--the ear itself isn't linear aka distortion free itself. Shall we prepare for a journey down to the ol' shipwreck?

 

[dominikz]

Very low frequency distortion is perceived “inflated,” based on Fletcher-Munson (ISO226). For example in the chart (transposed as an Equal-SPL contour), at 30Hz a typical mid-quality SW measuring 3% THD sounds like 25%; like 10% at 60Hz. The harmonic artifacts generated, mostly by the SW driver, are post crossover, so are not filtered by it, causing auditory confusion with the main speakers’ “soundstage.”

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Interesting approach (thanks for sharing!), but it seems to boil-down to how the distortion figures are represented/calculated - not necessarily to their audibility. Audibility would be tested by controlled listening tests because various perceptual mechanisms can influence it - Fletcher-Munson curves are only one of them.
Has the author provided any listening test results supporting their hypothesis of inflated perception of distortion at LF? Unfortunately I haven't had a change to read the full article.

E.g. the Fletcher-Munson curves do not take into account auditory masking so I'm not convinced we can say "3% at 30Hz sounds as 25%" - at least not without confirming this hypothesis with a controlled listening test. IMHO it would be more precise to say "3% distortion at 30Hz can also be represented as 25% when normalized to the 85 dB SPL Fletcher-Munson curve".

To my knowledge, prior research into low-frequency distortion audibility has shown that humans seem to be less sensitive to low-frequency distortion - which seems contrary to the proposed hypothesis of inflated perception of LF distortion.

 

[ocinn]

Warning, Very subjective reply:

I do live sound, a huge part of my job is designing and tuning ultra high spl subwoofer arrays. I am quite familiar with pushing subwoofers to their absolute limit, and both objective and subjective analysis of systems.

I find reasonable harmonic distortion absolutely a non-issue, in a music context. Sure you could likely hear in test tones but they disappear in music. Not to mention most instruments that produce sub-bass frequencies (bass guitars, synths, kick drums) naturally have huge sprays of harmonics and other audible information and therefore reasonable HD from the speakers themselves, wouldn’t sound like “distortion” and in fact they would sound like a “different tonality” of the instrument. I.e a “brighter” sounding bass tone.

In subjective analysis, perfect integration thru the crossover region and linearity of spl across the passband are, imo, hugely more important than reasonable harmonic distortions.

Considering most people do not have a highly treated rooms nor DSP, obsessing over subwoofer THD is likely the least effective thing to chase after for overall system fidelity.

Obviously if your subwoofer is too small or the amplifiers are underpowered and you are running into mechanical limits or amplifier clipping that’s a different story.

 

[dasdoing]

wow, this is a very dramatic logical error. 30dB down at 1000Hz will psychologically roughly mean 60dB down at 25Hz. So it's actually the opposite of what is being claimed. And that is reason we are not as strict with distortion down there

 

[dasdoing]

30dB down at 1000Hz will psychologically roughly mean 60dB down at 25Hz

meaning, for that the distortion is perceived as loud as at 1000Hz it would have to be twice as bad at 25Hz

 

[dominikz]

30dB down at 1000Hz will psychologically roughly mean 60dB down at 25Hz. So it's actually the opposite of what is being claimed.

I agree, I just tried quickly drawing a fundamental at 30Hz with 90dB SPL and its harmonic at 60Hz with 60 dB SPL (i.e. roughly 3% THD) over the Fletcher-Munson equal loudness contour overlay:

We can see that 90 dB SPL at 30 Hz would be perceived equally loud as 80 dB SPL at 1kHz, while its 60Hz harmonic at 60 dB SPL would be perceived equally loud as ~25dB SPL at 1kHz - which gives a normalized difference of 55dB or approx. 0.2% normalized distortion.
But again, even such analysis disregards masking effects that happen when you introduce a second tone. To my knowledge equal loudness contours were derived using a single tone stimulus.
This is why I'd expect that controlled listening tests would show sensitivity to distortion at low frequencies is even lower than predicted by this kind of Fletcher-Munson normalization alone.

