I've always had problems with tuplets (3/2, 4/3, etc), until I was taught this nifty trick:

  • subdivide the total duration (4 quartuplets, 3 triplets, etc) by the least common multiple (12, for 4/3)
  • place the tuplets along the appropriate subdivisions (4/3: quartuplets = 12/4 = every 3 subdivisions, triplets = 12/3 = every 4 subdivisions)
  • tap out, and learn, the rhythm

For example, for 4/3:

|           |           |           |           |
|           |           |           |           |

This works fine for simple rhythms (3/2, 3/2, 3/4, 4/3, 2/5, etc), but Leo Ornstein's 4th sonata (or Cowel's Fabric) is too complicated:

  • Rhythms shift to quickly (4/7 -> 2/4 -> 2/6 -> 4/2.5 -> 3/2.5 -> 8/5 -> 12/10)
  • Rhythms are too plentiful and exotic to be learned using the above method

Right now I'm just guessing when to play the notes by their positions on page. Unfortunately, there's just something about this approach that hinders (muscle) memorization and practice. For example, while I have already learned and am consistently playing - at a slower tempo - sections of equal or greater technically difficulty with straightforward (or simple, 3/2, 4/3, 5/2) rhythm, I am still stumbling through sections with unusual rhythms, despite having practiced them more.

In situations such as these, with much more practice than I'd prefer, over time I become sufficiently familiar these poly-rhythmic sections that eventually my hands intuitively, subconsciously converge towards a "good-enough" estimation of the actual rhythm. Then, I learn the section "normally", as if were a mono-rhythmic passage. So you see, this "two-pass" learning procedure is very inefficient. Eventually, with sufficient mastery, I can adjust the speed/rhythms of each hand independently.

I've been told, "just practice each hand separately, then put them together". First, I've never been able to, or just never understood, this. Of course it helps to practice each hand independently, but I've never had a piece "magically" come together with both hands, after each has achieved independent fluidity. Perhaps this is because I'm a notorious sheet/sight reader - I'm always looking at the page, never my hands - and I (almost) never memorize music. Secondly, even if I was able to "put them together", the rhythms are just to exotic to practice independently in the first place. As I mentioned near the beginning, I'm used to practicing rhythms against each other - for example, triplets against the steady beat of quartuplets.

Anyway, I'm curious about your techniques for efficiently & quickly learning difficult poly-rhythmic passages, such as from Ornstein's 4th sonata (in particular, PDF pp 6-7 or numbered pp 4-5, starting with "Tempo I°").

P.S. If you do recommend "practicing each hand independently", please calibrate to my shortcomings and experience with that method, as I've described.


I've settled on practicing each hand separately, with a metronome, for measures 45 - 52 (starting with Tempo I). The hands are sufficiently independent and even-rhythmed that I think I do a decent job when practicing them together. Since the left hand is arpeggiated with a strong tempo while the right hand plays a simple, repetitive, and catchy melody, I find it simpler to just "fit/squish" the few single-beat occurrences of 3/7 or 4/7 into the overall beat. For longer repetitions of the more complicated rhythms (more than just a beat) I would practice as suggested by Scott Wallace. I'm impressed that he's already on 7/4 - I've just mastered 4/3. However, I don't think anyone realizes how chaotic measures 54 and 56 are - how dynamic the poly-rhythms are. I've inscribed those measures in Denemo to produce a training PDF. Each measure is preceded by a duplicate identical in all respects, except the notes have been normalized per-staff (much as in drum notation). I've then recorded the resulting MIDI using the Salamander Grand Piano V3 soundfont, at 15bpm and 50bpm (published tempo is 76bpm). Some friends commented, "so basically, it's a play-whatever-the-#$@&%*! you want measure". To contrast: the least-common-multiple-method that Scott Wallace and I mention would require dividing each measure into 120(!!) subdivisions (60 excluding the 16th-triplets) to ensure that each note falls evenly on an interval. Anyway, I plan on leaving the question unanswered for a while longer - I was hoping to generate a wider range of answers.

