Programming Perilous Polyrhythms
By Steve De Furia
Keyboard, February, 1987
NO DRUM MACHINE THAT I KNOW OF will let you step – enter complex tuplet rhythms – five against seven, or a quarternote triplet whose last note is actually the fifth in a nested quintuplet. If you want your drum machines to play really hairy polyrhythms like these, you'll need to create the rhythms on, and control the drums with, another device. The other device is – you guessed it – a sequencer (that is, if your sequencer can handle complex tuplets).
When I tried to follow through on my interest in such matters, I found that not every sequencer offers the necessary flexibility.
Yamaha's QX1 was mentioned often as one that "should be able to do the job," although nobody I talked with had ever actually tried to program polyrhythms into the thing. So I got hold of one, and it did seem to have the right stuff. In fact, it even has some features that seem to have been created with us polyrhythmoids in mind. Along with a high-res clock (384 pulses per MIDI beat), the QX1 has six default note duration values that can be reset to any number of clocks from 1 to 9,999. There are also functions for tying and dotting durations and, best of all, a note fraction key (my heart beat a rapid five against three when I spied that!).
If you have access to a QX1, the rest of this column will be directly applicable. If not, I suggest that you read on anyway. You may find my approach to the polyrhythmic problem instructive in a general way, and the specific techniques presented here, for example the approach to figuring out tuplet clock values, may well be applicable with other sequencers.
After choosing a sequencer, the next step was to find a challenging musical example. Since my own appreciation of polyrhythms was heightened greatly during my tenure at the Utility Muffin Research Kitchen (Zappa's composition/production facility), I could think of no finer source than the Muffin Man himself. He recommended "The Black Page," which, as it turns out, can be heard on this month's Soundpage (see page 66). It's a perfect example – short, sweet, and to the point. Oh yeah, and did I mention challenging? The leadsheet is included alongside the Soundpage for your sequencing pleasure.
I found that the QX1 has editing features that made step-entering the rhythms in this piece a snap. You just have to understand the note length and fraction functions. The documentation doesn't explain how to use these two features in any detail. Only two sentences are expended on the fraction key, and, not surprisingly, this is the most important function for those of us with polyrhythmic inclinations. By teaching the QX1 how to play "The Black Page," I learned that the fraction key could do things that none of the QX1 users I know, nor even the kindly folks at Yamaha here in the U.S., ever suspected.
The fraction key can divide any of the six note lengths into a number of subdivisions from two to nine. That's how to get the triplet, quintuplet, and septuplet figures in bars 2 and 4. For example, the fraction key can divide an eighth-note by 3 to get the duration for sixteenth-note triplets; the same technique is used for the eighth-note quintuplets. Use the fraction key to divide a half-note by 5.
How about those 11-tuplets in bars 27 and 29? (Cute, aren't they?) These figures divide a quarter-note into 11 divisions. We can't use the fraction function here, since it can only split a duration into nine or fewer units. The QX1 has us covered, though. Using job command 13, you can enter new values for any of the six default note lengths. Take out your calculator and divide the number of clocks in a quarter-note by 11.The equation looks like this: 384/11=34.909.Throwaway the digits to the right of the decimal point (but hold onto the calculator), since rounding up would keep your 11-tuplets from fitting into a quarter- note. You end up with 34. Replace one of the default note lengths with this value. You've just created an 11-tuplet note length key. What about the portion I had you throw away? After all, there should be another .9090 . . . clocks per 11-tuplet note. Well, the QX1 seems to compensate for this discrepancy automatically, although the documentation doesn't explain how. Your 11-tuplets (or 13-, 17-, or 21-tuplets, for that matter) will always be rock-steady and resolve correctly to the desired down-beat.
Now take a look at bar 5. Sixteenth-note quintuplets and a sixteenth-note sextuplet, nested within a quarter-note triplet I Within one bar, 30 of those quintuplets would occur. We can't use the fraction key to divide by numbers greater than nine, but we can use our calculators to divide the number of clocks in a bar by 30 to find the number of clocks per quintuplet note. Simply put: 1,536/30=51.2. (Don't forget to throwaway the decimal portion of the answer.) Change one of the note lengths to 51 in order to produce quintuplet rhythms.
We could stop here. Between the fraction function and redefinable note lengths (not to mention the QX1's ability to deal with roundoffs) you have all you need to program almost any rhythm. If this all seems a wee bit tedious, you're right. But then again, think what this kind of polyrhythmic freedom might do for your sequencer and drum machine programming.
Never content to leave well enough alone, I kept playing around with that fraction key. I found out that you can enter all the rhythms in this piece, except the 11-tuplets, without ever having to use a calculator and without changing any default note lengths. You can use the fraction key repetitively! The trick is not to hit the enter key until you've finished. Apparently it's just something that no one had thought to do before (or at least no one in a position to pass the information on). And let's give Yamaha some credit. Although none of their documentation says you can do this, they never said you can't. Some clever person designed the QX1 to work this way.
You can get the nested quintuplets in bar 5 by using the fraction key to divide a halfnote by 3, and then using it again to divide the resulting quarter-note triplet by 5. For the nested sextuplets in the same bar, use the fraction key to divide a half-note by 3 and then again to divide the half-note triplet by 6.
The seven-against-two figure in bar 15 is a little tricky, but ultimately it's as easy to program as any of them. The figure is nested within a half-note triplet (one third of a bar). The three sixteenth-notes in the figure are each one-seventh of one-third of one bar. On the QX1, use the fraction key to divide a whole-note by 3, and then again to divide the resulting half-note triplet by 7.
The eighth-notes are, of course, twice the length of the sixteenth-notes. They are each one-seventh of one-third of two bars. Use the tie key to tie two whole notes together, creating a two-bar note length. Then use the fraction key to divide this by 3, and then again to divide the resulting whole-note triplet by 7. Yes, that's right: You can use the tie key in conjunction with the fraction key. In fact, you can use all of the note-length-related keys together, and repetitively, as long as you don't hit the enter key until you've gotten the final value you're after.
If you have access to a QX1, tryout these techniques by entering "The Black Page." It's so easy to do, once you get the hang of it, that I'm sure you'll find the results well worth the effort. Don't overlook using the QX1 as a polyrhythmic drum controller as well. If you can't get hold of a QX1, use the ideas here to help you figure out how to enter this piece into whatever sequencer you have on hand. Perhaps in future months we'll look at how to create music like this on other sequencers. Let me know what you're using, and what questions you have.
Read by OCR software. If you spot errors, let me know afka (at) afka.net