It's definitely correct that as the roll is played, the effective
diameter of the take-up spool increases in a way which is mathematically
predictable, and that therefore the amount of paper that ends up on the
take-up spool increases every revolution, increasing the effective
speed if the shaft revolutions per minute (RPM) are constant.  Harald's
calculations look right to me, though I've not been through them in
detail.  Thanks for that.

However, surely if when the roll is punched it is taken up onto a spool
of the same diameter as the player piano's, the note length and hole
spacing when it's being punched will increase by the right amount to
make the roll play correctly at constant Tempo?  (Regardless of speed,
the increase of linear distance with increase of diameter is the same).

Therefore if I'm building a roll perforating machine, I ought to make
a take-up spool that is the same diameter as the one in my pianola,
then pull the paper through the cutter by driving the take-up spool
(rather than, for instance, using separate feed rollers that grip the
paper either side and turn at a constant rate) so that the diameter
buildup is automatically the same as it will be in the piano, and
everything compensates naturally?  Was this what roll manufacturers
did?  (I really hope this is true, or I'm a bit over-supplied with
large-diameter aluminium bar...)

I can fairly easily amend the way I calculate roll hole positions to
stretch out the holes towards the end of the roll, but I'd much rather
just make the machine deal with it intrinsically.  I suppose if I were
cutting by hand with a ruler, I would need to either calculate length
increases correctly, or still make sure I had a correct-size take-up
spool and move it by constant angle (maybe a with a sort of ratchet
wheel or detent) rather than constant linear surface distance.  Is that
the usual approach?

Lester Hawksby, UK