Hello, Head-Fi Sound Science! I'm looking for critique on my current view on distortion.
I've been looking recently into the audibility of nonlinearities. As established by studies by both ALMA International  and Geddes , we know that traditional forms of measuring nonlinearity (THD and IMD) fail to accurately depict the audibility of the nonlinearities. Large amounts (30%+) of 2nd and 3rd order distortion, for example, can go unnoticed to a listener thanks to psychoacoustics.
We will focus on headphones in particular for this analysis, rather than source equipment. Headphones are known to generally be heavy in 2nd and 3rd order distortion when they distort, unlike electronic components. This suggests that the distortion effects should be relatively benign.
Flaws in the Traditional Methods (THD/IMD)
It appears that the typical forms of measuring distortion have several flaws as established by :
1. Distortion higher in frequency is harder to distinguish from lower frequency distortion. This is backed up by the studies cited in . For example, we should expect distortion at 300hz to be more noticeable than higher frequency distortion.
2. Distortion farther from the original excitation is easier to perceive. To tie back to THD/IMD, this means higher order distortion is worse than lower level distortion. The masking effect of the ear can sometimes mask massive amounts of low order distortion, but it will fail to mask massive amounts of high order distortion. Recognize that THD is normally DOMINATED by lower order distortion and this makes THD very difficult to use.
3. Distortion byproducts at low signal levels are easier to perceive than at high signal levels. Basically, this means amplifier and DAC distortion is worse than headphone distortion. Headphones and loudspeakers distort a lot more as they get louder, but source equipment can sometimes distort even at low signal levels. To quote Geddes, "Haven't you ever wondered how it is that you could hear .1% of electronic distortion through a loudspeaker that is typically 1-5%?" Since the masking effect is stronger with louder signal, we can expect a lot of the distortion from headphones to be masked by the louder volume.
Consider this a perfect example of how we aren't just listening to sine waves. Sine wave testing fails to capture the psychoacoustic effects that can make distortion difficult to perceive. It seems like sine waves are likely the "worst case scenario" for distortion.
What Does That Mean for Us?
We don't have access to measurements like PTHD or Gm for most headphones which adjust for those problems. What we do have access to are regular distortion measurements, sometimes with the different orders of distortion shown on the graph.
Although our methods can't be perfect, I believe that we can improve our interpretation of the information available to us in the following ways:
1. Weigh distortion measurements in lower frequencies more than higher frequencies.
2. Avoid making many judgments about 2nd and 3rd order distortion measurements -- focus on 4th and higher level distortion.
3. If information about the order of the distortion is not available like from sites like InnerFidelity, recognize that the distortion data may not be as useful as we originally expected. If the THD in the measurements are caused almost entirely by 2nd order distortion, for example, it may not be audible at all.
4. Weigh power handling less -- the louder the signal, the greater the masking effect, so an increasing amount of distortion can be acceptable.
5. Don't compare raw distortion numbers directly. 5% THD on one headphone may have a relatively benign effect whereas 1% THD in another may be nasty.
Furthermore, we should weigh typical distortion measurements less in general. They're just not descriptive enough to be useful in many contexts.
Addressing Ethan Winer's Critique of Geddes Work
After noticing the video posted about the AES Damn Lies workshop, I feel the need to address this argument. Winer presents two arguments in the video:
1. The Geddens study uses contrived distortions from complex mathematical formulas, and it doesn't accurately depict actual distortion characteristics.
This is completely true, but kind of misses the point of the paper. The point of the paper isn't to prove the complete inaudibility of nonlinearities, but to show a failing in the THD measurement. The examples are totally contrived to make a point -- the point being that there are types of distortion that THD fails to accurately depict in terms of audibility and that THD overly punishes certain types of distortion that are not very audible.
2. Distortion is more about the audibility of artifacts, regardless of their type or cause. If the sum of all artifacts is 80dB or lower below the music, it won't be heard regardless of its make-up.
In general, I feel this argument is correct, but I don't think it applies much to headphones. Headphones rarely have distortion that low. It doesn't actually seem like a critique of Geddes' work, though -- current psychoacoustic research suggests that we hear different types of distortion differently, so a straight sum of the distortion products (or their square) is an inaccurate measure of the audibility of the distortion. I don't believe this dismisses the arguments shown in this post.
Edited by SanjiWatsuki - 1/3/14 at 12:24pm