I am not an expert on the history or roll perforators but I think that
commercial roll perforation did not use the simple method of matching
a take up spool in the perforator with the one in the target piano.
This is because multiple sheets were punched and a simple take up spool
would not work.

I believe that all commercial perforators used some sort of device that
gripped the paper stack and moved it by a fixed increment.  I sort of
remember that on at least one machine used to punch Wurlitzer multi-tune
rolls, that the step rate was adjustable and was changed for tunes later
in the roll.  However it is possible that a master could be created with
tempo acceleration compensation in this way but I believe that masters
were generally not the same length as the finished roll.

There is one other thing that I don't think was considered in this
thread and which may have no basis in fact but was discussed in the
past.  It was suggested that some piano take-up mechanisms might
gradually slow down as the roll builds due to limited power available
from the wind motor.  The speed is controlled by the volume of [air
under] vacuum drawn from the wind motor.  A vacuum regulator keeps the
vacuum constant but the speed is controlled by volume.

Is it possible that with fixed volume and an increased load on the wind
motor that the load would increase as more paper was added to the take
up spool and the take up speed would slow down possibly correcting for
the effect of the increased diameter?  Is there any reason that the load
would increase as the paper builds?

This is more than I can try to make sense out of.  I just remember
someone proposing the idea in the past.  If this were the case then roll
acceleration compensation in the perforating might not be necessary.

Spencer Chase