 

[dasdoing]

To my knowledge equal loudness contours were derived using a single tone stimulus.

actually the ISO is a meta-study of dozens of equal-loudness studies, including FM. FM is used as a placeholder for the ISO it seams, at least by Americans. FM shouldn't be used anymore

 

[RCAguy]

actually the ISO is a meta-study of dozens of equal-loudness studies, including FM. FM is used as a placeholder for the ISO it seams, at least by Americans. FM shouldn't be used anymore

We used ISO226:2003 as :2023 data isn't widely available yet [OP edited].

 

[fineMen]

We used ISO226:2003 as :2023 data isn't widely available yet [OP edited].

Do you think to differentiate one ISO v/s the other makes a difference when the concept behind your musings isn't clear?

I mean, what are you after? Frankly spoken, your attempt doesn't conclude. Mainly because is it formulated as a question, logically. Only now I see that there's a commercial offer behind it.

So: I vote for no, by no means is there need to have lower distortion in subwoofers.

Reason: if there is any data regarding the annoyance factor or perceivability or objectionability of distortion in bass for human subjects it is related to frequency and the base tone's loudness and the harmonics' loudness. What you'll not find is any data that is evaluated along your proposal. Because the reference to the human hearing is already there, because the investigations are done sporting human subjects. In short, your re-calculation doesn't make no sense at all, once you want to compare some readings with arbitrary speakers to related investigations (of course done by others) and--humans.

Of course will go on, please discuss; no offense.

 

[RCAguy]

Thank for all responses. Editor Gil & I are checking and will reply - we know science is not a destination, but a journey.

 

[FrantzM]

Do you think to differentiate one ISO v/s the other makes a difference when the concept behind your musings isn't clear?

I mean, what are you after? Frankly spoken, your attempt doesn't conclude. Mainly because is it formulated as a question, logically. Only now I see that there's a commercial offer behind it.

So: I vote for no, by no means is there need to have lower distortion in subwoofers.

Reason: if there is any data regarding the annoyance factor or perceivability or objectionability of distortion in bass for human subjects it is related to frequency and the base tone's loudness and the harmonics' loudness. What you'll not find is any data that is evaluated along your proposal. Because the reference to the human hearing is already there, because the investigations are done sporting human subjects. In short, your re-calculation doesn't make no sense at all, once you want to compare some readings with arbitrary speakers to related investigations (of course done by others) and--humans.

Of course will go on, please discuss; no offense.

what he said... plus
this:
https://www.axiomaudio.com/blog/distortion

TLDR 1:our detection threshold for noise (made up of harmonically related and non-harmonically related test tones) is practically non-existent at low frequencies.

TLDR 2": the results show we are virtually deaf to these distortions at those frequencies. Even in the mid-bass at 280 Hz and lower, the noise can be around -14 dB (20% distortion), about half as loud as the music itself, before we hear it.

Peace.

 

[RCAguy]

Using ISO 226:2003 - 70yr newer data than F-M - Fig.2 (reproduced below) of the cited paper "Subwoofer Camp 2" shows that a pure 30Hz fundamental at 90SPL "sounds like" 40phons, while a 3% 2nd harmonic of 60Hz at 60SPL is heard as 20phons, a 20dB difference equivalent to 10% perceived distortion. And this "inflated" perception of LF distortion is greater still when other harmonics comprising THD are included, as in the paper. E.g. an often equal if not greater 3rd harmonic distortion product of 90Hz sounds like 30phons, 10dB below the fundamental, perceived as 30% distortion, etc. The paper is new analysis that refutes conventional wisdom on the perception of LF distortion.

Fig.2 of the cited paper "Subwoofer Camp 2"

We appreciate 'FineMen' and others above checking us on this, however discussion might be more productive reading the paper first.

We agree with 'FineMen's' points about conducting listening tests as an ultimate determination of the paper's hypothesis. And it pertains to all woofers reproducing <500Hz, not just SW. Such blind testing is beyond the scope of this hypothesis paper. But someone should do so - perhaps an academic with more resources than we have?

