After a stimulating discussion in another thread here, I became curious. At what point is harmonic distortion audible? I know with THD, people say the threshold for audibility is about 1% (or -40dB below the fundamental).
However, different distortion products (e.g. 3rd order vs. 2nd order) are more noxious than others, and so should have different thresholds for audibilty. Also, I would guess that we are more sensitive at different frequencies than others, especially in light of the equal-loudness phon curve. Does anybody have additional information on what levels of various orders of HD at various frequencies are audible?
SG
However, different distortion products (e.g. 3rd order vs. 2nd order) are more noxious than others, and so should have different thresholds for audibilty. Also, I would guess that we are more sensitive at different frequencies than others, especially in light of the equal-loudness phon curve. Does anybody have additional information on what levels of various orders of HD at various frequencies are audible?
SG
I'm thinking that we don't really know. I did stumble across a paper in the AES journal, where the author (Toole) cited another author that claimed a target THD <0.05% was desirable, provided higher-order harmonics were not dominant. 0.05%, though, is very low (-66dB).
Does anyone know? Because there area lot of people (i.e. Zaph, Linkwitz, others) out there that publish tweeter distortion plots, and people here seem to be able to determine that one tweeter is better than the next based on distortion measurements. How can this be done if nobody knows what is audible and what is not?
SG
Does anyone know? Because there area lot of people (i.e. Zaph, Linkwitz, others) out there that publish tweeter distortion plots, and people here seem to be able to determine that one tweeter is better than the next based on distortion measurements. How can this be done if nobody knows what is audible and what is not?
SG
I think it's pretty much impossible to predict the ability of a piece of music to mask the audibility of a particular harmonic distortion component generated in playback due to that piece of music. That's why we hear these "nasties" intermittently, only on certain passages.
In tweeters the problem of THD quickly becomes mute. I can't hear the 3rd harmonic of 6KHz while the 2nd harmonic is musical and probably acceptable/preferred. What is probably worst is high THD at frequencies just below the XO freq where the tweeter is still contributing. The harmonics below f3 may well be louder than the fundamental put out by the tweeter (mid driver is dominant here of course but are tweeter harmonics audible?)
In the absence of psychoacoustics & perception knowledge it behooves us to learn all we can to reduce distortion mechanisms.
In tweeters the problem of THD quickly becomes mute. I can't hear the 3rd harmonic of 6KHz while the 2nd harmonic is musical and probably acceptable/preferred. What is probably worst is high THD at frequencies just below the XO freq where the tweeter is still contributing. The harmonics below f3 may well be louder than the fundamental put out by the tweeter (mid driver is dominant here of course but are tweeter harmonics audible?)
In the absence of psychoacoustics & perception knowledge it behooves us to learn all we can to reduce distortion mechanisms.
I agree completely with your post Iain.
Buried somewhere in the Geddes threads, and probably on his site, there are references to tests he did on the audibility of THD using compression drivers. IIRC the levels were very high before becoming audible; something like 10% at HF I think. The lower end of the band would seem to be most likely to be audibly problematic to me, again depending on the driver, xover etc..
Found it here.
Geddes theory page
Buried somewhere in the Geddes threads, and probably on his site, there are references to tests he did on the audibility of THD using compression drivers. IIRC the levels were very high before becoming audible; something like 10% at HF I think. The lower end of the band would seem to be most likely to be audibly problematic to me, again depending on the driver, xover etc..
Found it here.
Geddes theory page
Brett said:
Woh, these were some very interesting papers from Geddes. Thanks for the link! I don't fully understand the math, but he basically showed that there is only a very weak correlation between IMD/THD and listener perception. He didn't include the actual % or dB levels of distortion, which makes it difficult for me to interpret. However, what this likely means is that simple measurement of IMD or THD levels does NOT correlate very well with audible problems with the sound. He does, however, create his own composite formula for quanitfying the amount of distortion present (not strictly HD or IMD) that correlates VERY well with listener preference (we're talking R^2 of 0.9). This tells me that increasing distortion is definitely objectionable, but increasing HD or IMD does NOT necessariliy correlate with objectioable sound. Maybe someone else can interpret the article better than me. Interesting.
