1. Debussy Arabesque No. 1 in E major (YouTube):
2. Brahms Intermezzo in A major Op. 118 No. 2 (YouTube):
Practically all major composers use polyrhythms in their music yet there are very few technical exercises that offer a "friendly" introduction to the early intermediate pianist. For instance, there are no polyrhythms in Hanon (or rhythmic variation exercises for that matter). Brahms wrote 51 exercises that incorporate it but they have other technical difficulties that suit the late intermediate pianists:
For the newbies to polyrhythms, I suggest the following steps to learning it:
1. Let the ear and mind internalize this rhythmic peculiarity. Try listening to the following examples: Example 1 and Example 2. Count the beat as you listen. Some have suggested to verbalize the notes for 2 against 3 as "Not dif-Fi-cult" although I must confess I have not really gotten the hang of it.
2. Download and print the exercise I have written. Do not play it right away.
3. Listen to the exercise in slow tempo (42 bpm, download), follow the score, and count the beats:
4. Play the first part of the exercise (2 against 3, up to the double bar) hands separate (start with the left hand and then the right) at 60 bpm. It is essential to use a metronome.
5. Play both hands at 42 bpm until flowing.
6. Gradually increase the tempo. I recommend the following tempi increases:
60 bpm download
78 bpm download
96 bpm download
108 bpm download
7. Work out the second part of the exercise (3 against 4).
A closer look at the exercise: It is actually a twist on the Hanon exercise #46. Each hand plays a trill while the other plays broken chords in triplets as accompaniment. There are two main parts.
The first part is an exercise in 2 against 3 or 3 against 2. The right hand begins playing short trills while the left hand provides a broken chord accompaniment.
The second part extends the first part as an exercise in 3 against 4 or 4 against 3. The broken chords remain as quarter note triplets but the trills are now in sixteenths notes, squeezing more for each beat. Each hand has the opportunity to play the trill and the accompaniment. Just like in the previous part.
When learning this exercise, begin by playing it forte but as soon as you are comfortable, the trills must be louder than the accompaniment.
Where to go from here? After the exercise is mastered, it makes sense to reinforce this newly learned skill with a real piece. Any of the pieces illustrated above (Debussy's Arabesque, Brahm's Intermezzo, or Chopin's Fantasie Impromptu) would be a good goal.
However, to lessen the frustration of learning a lengthy piece, one might attempt Chopin's Nouvelle Etude No. 1 in f minor first Youtube. It's only two pages long but it has just the right technical issues (wide arpeggios, polyrhythms) as well as interpretative challenges fit for the intermediate pianist.