Where does that hiss on the master come from?

If the master tape has been digitized there are processors/software that can reduce (3 to 10dB) the sound of tape hiss without harming the music signal. Just a small amount of noise reduction can make a big subjective listening difference.

TANSTAAFL
Or, "There Ain't No Such Thing As A Free Lunch"! Masters from the '60's and '70's used analog tape, and a miniscule amount of hiss in the higher frequency ranges is normal. Good master tapes would run at speeds of 30 i.p.s. (that's almost 1 meter of tape per second!) and were half-track stereo 1/4" (one direction recording only, couldn't flip them over). Better mastering tapes could be 2" or 3" width, so as to prevent over-saturation at high levels. Unfortunately, for the children of the digital age, tape hiss is something that is an anomaly, since digital recording masters have none. BUT, to get rid of analog hiss, requires processing of the original master, and "monkeying around" with it, that can lead to a loss of fidelity, making some "remasters" sound flat and lifeless when compared to the original master tapes. I always enjoy hearing a slight hiss on "remasters"; I know that no one tried to "goose it", getting rid of the hiss, as well as the fidelity! You may also notice another idiosyncrasy of analog tapes, called "print through". When tapes are stored, the magnetism of the adjacent layers print through, actually heard as a pre or post echo, only noticeable on very soft passages. Tapes (also VCR's) should always be stored "Tails Out"...DO NOT REWIND BEFORE STORING!!! Rewinding tightens the tape, making adjacent layers closer, thus worsening "print through".

Fatparrot, don't blame the signal processor for the mistakes made by the remastering engineer. Pro level noise reduction devices (i.e. Cedar or NoNoise) are powerful tools that can be easily misused. In the hands of a skillful and caring engineer that can produce "small miracles".

Yes analog tape has hiss.
But, (do I dare mention it) tubes hiss.