Musical Combinatorics

My mind rebels at stagnation - A.C.D.

I’ve been playing the drums casually for the past four or five years, and I only just recently started playing with other musicians. It’s been a rewarding experience, except that when I find myself needing to improvise I get caught in the common groove of a closed high-hat on every eighth note (in 4/4 time) with an alternating kick and snare on every other quarter boots ’n cats ’n boots ’n cats ’n boots ’n cats ’n boots ’n cats ’n…

This is the easiest groove in the world, the twinkle twinkle little star of drumming, if you will. You could sit at a kit and learn it in five minutes.

It’s certainly not the only groove I know how to play, but I would like there to be more. Often I’ll reach for another common groove (same as above but with two kicks on the three-and portion of the groove) and intersperse it with sixteenth note strikes on the snare to make it more interesting.

But this is still not that interesting. And this brought me back to an idea that I’ve thought was interesting for a while. I would like to treat a groove as a combinatorics problem, and see what interesting or unexpected patterns is produced by an exhaustive approach to grooves.

Some Parameters

I’ll start with eight notes (we’ll get to sixteenths in a bit), and restrict the combinations to be kick, closed high-hat, and snare. For quarter notes that means that every measure has eight “slots” in which a either a quarter rest, closed high-hat, kick, or snare strike can occur. More complex cases such as sixteenth notes (my primary goal if I’m being honest) and notes where more than one voice is chosen can be accounted for in future iterations.

My initial thought is to treat each measure as a number in base four with four quaternary digits (hereafter just digits, let’s not be pretentious) It’s commonly(?) known that the word “bits” is a portmanteu of “binary” and “digit”. Base ten numbers are obviously refered to as digits, harking back to digits as in, fingers (I assume). But there isn’t another word for quaternary digits. Though quits might be a nice one. I’ve heard trits for ternary digits in exactly one place, and caution should be exercised when suggesting names for base three digits in polite company.

and then enumerate from zero (an empty measure) to 33333333 (a measure where presumeably only one kind of thing is played). Let’s say we map the notes like this:

0 => quarter rest
1 => high-hat
2 => kick
3 => snare

That would mean that the count should go:

With 4^8 possible combinations (65536). Which should be plenty of space to find hopefully a few interesting patterns, but more likely than not a lot of uninteresting patterns.Two plus two is of course 10. In base 4.

The biggest problem (among several) so far is that this will exclude measures where there is a high-hat strike on every eigth note, which is quite common. For now I’ll have to deal with that at the kit, adding in high hat strikes where they feel needed. But there is a benefit to doing it this way in the sense that it will force me away from just using a high-hat strike as a metronome and building the groove around it, which is a bit of a bad habit imo.