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I would like to know how to compose tuplets of odd numbers against even numbers on the piano (ie. 3 against 2). How would you go around composing something like this? I have been composing for some time (mostly small stuff) and whenever I try to write something like this, it is either hit or miss.

I'm sure professional musicians don't randomly plug in tuplets here and there hoping they will sound good. (Chopin writes many tuplets on straight notes) I'm quite positive there is some harmonic relationship going on in there, but I just can't see it. (Perhaps they act something like passing tones?)

I am specifically looking for any rules (suggestions) or techniques for composing this way. If you know of any external articles or sources, I would greatly appreciate the link!

EDIT: Oh good point Matthew! I never considered the rhythmic effects of 3 against 2. How would that affect a composition?

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Are you unconcerned with the rhythmic effects? –  Matthew Read Apr 27 '11 at 21:35
Wait, you think Chopin "randomly plugs in tuplets" "hoping they will sound good"? Virtual -1. –  Rein Henrichs Apr 28 '11 at 14:43
@Rein Henrichs Oh no, I just worded that poorly. I ment to say that "I'm sure professional musicians don't randomly plug in tulets" like Chopin! I know that he knew what he was doing and I wanted to know more about techniques these composers used. –  Dasaru Apr 29 '11 at 18:05
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3 Answers

up vote 6 down vote accepted

As Matthew indicated, overlapping tuplets are most commonly used for rhythmic effect, called polyrhythm. Try writing an ostinato accompaniment in one subdivision (like triplets, or 6/8), and write a melodic line in the other subdivision (straight 8ths, or 2/4), while staying in the same key.

Almost certainly, some composers have used bitonality alongside polyrhythm, but I wouldn't think about that quite yet. I apologize if I sound patronizing, but I really think a big part of your answer is 'how to compose'! Go and listen to music that has those rhythmic ideas you want to integrate: Learn that music, learn how to perform it, and how to feel those rhythms, and sooner or later you'll be able to synthesize that into your composition.

The Chopin you're listening to is likely very harmonically interesting, but a lot of Chopin rhythms can be compounded into one--for a simple example, take a quarter note triplet vs. two quarter notes in 2/4 time. When overlapping, the overall rhythm you will hear is "quarter eighth eighth quarter" in a quarter note triplet. (Short version: any 2v3 -> Carol of the Bells.) Experiment with compounding overlapping rhythms to get a cohesive single line.

This may help: "POLYRHYTHMS"... an Introduction ( for all musicians )

Also, this: http://www.vai.com/LittleBlackDots/tempomental.html

Suggested listening, anyone?

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Would you know how to play the 5th measure in Moonlight Sonata? There are three triplets with a dotted eighth followed by a 16th on top of it. everynote.com/goods.pic/Bee_son14.gif –  Caleb 11 hours ago
My question is how can I figure out how to play this with out listening to it. I can hear how it is played, but I want to have a better understanding of how tuplets interfere with "normal" notes. –  Caleb 11 hours ago
@Caleb, do a search on the topic in the top right, and if you don't find anything useful, ask a question! –  NReilingh 11 hours ago
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Here are newly four invented rhythm loops to listen to that might give you some possibilities.

First idea, contrast sound of quadruplets with triplets

Second idea, contrast sound of triplets with duplets

Third idea, triplets stretched across two beats, with active quadruplet figures between for contrast

Fourth idea, subdivisions of beat tripleted, contrast with tripleted beat

What to do melodically with these ideas?

You can use triplets to quickly outline different aspects of the harmony that's happening at that instant. Especially valuable when the harmony is changing quickly.

It can help you move your melody quickly into a higher or lower range.

You can change direction within the triplet, hit a local maximum or minimum inside of it and zoom off in the opposite direction.

You can start on a sound in the harmony, move chromatically out of the harmony in the middle of the triplet and then move back into it. Can also do the opposite: start out, briefly come in, move back out to where you started.

When a triplet run is the last motion before a change of harmony, you can make use of forward motion, and start playing pitches of the new harmony early finally reaching a goal pitch once that harmony finally sounds. You'll give the listener a jolt of uncertainty which resolves once they hear where you were taking them.

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It sounds like one issue for you is that you might have difficulty hearing and playing polyrhythms in the first place - to get the rhythms solid in your ear and body, it's a good thing to practice tapping them out with your hands (2 vs. 3, 4 vs. 3, 5 vs. 4! etc.). To figure out what is going on, you can always write out one voice in terms of the other's rhythm - for instance, in the case of four notes played over three, each of the four notes takes up the duration of 3 16th notes. And, of course, there are the great net resources mentioned in the other answers.

Another way of thinking about the problem is "why use polyrhythms" in the first place? That is, what is their musical effect? This depends a lot on the musical context, and your intentions as a composer. As an example, one of my favorite uses of 4 vs. 3 in classical music is in this variation from Benjamin Britten's "Nocturnal" - it's marked "Restless", and is an incredible evocation of the dreamy anxiety we have all felt at some point, when, at 3 in the morning, we can't get back to sleep - go to 2'43" in the video:

Throughout the variation, Britten has written steady chords in groups of 3, with a melody in 2 or 4 flowing over the top (or underneath) them - the chords and the melodic lines are very much at odds with each other, reinforcing that feeling of edginess, and this particular player does a great job of helping you hear them as independent voices in different rhythms (and keep in mind that, with the guitar, he has to do all that with one hand...).

And finally, just have fun with these cross-rhythms - think of them as a new color on your palette!

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