The bass of the HD 800 is clearer to me while the HD 800 S went more into the direction of the HD 650. So what Tyll is saying makes sense to me. Atleast with the HD 800 and HD 800 S that I have.
So let’s assume there is no additional distortion. Then where is the extended bass frequencies coming which the HD 800 S has according to Sennheiser?
I’m curious to know if there are other theories that could explain how there could be more extended bass while there is no real sub bass observed in the frequency response.
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").