Edit #2:

I've inscribed the full first movement into MuseScore. It is available for online listening at Ornstein, Leo: Piano Sonata No.4, SO 360: I. In comparison, notice how - especially in measures 54 and 56 - the official Poon Hill Press edition on IMSLP actually places the noteheads incorrectly or even out-of-order for the more involved poly-rhythmic sections. It goes to show how little you can depend on note positions on the page.

3 Answers 3


The way I approach polyrhythms is this: I break them down much as you do, in terms of their lowest common denominator, but I try to memorize the sound of the pattern right away and not rely on seeing it graphically. At UC we learned an example for two against three: "FARMS in BERkeley". I then practice it in many different ways- tapping the two parts with my hands, or hands against feet (I spend a lot of time walking to work this way- probably looks pretty weird) or voice, and then I do it with the fingers, also counting up or down on them, preferably in some yet different number of beats. And then alternating hands. And so forth.

All of this happens before I try playing my double harp in this rhythm. This ensures that I have a polyrhythm really well internalized before worrying about melodies. Currently, I'm working on seven against four: my left hand plays seven, counting up and down to eight on the fingers, and my right hand plays four, counting up to five. It's fun, and when I get it down, I'll try making some music with it.

But what I do is relatively simple- no polyrhythms with both factors over four, and no complex shifts such as you describe. However, it might not be disadvantageous to get away from the printed page for a bit, and making sure you have the rhythms flexibly ingrained before tackling the melodies.

cheers from rainy Vienna, Scott

  • Good point about getting the rhythm down before tackling the melodies. May 4, 2016 at 17:53
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    Yes, good answer. Getting your ear familiar with the pattern as much as possible helps a lot, I think. This site bouncemetronome.com/video-resources/polyrhythms may be of some help. Despite promoting a commercial product it offers some free demonstrations with some quite complex polyrhythms. May 4, 2016 at 22:01
  • @joseem- yes, this is very much along the lines of what I do, but without looking at anything. Definitely worth checking out- thanks. May 5, 2016 at 7:55
  • After watching a couple more of these polyrhythm clips at joseem's link above, I can't help but wonder if any human being can halfway accurately do, say, 14 against 15. But some people can do amazing things. May 5, 2016 at 8:03
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    Readers outside the San Francisco Bay Area may not be familiar with the "FARMS in BERkeley" reference and the pacing of it. This was the closing line from the radio commercials for the Berkeley Farms dairy. (Or still is? I haven't heard it in a long time.) Berkeley, of course, is pronounced with two syllables, not three, and there's also a "moo" at the end of the line. So if you count out equal beats it goes "FARMS? (tap) (tap) in BERK-ley? (tap) (tap) MOO..." where the "moo" is about three beats, trailing off at the end, done in your best cow impersonation. Certainly a memorable line! Feb 14, 2018 at 7:26

You'd need to combine several strategies. Practising polyrhythms as such (away from keybord) until that's easy would be a good start. Break up the score, practise segments of two or three beats in isolation, first each hand separately, then together. Use a metronome and get a feeling for how to fit the required notes into the available time.

The midi rendering is of course much stiffer than the composer likely intended, so when you begin to master it, you can start thinking of adding rubato to taste.


I've settled on practicing each hand separately, with a metronome, for measures 45 - 52 (starting with Tempo I). The hands are sufficiently independent and even-rhythmed that I think I do a decent job when practicing them together. Since the left hand is arpeggiated with a strong tempo while the right hand plays a simple, repetitive, and catchy melody, I find it simpler to just "fit/squish" the few single-beat occurrences of 3/7 or 4/7 into the overall beat.

You got there. With a very few exceptions (e.g. Steve Reich's use of "phasing" with slowly shifting rhythms) it is wrong to be too literal or mathematical about this. Humans musicians don't usually play even "simple" rhythms with a mathematically accurate tempo, and if you get a computer to play them that way the result usually doesn't sound much like "music". In fact notation software like Finale has a "human playback" option with several different controls of how far to deviate from "the exact written notation".

The root of the problem is that when you started learning the piano, you spent a long time learning how to synchronize your two hands (and the pedals) in mathematically simple rhythms. Now, you have to unlearn how to do that when you don't want to.

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