Fox I think you may be looking into this way too deep to be honest. I'm still confused on the whole "pure sound" thing. When you record onto tape, is that considered pure sound? If you think it is, it's actually not as tape altered the original sound quite a bit. Digital gets a bad rap because most people that record using it after switching from tape, are blown away that the sounds they thought were great no longer stand up.
Digital only records what you put into it. If anything, math and science to the side, it's more pure as it captures the exact sound without tape coloration and saturation.
I just fired up my old 24 track 2 inch machine last week to do a song on it because I got tired of it sitting in the studio looking at me like "c'mon, use me or sell me biyotch!" So I striped a track of SMPTE so I could still use my pc and away I went. I've not recorded a single thing on tape in years. Well, needless to say I didn't miss it nor did I miss the sound. Since I've been recording digitally, my tones I use now have been altered for digital. My tastes have changed as well. What I was left with was a good sounding recording, but it was a bit dark with a more saturated sound than I'm used to. It's still good and stacks up against anything else I've done, but I'd not call it pure sounding. Colored and warm would be more my explanation.
Also, with digital transfers, your converters can really play a role in how things sound. I notice the sound I get out of my Realtek card is different than my Layla, Pro-Fire, and RME. Notice I say "different" not better or worse.
I have a few students I teach that were born and raised on analog and tape. The digital realm was quite a challenge to them because they were used to that tape saturation we can get when we run something hot. It does color the sound and does take away some of the highs we get with digital. But to me, the pure sound is the digital sound because it is recording exactly what you put into it without any coloration. If there is coloration for the worst...my first place to look would be in the soundcard or converters you're using as they can make a difference.
After my recording experience now though, I don't see me ever using my tape machine again other than if a client comes and requests it or I have to do a bounce from tape to disc for someone. However, I will say that I did like the way vocals and guitars sounded right out of the box. That said, the only thing I wasn't able to cop all the way was the tape saturation I'd achieved by going a little over 0dB. Digital and plugs don't have that aspect quite down in my opinion. But....copping the eq I get on tape in the digital realm to make the sound SOUND the same was easy and I could tell no difference at all. That's just my experience though. I stay away from all the math and science. It doesn't help me at all. Something either sounds good to me, or it doesn't.
-Danny