In point of fact many of the offerings on HD Tracks are fully remastered and remixed from the original multi-track masters.
And, quite often, that's what accounts for the huge difference in how some of them sound (and not everyone always agrees that it's an improvement.)
(They seem to have some exclusive offerings - but a lot of what they sell is available from several different online sources.)
HOWEVER, with the Grateful Dead albums, what they did on some in addition to that was quite interesting (they posted an article about it).
Tapes stretch, sometimes to varying degrees, resulting in some amount of wow and flutter, as well as slower speed variations, which can be audible...
Now ,we all know that, when a tape is recorded, a high frequency bias tone is applied to the record head (apparently around 80 kHz on the machines used to record certain of the Dead albums).
This tone is generated by a fixed-frequency oscillator and so is very frequency stable.
And, even though very little of this tone remains, there is a tiny residual amount which can be detected during playback with a specially designed playback head.
So what was done was to play back the tape using special heads which could actually detect and "play" the residual record bias tone.
The speed of the audio signal was then corrected using this information to REMOVE the wow and flutter that was present on the tape... and so correct speed errors in the master tape.
(They basically recovered the residual record oscillator tone and used it as a "servo track" to correct the speed errors and fluctuations on the tape.)
The result was audio playback that was virtually speed perfect - with no speed drift or wow and flutter.
(Which actually made it more correct than the physical playback of those same tracks that was used to master the original vinyl.)
I believe they may also have used the level of the high frequency residual tone to slightly correct high frequency playback levels...
However, since I read the article several years ago, I don't recall all the additional details, so I'm not sure about that.
They also did an obvious re-mix, and seriously altered the EQ, resulting in a new mix with much better detail and clarity than the original pressings (or CDs or tapes).
As far as I know the speed correction was only used on certain of the Grateful Dead albums...
And I'm not sure exactly what they did or didn't do on the Eagles....
To be fair, I've always been an Eagles fan, and I had that album on vinyl.
However, it's been remastered many times, and I find several of the digital remasters to sound better than the original vinyl.
(And, yes, from the age, I'm sure it was originally mastered on analog tape, although I've never looked up the details.)
Obviously things like sampling algorithms don't in and of themselves improve anything...
However one thing they can do is to improve the overall result by minimizing the damage along the way.
(After all the goal of high fidelity audio is to reproduce the original signal as precisely as possible... right?)
For example, a high quality analog-to-digital conversion, followed by a high quality digital-to analog conversion, can deliver a signal that has a THD somewhere around 0.003% (for a 24 bit depth).
And, of course, if it's handled properly, the signal will not change at all in between those two.
They seem to be... err.... just a bit worse.
(I found only a few other references... but they all seemed to agree that, with a -20 dB signal, the distortion on vinyl was "only" about 100x worse than with a decent ADC/DAC combination.)
And let's not even discuss things like surface noise, dynamic range, and accurate frequency response.
Now, to be fair, most of these flaws aren't audibly especially obvious, or even all that unpleasant...
However, if you're going to compare numerical performance, in the context of "cause no harm", it's pretty clear who's going to win.
You also have that neat little detail that digital files don't suffer from "generational errors"...
Unless you do it wrong... a copy, of a copy, of a copy, of a copy, sent around the globe a dozen times, then copied a few more times, will be identical to the original...
And you can not only take steps to ensure that this is the case... but you can easily TEST the copy you have and CONFIRM that it is a perfect copy of that original...
But, beyond that, and notwithstanding that I've only ever heard of that trick they did with the Grateful Dead albums being done on a very few others, digital processing offers many superior options for correcting things.
If your album has a tick a tiny split second of the signal is gone... forever.
But, with a digital editor, you can delete the tick, and replace it with a split second of silence... which will be an improvement.
Or, if you want to get fancy, you can replace it with a split second of the music from a millisecond before that, which will be pretty close, or even with a better guess about what should have been there.
Still not a perfect solution... but a heckuva lot better than "TICK!"
(And you can do this with a program you can get for free.... and, if you do it carefully, without making any alteration to the rest of the file.)
There is even an equally cool trick that lets you "partially unmix tracks".
So, if you don't have the original separate tracks, you can still do a "remix" by adjusting the levels of individual instruments (to a limited degree).
Now, to be quite fair, a lot of these capabilities open up vast new vistas for screwing things up, and making a recording downright horrible...
But, when done properly, they offer opportunities that simply didn't exist in the analog world.
And this all sort of appears once we have a digital audio file rather than an analog audio signal.
And, to be equally fair, there were plenty of really awful sounding vinyl recordings as well... but those we've chosen to forget.
Were the Eagles and the Dead originally recorded on analog recorders? If so, how did the sampling algorithms of cds or hd tracks improve on them?