Quick question about the tempo on a payer piano. The numbers on the tempo gauge relate to the amount of paper turned in a minute (80 equals 8 feet per minute) but how does that relate to the BPM on a music roll? How many BPM should 80 be?

The paper feet / minute does not have a direct relationship to the beats per minute in a piece of music. The amount of paper turned in a minute is set when the piano roll is cut. Ideally, the tempo marking for the roll would equate to the tempo of the performer while cutting the roll. But with many rolls cut at "80," there are many pieces at different tempos (BPM).

I'm not sure why different paper speeds were used. One factor is the length of the piece (a longer piece would necessitate a slower paper speed as the amount of paper that can be put on a roll - even a large one - is finite). Slow pieces tended to have slower paper speeds, and fast pieces tended to have faster paper speeds. This may have to do with the physical ability of the pneumatic player mechanism to play fast runs of notes, tremolos, etc., and the timing with which the cut-outs in the roll passes over the the bar.

I've seen some rolls that have directions for the operator of the piano to vary the dynamics and tempo setting on the player piano as well. With those rolls, the performer who cut the roll played at a steady, metronomic tempo, and expected the player piano operator to add the dynamics and tempo changes.