Drumming & Maths

I've been on about this for a while - asking if any students could come up with how many variations of single stroke roll are possible. I knew it would turn out to be a big number, but finally we have been lucky enough to find someone with the time and inclination to give it some proper thought! Step forward Musiclab drum student and maths man Simon Dray.....

"You dropped enough hints, so here's my calculation of the number of different possibilities you have in a one bar, single stroke roll (ie sixteen consecutive notes).

I have assumed a simple scenario:
- we're sticking (no pun intended) to the snare;
- on any beat, you can play a stroke, an accent, or a rest; and
 - what you play on one beat has no bearing to what you play on the next (therefore some will sound a little lame - eg a bar of 16 rests).

The answer is quite a lot.

You have 3 choices of what to play on the first note. For each of these choices, there are 3 further choices of what to play on the second note, so there are 9 variations (3x3) across 2 notes. Add in another note, and you've got 27 variations (3x3x3).

Across 16 notes, there are 3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3 (3 to the power of 16) individual ways of playing your bar - that's 43,046,721!

Put another way, if you played each combination back to back at 120bpm (ie 30 bars per minute), it would take you a little under 2 years and 9 months to complete (assuming you didn't die first; or even worse, the bass player cuts in with his solo).

Why don't you see if anyone can work out how many different ways you can play a single note once you bring in the toms, cymbals and bass drum, not to mention doubles and drags; and therefore how many variations you have across the whole kit?"