SG
Iain McNeill said:
Nope becasue THD is only a sign of nonlinearity and the result of feeding a sinewave into the system. Music contains plenty of spectral components and other distortion products than what you see with sine waves.
If you play a 5kHz and 6kHz component you will not only see partials at 10, 15, 12, 18kHz but also IMD products at 1kHz an also some sidebands 1kHz above and below the 10-18kHz series.
/Peter
I skimmed thru some of Geddes texts:
This is not correct since the ability to hear distortion decreases both as the signal level is decreased and increased.. meaning that there is a range in the middle of our hearing around 80dB SPL or so where we are most sensitive to distortion.
To get a rough idea of what can be heard, play sinewaves on your speakers and headphones. THD levels at 0.5% is easily heard as unpleasant coloration on a sinewave.
On the Klippel website there is some interesting tests that can be done as well.
To me and many ohers speakers with low distortion sounds better than high distortion and that should be read as 0.1% is low while 0.5% is high for medium SPL's.
A speaker with 10% distortion would make me press "paus" or get out of the room.
/Peter
This is not correct since the ability to hear distortion decreases both as the signal level is decreased and increased.. meaning that there is a range in the middle of our hearing around 80dB SPL or so where we are most sensitive to distortion.
To get a rough idea of what can be heard, play sinewaves on your speakers and headphones. THD levels at 0.5% is easily heard as unpleasant coloration on a sinewave.
On the Klippel website there is some interesting tests that can be done as well.
To me and many ohers speakers with low distortion sounds better than high distortion and that should be read as 0.1% is low while 0.5% is high for medium SPL's.
A speaker with 10% distortion would make me press "paus" or get out of the room.
/Peter
Pan said:
I disagree. We don't listen to sine waves and music will have MUCH more masking ability than a single tone. The percentage values that you can hear with sine waves won't have any relevance to distortion audibility in music.
BTW, generating a specific % THD is pretty difficult unless you're just mixing in a single harmonic component. I'd really like to have a box that added a certain amount of distortion to a music signal, with control over the harmonic ratios as well. Kinda like a precision fuzz box
smellygas said:
Let me interpret since I did the work. The "weak correlation" of THD and IMD to perception was NEGATIVE - you forgot to mention that. This means that, as a metric of perception, one should increase the THD to make it sound better. This is of course absurd, but it's the absurdity of THD and IMD measures that is the culprit not the results of the test.
The THD and IMD numbers are indeed shown in all the graphs. They are the X-axis.
Its NOT the level of the harmonics that matter but where the nonlinearity occurs - at low levels or high levels and the order, 2nd, sixth, etc. Low level nonlinearity is by far the most insidious especially if high order - like crossover distortion in an amp. This is why an amp with extremely low levels of THD can still sound terrible. But loudspeakers, on the other hand, tend to have nonlinearities that increase with level and are likely very low level like second or third. This makes them fairly benign. In fact, for the most part, nonlinearity in a loudspeaker (as long as its not broke) is a non-issue. In a test of compression drivers we had twenty five people evaluate distortion levels up to 25% and statistically noone could detect it at those levels.
Its hard to make blanket statements about the audibility of nonlinearities in specific cases, but for the most part nonlinearity is a major concern in electronics, but so much so in loudspeakers.
There are, of course, going to be exceptions to this.
Iain McNeill said:BTW, generating a specific % THD is pretty difficult unless you're just mixing in a single harmonic component. I'd really like to have a box that added a certain amount of distortion to a music signal, with control over the harmonic ratios as well. Kinda like a precision fuzz box
I have a MathCAD program that will do that, but you need MathCAD to run it.
Maybe I can post some examples if we can agree on what to post. (Agreement on this topic is all but nonexistant.)
gedlee said:
Oh, geez, I only skimmed the paper. The p-values were actually not-significant, so it's actually "no correlation." The R and R^2 are useless with p>0.05. Anyway, not important.
Right, but what are the units?
So basically, the Gm explains at least 80% of the variability in perception of distortion. I see that it's weighted for higher-order distortion and distortion present at lower levels. So shouldn't it be possible to plug in values of a certain order of HD specifically (not total HD) and kick out the Gm, and see what it correlates to on the perception scale?
