Where does that hiss on the master come from?

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

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".

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".

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.

South Philly. No, really. Hissing occurs in the upper registers and usually means the recording has beeen mostly left alone allowing a more natural sound in that region. Vocals are more natural, symbals ring truer, an openess occurs surpressed by Dolby treatment which also introduces phase shift. Usually more dynamic too. I'll live with the tape hiss as opposed to the un-natural sound of processors.

It is noise inherrent as a result of the electronics (recorders) of the day, the tape formulation, the tape width, and the tape speed. Early studio electronics also had lots of noise of their own that aren't attributed to the recorders. Early noise reduction (Dolby-A) was heralded as a breakthrough in reducing tape hiss. It was further advanced with Dolby SR that all but eliminated tape hiss. A modern recorder such as an overhauled Ampex ATR running at 30 ips with modern tape formulations (Quantegy GP-9) have eliminated tape hiss and don't require noise reduction schemes anymore.

This noise cannot be removed nor would you want to try. Removing the noise would be about the worst thing you could attempt to do to the master as it would remove sound content as well.

That's analog tape hiss (noise) that you are hearing. It is inherent in the analog recording process and can't be totally removed from a remastering either for analog or digital. It is the noise from the tape transport and electronics that gets "recorded" onto magnetic tape along with the actual musical signal that you are hearing.

Are you talking about analog tape hiss? Common from the early days of stereo (listen to any Mercury Living Presence record or CD and you'll hear it), and an "evil" of analog tape vs. digital tape (one of the aspects of digital recording that many felt enough of an improvement over analog to overlook the flaws of early digital). There are some programs available to eliminate that noise from a master tape; some remasterers try to eliminate it, others don't because they feel it compromises the high frequency content of the music.