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I'm practicing playing polyrhythms, and starting out with 2 against 3, since I hear that is the easier.

I understand how the notes are played in relation to each other (e.g. together, right, left, right), but as I play the hand playing triplets seems to play choppy. The other hand plays normally but then the triplets are like start and stop. I find that when i play the polyrhythm quickly it's not choppy like when I play it slowly.

Is there a way to play 2 against 3 slowly and evenly because whenever I try the triplets always are choppy and broken up.

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The combined 3-against-2 rhythm is exactly the same as "quarter-note, two 8th-notes, quarter-note" in 3/4 time. Start by practising just the triplets. Then add the other hand and play the second note half-way through the second "beat" of the triplet. Starting with the duplets and trying to add the triplets is harder, so practice it the easy way round.

It's similar to learning to ride a bike. Eventually, you will just "get it," and from that point onwards, it's easy.

More complicated polyrhythms (4 against 3, 5 against 3, etc) can be easier to play faster rather than slow. Don't try to figure them out "mathematically". Practice each hand separately (using a metronome) and concentrate on getting the main beats absolutely correct. Then just "go for it" and play both hands together. If both hands together doesn't work, go back to practicing each hand separately until you can play it without "thinking" at all. You want to get the rhythm into your muscles, not just into your brain. You can make this sort of practice more "interesting" (i.e. more challenging!) by playing one hand strictly in time with a metronome, while simultaneously doing something completely different to keep your brain from getting too involved - for example, recite the alphabet out loud, backwards (and out of time with the music).

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  • 1
    Another trick for thinking about 3 on 2: imagine Carol of the Bells.
    – cjm
    Mar 16, 2016 at 4:53
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    Perhaps it depends on temperament, but as someone who spends a great deal of time doing polyrhythms (on my double harp), I do find it helpful to figure the rhythms out mathematically, practice them slowly, subdividing in my head, and then work up to speed. But to each his or her own.
    – Scott Wallace
    Mar 16, 2016 at 10:21
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The trick is simply to flatten it:

1           2           1           2           1
*           *           *           *           *
*       *       *       *       *       *       *
1       2       3       1       2       3       1

|       |   |   |       |       
v       v   v   v       v

*       *   *   *       *       *   *   *       *

The 2 of the slower 1-2 rhythm lands exactly halfway between the 2-3 of the faster 1-2-3 rhythm, creating a taa-ta-ta-taa, taa-ta-ta-taa, ... pattern: quarter-eighth-eight-quarter, quarter-eight-eighth-quarter.

Another way to see it is that there are 6 beats (mathematically, LCM of 2 and 3). Beats 2 and 6 are not played:

*       *   *   *       *       *   *   *       *
1  (2)  3   4   5  (6)  1  (2)  3   4   5  (6)  1

This trick works for any polyrhythm. Calculate the LCM of all the counts. That gives you the underlying time divisions in the master measure which fits all of the rhythms. Then just fill in these time divisions. For instance, suppose we want a 3, 5 polyrhythm. LCM(3, 5) is 15. So we create a measure with 15 beats and fill those in:

| | | | | | | | | | | | | | |
1         2         3         1
1     2     3     4     5     1
*     *   * *     * *   *     *

Then we can visualize it as being divided into five triplets:

 | | | | | | | | | | | | | | |
 1         2         3         1
 1     2     3     4     5     1
 *     *   * *     * *   *     * 
|-----|-----|-----|-----|-----|

Now it's pretty easy to follow and tap out with two hands.

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In the same rhythm as Carol of the Bells (suggestion above), say, "Not very hard, not very hard" as you play your 2s against 3s. Eighth notes in the left hand, triplets in the right hand. Start real slowly. Begin both hands together on "Not." Try it first by patting it on your thighs. "Not very hard, not very hard." Then try it on the keys. I've had lots of success with this. You can do it!

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The ultimate goal is to feel each rhythm independently – triplet in one hand, duplet in the other. There are multiple ways to get there, but the Carol of the Bells example given above is great. Sing the rhythm in syllables (dum da dee da), and clap both hands on your lap. Both hands start together on "dum," right hand "da," left hand "dee," and right hand on the final "da." Really accent the down beat, and keep feeling the downbeats of each hand and try to hear each hand separately. (This is one of those rare times when it's actually easier to start faster, then slow it down.) At first, you'll be focused on the problem-solving task of making it work, and it may feel and sound choppy, but after you start to feel the triplet and (not vs.) duplet independent of each, especially their downbeats, it will feel like you have two hands and two brains!

