MattF
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Might do, depends on the position of the banjo relative to the spindle, the teeth with be the wrong DP but will probably work it is hardly a huge amount of power from a 1/2 or 3/4 HP motor.
The gears, if different pitches, will mesh, but they need a larger gap than normal else they bind. Suspend a couple of gears, one between thumb & middle finger on each hand, and run one round the other, & you can feel the difference in smoothness, between mismatched pitches.