In one of the Jane Sebba’s Abracadabra piano books, I found the most useful word rhythms to teach one of the most commonly used polyrhythms; 3 against 2.  She gives us a tune called ‘Cold Cup of Tea’.  This is how both hands fit into the syllables. 3 against 2 As you may find out, it works instantly without any complication.  Now, can we use this brilliant idea to learn trickier polyrhythms such as 4 against 3.  How about this: 4 against 3 Works for you? Next step is to apply this exercise to your playing.  Instead of tapping every syllable with your hand, try using different finger for each syllable. For 3 against 2: 3 against 2-fingers For 4 against 3: 4 against 3-fingers When you become comfortable with the above finger exercises, try swap the patterns between the hands. For 3 against 2: 3 against 2-fingers-2 For 4 against 3: 4 against 3-fingers-2 Are you ready for the final challenge?  Try saying ‘1, 2, 3’ instead of ‘Cold Cup of Tea’ and ‘1, 2, 3, 4’ instead of ‘Cold Cup of Tea and Buns’. To go further, pick the notes of your choice on the piano and try with the sound.  You can also try different fingerings. Working on such polyrhythms as these certainly work hard on improving your coordination between the hands, eyes and also ears (always listen attentively to what you’re hearing, which will play a great part in improving your coordination!). Good luck!