Another trick. Sing triplets while you're walking. Your feet are the duplets, and your singing is the triplets. If you don't fall or look like Frankenstein, you've succeeded! Again, feel and stress the downbeats.

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It's sometimes useful to think of 2 against 3 as being in 6, one gets accented on 1&4 and the other on 1&3&5. This gets a bit tougher with more complicated rhythmic arrangements. Some (especially Latin American) pieces are written in a nominal 6/8 but with one part actually accented as in 3/4 (easy to read if the beaming shows the rhythm).

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Like @alephzero said, once you get the polyrhythm, it'll really sink in and it will be hard for you to forget it again.

However, I personally have found it very useful to think of polyrhythms mathematically. Whenever I run into a complex polyrhythm (such as the 7 on 8 in the cadenza of Grieg's 1st Piano Concerto), I draw three bars, one representing one rhythm, one representing the other rhythm, and the last one combining the other two bars. Colorcoding the different rhythms may help further. Then, while practicing, I look at the combined bar and see how the rhythms are supposed to fit together, try playing the polyrhythm a few times to get a feel for it, then I usually am able to play the polyrhythm.

Another fairly common way to work out polyrhythms is to divide the rhythm into the smallest subdivision necessary to play each note on one beat. Then, once you get a feel for the polyrhythm at a very slow tempo with each note on one beat, increase the speed gradually until you can play it at tempo.

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The learning pathway which makes the most sense to me:

  1. understand intellectually how it works
  2. be able to play it slowly
  3. be able to play it faster
  4. be able to feel the two rhythms independently

I've written an article about two against three rhythms on the piano with that approach in mind: http://jeromejaglale.com/blog/two_against_three_rhythms_on_the_piano

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The trick is simply to flatten it:

1           2           1           2           1
*           *           *           *           *
*       *       *       *       *       *       *
1       2       3       1       2       3       1

|       |   |   |       |       
v       v   v   v       v

*       *   *   *       *       *   *   *       *

The 2 of the slower 1-2 rhythm lands exactly halfway between the 2-3 of the faster 1-2-3 rhythm, creating a taa-ta-ta-taa, taa-ta-ta-taa, ... pattern: quarter-eighth-eight-quarter, quarter-eight-eighth-quarter.

Another way to see it is that there are 6 beats (mathematically, LCM of 2 and 3). Beats 2 and 6 are not played:

*       *   *   *       *       *   *   *       *
1  (2)  3   4   5  (6)  1  (2)  3   4   5  (6)  1

The LCM approach works for harder polyrhythms such as 3-4. The LCM of 3 and 4 is 12, so we subdivide the metre into twelve:

* * * * * * * * * * * *
1 2 3 4 5 6 7 8 9 1 1 1
                  0 1 2

Then overlay the rhythm patterns:

--------3--------
@       @       @       @
------- -4--------- 
#     #     #     #     #
* * * * * * * * * * * * *
1 2 3 4 5 6 7 8 9 1 1 1 1
                  0 1 2

Now work it out in the context of the underlying 12-beat measure. To simplify it, break the 12 into smaller units, like four units of 3. (These four units give you a 4/4 time pattern):

@    |  @  |    @|     |@
#    |#    |#    |#    |#
* * *|* * *|* * *|* * *|*
1 2 3 4 5 6 7 8 9 1 1 1 1
                  0 1 2
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  • I wonder if this answer meant to be an edit for another answer you made in this question?
    – user1079505
    Jun 14 at 1:59
  • @user1079505 Thanks. It clearly is; it looks like a browser back button error. This looks newer and has better diagrams.
    – Kaz
    Jun 14 at 2:37
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You've been given some remarkably (one might say unnecessarily) detailed explainations of the "One Two Three vs. One Two-AND Three" solution to playing two-against-three.

But you're also going to run up against 5:2, 7:3 (and even worse) and the mathematical approach isn't really going to help! And there's another point - in real, expressive music, these phrases aren't MEANT to be played with strict mathematical precision. Enter them into a sequencer and you'll see what I mean - horrible isn't it? The real answer is to practice the two parts seperately as music, not as maths. When your hands know them well enough, they will flow together naturally.

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