Increasing Speed of Roll, Part 2
By Bill Jelen
Earlier today, I wrote that if you ignored the increasing mass of paper on the take-up spool, a piano roll that started at a tempo of 70 would be traveling at a speed of 85 after 25 feet. After arriving home, I checked my notes. The actual value I calculated was a tempo of 82.6. Here is my derivation:
I measured an empty take-up spool to have a circumference of 5.25". After 41 rotations of QRS transparent white paper (circa 1970's), the circumference had grown to 6". The radius of the take-up spool was increasing by 0.00289" with each rotation.
I then calculated that after 52 rotations, 24.8 feet of roll is wound on to the take-up spool. The circumference of the spool is now 6.2". If we could assume the take-up spool is still turning at 16 RPM, the roll would be traveling over the tracker bar at a tempo of 82.6. It seems that you would be able to notice this change. I can not. Therefore, a significant amount of this increase must be offset by the increasing mass of paper on the take-up spool.
--Bill Jelen
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(Message sent Sun 11 Jun 1995, 22:41:09 GMT, from time zone GMT-0400.) |
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