We also agree about the mitigating effect of masking. This is especially true with popular music that 1) to be novel contains copious intended harmonics; and 2) that is typically electric instruments for which listeners have little if any reference for their original undistorted sound. How fuzz-toned was it this time? However, masking has less effect when listening to acoustic music (classical, jazz, etc) for which most listeners have an accurate remembered reference, having attended unamplified concerts, or themselves playing acoustic instruments. For this once majority of listeners of reproduced music, low distortion means instruments are not artificially "brightened" by added distortion harmonics.

This reply is not intended to stymie further discussion - please weigh in. We all have a lot to learn!

PS - FrantzM's link to https://www.axiomaudio.com/blog/distortion incorrectly states "-14 dB (20% distortion), about half as loud as the music itself" when the accepted value is ~10dB. Furthermore that is at frequencies >500Hz - the cited paper shows that at subwoofer frequencies, the value is about ±5dB change of SPL for a perceived doubling\halving of loudness.

 

[fineMen]

We appreciate 'FineMen' and others above checking us on this, however discussion might be more productive reading the paper first.

I appreciate to be mentioned again. It is only so that my argument wasn't meant to close the case with some other listening test.

It was the other way round: we already have listening tests that show that the sensitivity (generally speaking) of the human hearing for harmonic distortion in (sub)bass is quite limited. That already includes the effects of the F/M-curves. There is no need to recalculate numbers, because the all so far conducted tests already consider them implicitely. Namely in asking the test panel if they could hear the distortion or not which implies them to use their own ears which implies the elevated sensitivity depicted by the F/M-curves.

As we took real people we wondered why the elevated sensitivity at higher frequencies still left the detection threshold for distortion products at multiples of the base tone that high.

But, so it is, simply.

Maybe your problem statement was not quite to the point, I don't know exactly? When it comes to distortion products above the x/over frequency, I might correct you. Of course distortion is never filtered out, because you filter the generating tone, but never the harmonics. Because the latter are generated by the speaker itself and so are not accessible to the x/over. This applies likewise to the passband below the x/over frequency. I for sure got you completely wrong.

 

[RCAguy]

It was the other way round: we already have listening tests that show that the sensitivity (generally speaking) of the human hearing for harmonic distortion in (sub)bass is quite limited. That already includes the effects of the F/M-curves. There is no need to recalculate numbers, because the all so far conducted tests already consider them implicitely. Namely in asking the test panel if they could hear the distortion or not which implies them to use their own ears which implies the elevated sensitivity depicted by the F/M-curves.

As we took real people we wondered why the elevated sesitivity at higher frequencies still left the detection threshold for distortion at multiples of the base tone that high.

My editor & I would be interested in the results of the test you cite, which as you say apply no matter F-M in 1933 or ISO226 in 2003\2023. However 1) Were the subjects listening to rock & roll? 2) Were signals LPFd to the subwoofers AND HPFd to the main speakers? 3) Were the subjects students, who in my experience doing blind listening tests are often less reliable due to inexperience? [Subject of an AES paper.] My informal listening "tests" with three very experienced musicians and professionals in audio - seniors, but who still easily hear LF distortion artifacts - show that SW reproduction in the 32~120Hz range with <0.5%THD drivers playing orchestral music sounds discernably more authentic (double bass viols with C-extension, tuba, 40in bass drum, contra-bassoon, grand piano, etc.). Our test recordings are from my years as recordist of the Greenwich Village Orchestra to countless studio sessions. I know you agree it's very interesting, if not critical!

 

[fineMen]

My editor & I would be interested in the results of the test you cite, which as you say apply no matter F-M in 1933 or ISO226 in 2003\2023. However 1) Were the subjects listening to rock & roll? 2) Were signals LPFd to the subwoofers AND HPFd to the main speakers? 3) Were the subjects students, who in my experience doing blind listening tests are often less reliable due to inexperience? [Subject of an AES paper.] My informal listening "tests" with three very experienced musicians and professionals in audio - seniors, but who still easily hear LF distortion artifacts - show that SW reproduction in the 32~120Hz range with <0.5%THD drivers playing orchestral music sounds discernably more authentic (double bass viols with C-extension, tuba, 40in bass drum, contra-bassoon, grand piano, etc.). Our test recordings are from my years as recordist of the Greenwich Village Orchestra to countless studio sessions. I know you agree it's very interesting, if not critical!