SG
P.S. very cool that you're responding to this
Precision distortion generator
I thought about processing a wave file to create frequency doubled, tripled, quadrupled etc versions of the original music using FFT-IFFT processing but never found the time to work through the math.
Besides, this wouldn't be of any use to synthesize IMD.
Is there an easy way to create the harmonic components of the input wave file or is it simpler to just model the non-linear mechanism that creates the distortion?
I thought about processing a wave file to create frequency doubled, tripled, quadrupled etc versions of the original music using FFT-IFFT processing but never found the time to work through the math.
Besides, this wouldn't be of any use to synthesize IMD.
Is there an easy way to create the harmonic components of the input wave file or is it simpler to just model the non-linear mechanism that creates the distortion?
smellygas said:
Percent!
smellygas said:
Only if you know the precise combination of the orders. You can't find an array of metrics for the orders and get the answer by simply summing the weighted metrics of this array. The exact relationship between the orders is a strong factor. For instance a sixth order nonlinearity that occurs near zero level will be much more audible that the same level of sixth order occuring at the full signal limits.
What's basically missing in most distortion studies is how the distortion goes as the signal drops - not how it grows with signal level. The later is almost irrelavent while the prior is critical. When I looked at the harmonics for amps as the signal went down into the noise floor I found significant differences that correlated very well with the subjective perception. In a poor amp the levels of the harmonics rise as the signal falls and it can be very high order. A clean amp shows nothing as the signal falls. What it does near clipping is almost unimportant and in fact, I claim that a soft clipped amp sounds better.
Actually modeling the nonlinearity curve is the only way to do this. Thats because THD and IMD are only symptoms of the problem which occur when precise waveforms are used. To hear the effects of these same nonlinearities on an actual music waveform you have to model the underlying root caues nonlinearity. Thats what my MathCAD program does. You can use any wave file. Lets decide on an example wav file and nonlinear characteristic and I'll post the results. First would obviously be a strong third order soft clip, because you will be amazed that at 50% THD the effect is completely inaudible. Then a .1% example of crossover distortion which will sound terrible.
gedlee said:
Ohhhhh gotcha. Woh, then that's a LOT of THD/IMD that people couldn't differentiate. Interesting.
Only if you know the precise combination of the orders. You can't find an array of metrics for the orders and get the answer by simply summing the weighted metrics of this array. The exact relationship between the orders is a strong factor. For instance a sixth order nonlinearity that occurs near zero level will be much more audible that the same level of sixth order occuring at the full signal limits.
What's basically missing in most distortion studies is how the distortion goes as the signal drops - not how it grows with signal level. The later is almost irrelavent while the prior is critical. When I looked at the harmonics for amps as the signal went down into the noise floor I found significant differences that correlated very well with the subjective perception. In a poor amp the levels of the harmonics rise as the signal falls and it can be very high order. A clean amp shows nothing as the signal falls. What it does near clipping is almost unimportant and in fact, I claim that a soft clipped amp sounds better. [/QUOTE]
Oh, I see. Well what if you hold constant the magnitude/level of the distortion at the signal rise and the magnitude/level at the signal low. Then only change the order of the distortion. How much would this affect the Gm value? Is this easy to calculate? Also, your Gm metric seems so useful because it reliably relates the full spectrum of sound perception (imperceptible to annoying) with measured/calculated data. There MUST be some kind of practical application for this - perhaps with a loudspeaker manufacturer or with evaluating drivers or something!
SG
smellygas said:
That work was done almost seven years ago now. The funny thing is that no one cares. You see nobody believes any measurements in audio anymore so the fact that THD and IMD are meaningless is of no real significance. And replace it with something meaningful!? That would only confuse people more and well, marketing doesn't really want something meaningful, there is no way to put a "spin" on that.
You have to ask yourself what's wrong with a marketplace that prefers to use things that are completely meaningless when absolutely valid representations are available. And its not just distortion, it's in everything about audio. The most recent one now is everybody is talking about how important constant directivity and polar control is, but very very few are actually doing anything different. What's changed? Piston loudspeakers aren't and can't ever be constant directivity. Well enough of this for tonight - I need to get some sleep.
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