Teaching and playing polyrhythms correctly is one of those skills that is peculiar to piano playing. The issues arise because pianists have to coordinate the hands in a particular way; sometimes together and other times by the hands cueing each other.
This article will show how they are easy to manage if you have a fail-safe strategy for working them out and practising them.
Firstly, the least successful strategy for practising polyrhythms is to learn first one hand then the other, usually with the metronome, and then “just put them together”, crossing your fingers and hoping that with enough practise, they will somehow integrate with each other. This was certainly the advice I grew up with.
But it never works because it ignores that the hands must cue each other from note to note; the hands must learn their interdependence.
The easiest polyrhythm that students come across is three against two such as in Chopin’s Prelude Op 28 no 4 (third measure of the example):
Step one for working any polyrhythm out is to determine the mathematical relationship between the two parts.
First, work out the lowest common multiple (LCM) of the two rhythms. For two against, three, the LCM is 6. Using a ruler, rule seven evenly spaced vertical lines (the extra line denotes the next beat).
Each triple quaver will take up two spaces and the duplet part will take up three. It will form this alignment:
You will see the hands are together on the first note and then there is an alternation of the hands; in this case it is both hands, and then a quick succession of cueing from right to left to right before the hands come together again. The red arrows denote when one note quickly cues the next note in.
From right hand side of the diagram, you can see that the overall polyrhythm is a (triplet) quaver, followed by two semi-quavers, followed by a quaver. French time names are useful: Ta ta-te ta, or you can say 1-trip-a-let or “Not ve-ry hard”.
I apologise to my students in advance in case they think that this is condescending, because of course the polyrhythm is tricky at first, especially since there is usually some dynamic control that is required to separate the melody from the accompaniment part.
This excerpt from Grieg’s Notturno (Op 54 no 4) has the 3:2 rhythm (measure 5):
This is not quite the same as the Chopin example as there are notes that are tied. This one will be practised with the beat note by itself and then a quick succession of L-R-L played soft-loud-soft to get the voicing of the melody distinct from the accompaniment.
Interdependence in Trills Over an Alberti Bass
Trills in the classical period are often measured 3:2 and when practising them, the student must ensure that the interdependence is always played the same – no matter what the speed. The common pitfall is that the student practises the LH at various speeds, with the RH always playing as many trill iterations as possible. In this case, the student is not learning anything or worse, probably confusing their brain and hands.
When a trill is measured as 3:2, the student should note that every second iteration of the trill will alternate between either the upper or main note of the trill no matter what the speed of practise.
Some students might prefer to play 4 notes against 2 to make it easier or because they can handle a quicker trill. In the end, it matters little whether it is played 3:2 or 4:2 or whatever, just that it is worked out and practised consistently. Other options might include starting the trill slowly at first and then speed up towards the end. This is all fine, but certainly in the learning stages, I want my students to know exactly what they are doing so that they feel secure when they are performing it. I ask them to make their choice, or help them make it for them, write it out and then practise it precisely.
Four Against Three
This is a very common polyrhythm and I was most recently teaching this in Chopin’s nocturne Op 9 no 3 (measure two in the example):
The LCM = 12 and so the quadruplet receives three spaces and the triplet receives four:
Once again the red arrows denote notes that are cued quickly from one hand to the next. You will see that the hands begin together. This needs to be experienced as one action, the hands come down together (not two separate hands playing at the same time).
The next moment is experienced as the right passing to the left - felt as one gesture – the right hand passes immediately to the left in a kind of staggered or drunken relationship, or perhaps like a grace note.
The right hand then plays once again by itself. And finally the left hand brings the right hand