There was one of a plethora of tests quoted above already. Was it this one: https://www.axiomaudio.com/blog/distortion ?

First of all, in regard to distortion we must not single out the 'harmonic distortion', because it always is indicative of at least 'intermodulation distortion'. We have Doppler distortion also, while, admitted some ignore it actively. We have wind noises from the port and maybe leaks.

If you claim that a lower level of 'harmonic distortion' is advizable, how could I speak against it? Of course it is, but to what extent? This was addressed many times, and the general outcome was that bass distortion is a minor problem. Some say 10% is ok, some say 1% is for sure not objectional. I'm in the latter camp. But only so, because I actually achieved it. I wouldn't pay a penny to go lower. Even if it was 3% I wouldn't as long as nobody else would blame me for that.

You still don't address my argument, that there are weakly established figures, and these figures are determined while taking the Fletcher/Munson curve fully into account. Now it seems that you are after making a case with the argument, that the Fletcher/Munson isn't taken in properly.

You write, referring to F/M curves: " ... at 30Hz a typical mid-quality SW measuring 3% THD sounds like 25%; like 10% at 60Hz ..."

There is no "sound like", your calculation is a fallacy. You may want to think it the other way round, and that is what all the experiments did.

Given: base tone, add a second tone 2, 3, 4, n times the base tone with increasing amplitude
Ask people: at which level of the second tone it becomes audible in presence of the base tone
Conclude: that is the threshold for the audibility of the n'th harmonic of the base tone, express in percent

You could do that for a range of basic loudnesses of the base tone. Done. Nice, isn't it? Fletcher/Munson all in.

 

[dominikz]

We also agree about the mitigating effect of masking. This is especially true with popular music that 1) to be novel contains copious intended harmonics; and 2) that is typically electric instruments for which listeners have little if any reference for their original undistorted sound. How fuzz-toned was it this time? However, masking has less effect when listening to acoustic music (classical, jazz, etc) for which most listeners have an accurate remembered reference, having attended unamplified concerts, or themselves playing acoustic instruments. For this once majority of listeners of reproduced music, low distortion means instruments are not artificially "brightened" by added distortion harmonics.

Auditory masking in the psychoacoustic sense is a characteristic of human auditory system and not strictly related to the type of music. Of course that denser spectrum of modern production causes more masking, but masking happens even with pure sine tones (as little as two sine tones are enough to demonstrate it).
In principle presence of one sound (masker) will raise the threshold of audibility in the nearby spectrum and can therefore mask other sounds that are close to it in spectrum and/or time.
The relevant Wikipedia article explains some of the concepts involved.
Given that in low frequencies auditory masking extends quite far into higher frequencies, harmonics are largely (or even fully) masked.
Here's an example of masking curves for a 150Hz masker at 3 levels (source: https://blogs.qsc.com/live-sound/auditory-masking-and-its-effect-on-our-perception-of-sound/):

We can see that e.g. 70 dB 150Hz fundamental would fully mask its 300Hz harmonic if it is below ~45dB (around 5% distortion). To my knowledge masking becomes stronger the lower in frequency we go (which would explain why formal listening tests showed humans are insensitive to LF distortion).

 

[RCAguy]

There was one of a plethora of tests quoted above already. Was it this one: https://www.axiomaudio.com/blog/distortion ?

First of all, in regard to distortion we must not single out the 'harmonic distortion', because it always is indicative of at least 'intermodulation distortion'. We have Doppler distortion also, while, admitted some ignore it actively. We have wind noises from the port and maybe leaks.

If you claim that a lower level of 'harmonic distortion' is advizable, how could I speak against it? Of course it is, but to what extent? This was addressed many times, and the general outcome was that bass distortion is a minor problem. Some say 10% is ok, some say 1% is for sure not objectional. I'm in the latter camp. But only so, because I actually achieved it. I wouldn't pay a penny to go lower. Even if it was 3% I wouldn't as long as nobody else would blame me for that.

