To quote The Onion's Jim Anchower, I know it's been a long time since I rapped at ya...
One of my main preoccupations over the last 15 years or so has been the division of time. For the most part I'm talking about musical time here, although lately I've realized how much I actually conceive of clock time and the distribution of everyday tasks in relation to musical time (but that's another story). I got a fairly late start in music, playing snare drum in grade school and drum set in high school but with no real training. I didn't learn to read beyond simple percussion music until my first year of college when I happened to be accepted into a very small state university music program. My two first points of contact were Stuart S. Smith, a highly uncompromising Free Jazz drummer turned Avant Garde composer; and Ken Anoff, a former protege of Smith's turned New Age/Hippie percussion guru. These guys were the main tributaries to my rhythmic approach. Anoff defined "rhythm" in the simplest of terms: the placement of events in time. This idea really stuck with me and helped forge my twin-pronged approach to rhythm. First, is the understanding that it doesn't necessarily mean
musical events in
musical time. Second, that it doesn't suggest equidistant placement. So from a very early point in my serious musical life I was interested in complex rhythms, from both "inside" and "outside" of music. Anoff's music is informed by the rhythmic languages of Indian and African music. Smith's music is riddled with tuplets, especially the dreaded
irrational ones - eg., 7:5. The stuff of the so-called "New Complexity" (Brian Ferneyhough, Michael Finnissy, Richard Barrett, etc.). Though I think Smith's formulation of these rhythms is more aligned with speech rhythms and Free Jazz temporal flow than any post-Serial number crunching. Smith is more like Finnissy (not coincidentally another one of my teachers) than Ferneyhough.
As I stumbled my way through three degrees in Music Composition, I realized that I was in a minority as a composer and a performer in my interest in these sorts of rhythms. In fact, dealing with audience and performer response to these rhythms has been a salient feature of my career, certainly even after my student days. I could tell a lot of stories, but this one is my favorite and gets right to a certain point. During a reading of a piece of mine in grad school, the horn player of the ensemble attempted to use my music as way to take young composers to task for their rhythmic ambition/incompetence (in his estimation). One thing he suggested is that students challenge themselves by writing a piece in common time. Okay, fair enough, but he was talking to a room full of PhD composers in a very forward thinking department. Collective groan as we all thought "yeah, we did that...in undergrad, let's move on." Then he singled out a particular rhythm he was having difficulty with in my piece. It was 5:3 eighth notes. He said "why don't you just write eighth notes and then a note saying to play them a little faster." I was kind of speechless in that 5:3 is kind of kids' stuff. My friend and classmate Evan Johnson (himself a master of the division of time) piped up and said, "he did that, and told you exactly how much faster to play: five thirds as fast." I have to say the rest of the scenario is a bit unclear in a fog of vindication. But if it played out the same way similar exchanges have, it ended in me showing the guy how to play 5:3. And now we get to the point of this post. It's easy, I'll show you how!
Take the main pulse of the tuplet - the consequent number of the ratio - and divide it into equal divisions of the antecedent number. In this case three eighth notes, each divided into five 32nd notes. Then play every third one of those fifteen 32nd notes, counting like this:
1-2-3-
4-5, 2-
2-3-4-
5, 3-2-
3-4-5. Below is a sloppy little diagram I made, maybe next time I'll be more pro.
This is just the tip of the tip of the iceberg and of course you can use this method for any irrational tuplet. I've spent a lot of time working such rhythms out making charts of 5:4, 5:3, 6:5, 7:6, 7:5, 8:5, 8:7, and so on. Then adapting these rhythms to drum set techniques as well as using them in my compositions. I clearly recall learning 13:12 to the four-on-the-floor thump of techno music pouring out of boutiques in London's Camden Town while waiting for my girlfriend (now wife) to do some shopping. It's also great to snap or clap these rhythms out against your walking pace, since your pace will remain quite steady. Though I do have a friend that was picked up by cops for this kind of behavior. It does look odd. But it sounds great.