It's an interesting idea.... but probably not very practical.
First off, it would only help if you had multiple copies of the master tape.
I would expect tape noise to far exceed electrical noise caused by the playback tape machine.
Both tape noise, and noise caused by the recorder, are going to be the same for a given tape.... and should be mostly the same on each of multiple playings of that same tape.
There is also an interesting relationship between the head gap width and frequency response.
Recording actually occurs at the trailing edge of the head gap; because of this, even tape heads with relatively wide gaps can still record high frequencies.
HOWEVER, playback is related to the overall width of the head gap.
The bottom line is that, since the frequency response of the recording isn't limited by a wide head gap, but the frequency response of the playback is...
you can often get better frequency response by playing a tape back on a BETTER quality deck than the one on which it was recorded.
(And, if the original quality was limited by poor head azimuth alignment, then using the original model, unless it is the actual original machine, isn't going to help much.)
There's also the issue that tapes tend to stretch and become uneven over time... which make sit difficult to "line up" multiple copies precisely enough to average them together.
In many situations, where multiple copies are available, but of varying or dubious quality, individual songs, or even individual parts of songs, may be "picked" from different versions.
And, yes, many were re-dubbed onto higher quality media over time...
But, with analog media like tape, there is also an inevitable loss of quality every time a copy is made...
These days there are also a variety of more powerful options for "reconstructing" and "improving" audio quality.
They range from simple things like frequency-selective filters and noise gates to algorithms designed specifically to fix certain problems.
(For example, software that automatically recognizes and removes record ticks and pops.)
In one recent example of an excellent restoration (the 24/192k remaster of the Grateful Dead Studio Recordings).....
A novel process was used to correct for speed variations due to tape stretch.
The record bias signal, which is used as part of the recording process to allow the tape to accept sound, is usually a very high frequency sine wave on professional machines.
Some of the original Grateful Dead studio master tapes were found to have significant speed issues.
However, it was also found that a tiny amount of the original 80 kHz record bias signal remained, and could be read with specially designed tape equipment.
The company that restored them used special software to "lock onto" that 80 kHz signal, treat it as a sort of servo reference signal, and use that reference to correct speed variations in the recording.
Of course, as usual, some of these techniques work far better than others, or only work under very specific circumstances.
And many can easily cause an extremely unnatural sound if used improperly or excessively.
(And some work really well - but only if a lot of time is dedicated to operating and adjusting them by hand.)
If you want to see some of the options available in commercial software, check out Izotope RX:
(and, yes, free trials are available)
In converting from Analog Masters to Digital -
Can they make multiple high-res digital recordings from SEPARATE PASSES of the Masters
Then "Average" the passes together using a common time-base?
I would assume that they would want to play-back the Master on the same equipment used to record it as stated earlier (or at least a "Head" with identical impedance and mechanical alignment), in order to retrieve "whatever is there" as faithfully as is practical.
Something like that could null-out random noise due to the tape machine and produce a "cleaner" output that emphasizes the Signal and minimizes certain types of noise.
(But it COULD also emphasize noise that is in the recording and is non-random.)
Not a Recording Enginerd, but I'm curious, and I also know that they use a similar technique in brain-mapping where they do a fast, "real-time average" of data from an array of EEG sensors.
(Would most Archives even ALLOW a new Recording Company to make multiple passes of their valuable masters? Do they typically charge "per-pass"? How carefully managed is this sort of stuff?)
I also know that Magnetic Tape has a tendency to "bleed" (STRONG magnetized spots tend to magnetize adjacent media particles over time, which can mask / de-grade the overall quality of the tape). The higher the feed-speed of the original tape, the farther apart such "strong spots" are and the longer it will take to de-grade.
[Likewise, the distance between adjacent "Tracks" - maybe some old 2 or 4-track may be better than 8 or more on the same tape width due to better physical separation of the tracks?]
I would assume that in some cases, over the years "valuable" Masters were probably duplicated onto higher-grade magnetic material that is less prone to do this (remember the different Casette Tapes basic FeO2 --> Metal?). Or are the "virgin" Original Masters still usually regarded as "best".
With ALL of these variables and the personal taste of the Artist and Recording / Mastering Engineers - it's half a miracle that we can hear ANYTHING remotely good...