You still don't address my argument, that there are weakly established figures, and these figures are determined while taking the Fletcher/Munson curve fully into account. Now it seems that you are after making a case with the argument, that the Fletcher/Munson isn't taken in properly.

You write, referring to F/M curves: " ... at 30Hz a typical mid-quality SW measuring 3% THD sounds like 25%; like 10% at 60Hz ..."

There is no "sound like", your calculation is a fallacy. You may want to think it the other way round, and that is what all the experiments did.

Given: base tone, add a second tone 2, 3, 4, n times the base tone with increasing amplitude
Ask people: at which level of the second tone it becomes audible in presence of the base tone
Conclude: that is the threshold for the audibility of the n'th harmonic of the base tone, express in percent

You could do that for a range of basic loudnesses of the base tone. Done. Nice, isn't it? Fletcher/Munson all in.

The "Subwoofer Camp 2" paper covers IMD, as it is often comparable to THD (and adds arithmetically as its artifacts are largely correlated with THD), but IM data are seldom published by mfgrs or reviewers. I also cover "port noise complaint,' etc.

https://www.axiomaudio.com/blog/distortion raises questions, such as the mistatement I've already mentioned: "-14 dB (20% distortion), about half as loud as the music itself" when -10dB is the accepted value >500Hz, but the paper shows it's about ±5dB for doubling\halving loudness in the SW range. "Eight subjects aged 20~60" is likely skewed younger, a demographic I've found unreliable. That "distortion detection does not vary with level" is suspect, as at some level each harmonic artifact becomes inaudible (below the hearing threshold). Bogus is "the nature of the particular music did not significantly change the results" as this test included three samples of only very similar highly produced electric pop music - not acoustic music, the reference for authenticity I've already addressed, and proven to the satisfaction of three senior audio professional subjects I trust. Neither the Axiom article nor my paper is peer-reviewed (yet): Axiom's is a manufacturer's word based on its own product. Or is it cited by biased owners of the product?

I've acknowledged your main argument, that proper listening testing would trump F-M or ISO226:2003\23, except that, for a hypothesis paper, these data average many subjects, and are already freely available. I do not question the masking effects, nor that a listening test would be desirable if a more proper regimen. Lacking the resources it implies, I must leave it to others (and welcome any references if it's already been done). I find nothing quite appropriate enough in Blauert.

For lay reader clarity, we use the term "sounds like" for Perceived Loudness (dBphons) to differentiate from "actual power [energy]" in SPLdB. Of course we'd argue that our "calculation" is not a "fallacy" - the paper is a hypothesis intended for further study, namely listening tests by others, who need to begin with an hypothesis.

 

[fineMen]

... need to begin with an hypothesis.

I'm not quite convinced that you've got my argument right as intended. Last chance?

You measure a speaker and then calculate the subjectively perceived strength of the harmonic content. Like you did above as 3% technical equals 25% subjectively @80dB at-the-ear level but subjectively 10% @90dB at-the-ear level.

Much of data. Now, what are you going to do with that?

To what subjective impression would you relate it? You're decidedly after subjective impressions, aren't you?

 

[RCAguy]

Auditory masking in the psychoacoustic sense is a characteristic of human auditory system and not strictly related to the type of music. Of course that denser spectrum of modern production causes more masking, but masking happens even with pure sine tones (as little as two sine tones are enough to demonstrate it).
In principle presence of one sound (masker) will raise the threshold of audibility in the nearby spectrum and can therefore mask other sounds that are close to it in spectrum and/or time.
The relevant Wikipedia article explains some of the concepts involved.
Given that in low frequencies auditory masking extends quite far into higher frequencies, harmonics are largely (or even fully) masked.
Here's an example of masking curves for a 150Hz masker at 3 levels (source: https://blogs.qsc.com/live-sound/auditory-masking-and-its-effect-on-our-perception-of-sound/):

The two articles do not jibe well in terms of masking harmonics. In the more conservative case, a 2nd harmonic is only masked 25dB below the fundamental, so not much masking is going on.

Regarding masking v. source material, you actually say "Of course that denser spectrum of modern production causes more masking," and I agree.