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You made the classic mistake of assuming since the HD 800 S bass sounded different than the HD 800, that it must be distorted.
You seem to imply here that in your impression, the HD 800 was "clearer" yet you recognize that the HD 800 S was "more extended". These two things are a bit at odds with each other. Having extended bass means having bass present which means having the overall bass presentation more clear.
A frequency response is good for some things, but you can't just isolate a single section of the frequency response, and assume you can consider that in a vacuum without the rest of the frequency response context. The frequency response represents the overall "tonal balance" of the headphone, and you need to consider the entire thing. In terms of detail retrieval (this includes hearing bass extension, details you never heard before such as background coughing, and so on), part of that is a function of the balance of the frequency response and which frequencies are emphasized in aggregate. You hear that cough because the frequency band the cough exists in is different than the previous sound source you were using. The same is true of bass, bass extension, and so on.
The HD 800 has sections of elevated treble, which can tilt the tonal balance and how you interpret the sound. By tuning the HD 800 S to have less treble, the bass becomes more balanced and potentially clearer and better extended to the listener.
Finally, at the end of the day, everybody needs to understand there are pretty fundamental problems with measurements. They will never be perfect. They are an imperfect tool we can use to try to have a discussion about things, but especially when it comes to bass response, there are a lot of potential issues and problems with putting a headphone on a dummy head and expecting the result to sound exactly the same as when you hear them. People's ear canals are different, different frequencies might be emphasized in your particular HRTF, and so on. It's possible Sennheiser tuned the headphone to a different target HRTF standard than Jude or Tyll's measurement set up.
My advice to anyone, when measurements differentiate from your listening impressions, trust your ears. Your enjoyment of the headphone is the only thing that matters. As a corollary, don't parrot things you hear online and try not to let other people's flawed impressions influence your own. Things like the HD 800 S have zero bass distortion. If you don't like the tonal balance of the HD 800 S, just say that. Don't pretend it has distortion (or, likewise with the HD 660 S, pretend that one has a "grainy treble").
The HD800 and HD800S makes comparisons very easy because how they share the same earpads and geometry.
What is shown on community setups and the innerfidelity setup is the HD800S has more THD at subbass frequencies than the HD800. It's in Jude's FFT measurements that two are very similar at 90dB SPL at 40Hz.
If Jude and Tyll swap headphones and both show the same results as they did before, which is what I think is likely, then the difference is coming from method and more knowledgeable people can argue over that.
1:30 onwards shows the differences between the HD800 and HD800S with flashlight illumination from the back. I expect the fabric hole covering the center and perhaps a slightly different screen behind the driver are the only differences between the HD800 and HD800S.
Again, it's the HD800 measurement in the FFT I'm most interested in, for a couple of reasons. First of all, I think it's the one from which this discussion originated. I'm not sure which of the HD800 serial numbers it was (as both of the ones from that post's measurement booklet do show as having been modified, one of them several times). Second, that FFT shows the HD800 as having higher H3 than H2, and it's labeled "HD 800 DP Mod" (see the red and white arrows below), and this (H3 > H2) seems to be the reason for the biggest difference (and the resultant theory).
As I've said before, I am not saying the HD800 in this FFT was modded -- I'm only pointing out that it was marked as "HD 800 DP Mod," so I think it reasonable to point out.
If you look at the HD800 that is being modded (in the video) with the resonator mod, the HD800 had seen at least one prior round of modifications (as mentioned around 6:45 in the video), and as is clear from the view around the driver:
Here's one that has had no driver or damping modifications performed on it (S/N 00342):
Again, while the FFT in question says "HD 800 DP Mod," I can not confirm whether or not that measurement reflects a modified HD800, a stock-and-never-before-modified HD800, or a modified-and-restored-to-stock HD800. Only InnerFidelity can clarify that.
As I said, so far we have measured two HD800's, both of which have noticeably higher H2 than H3 at varying drive levels. More are incoming, and we'll measure them all -- and perhaps we'll come across one that also has higher H3 than H2.
As for the other InnerFidelity HD800 measurements you linked to, I noticed something in common with all of them (whether modified or unmodified HD800's), in varying degrees, but never insignificant. In all of them there are large spikes at 200 Hz and 2 kHz. Here's what I'm talking about (arrow pointing to the spikes in question):
I am rather certain those are not from the headphone, but from the system, and I do not know how (if at all) whatever is causing those spikes would affect the THD readings. Also, they do not appear on the FFT.
Almost all of the other measurements I have seen have come from DIY measurement systems, most probably having been generated on one of the systems in the many DIY measurement system photos shown below (and in the following post): DIY headphone measurement systems
While I think it's great that people are building rigs for measuring headphones, when it comes to trying to figure this out, I do not believe those systems are up to the standards of precision that should be expected when measuring the THD of a headphone like the Sennheiser HD800 for anything other than personal information or casual discussion.
Even if the FFT measurement by Tyll at Innerfidelity was wrong due to it being a DP modded HD800 instead of a stock HD800 it would not explain the clear differences in THD shown consistently. If you could do THD measurements of the HD800 and HD800S when you get back from CES that would be much appreciated.