[POLYRHYTHMS]
Playing Duple Time Against Triple
How must I execute triplets played against two-eighths? In Clementi's Sonatina, Opus 37, No. 3, first page, you will find such bars.
In a slow tempo it may serve you to think of the second eighth-note of the triplet as being subdivided into two sixteenths. After both hands have played the first note of their respective groups simultaneously, the place of the aforesaid second sixteenth is to be filled by the second note of the couplet. In faster motion it is far better to practise at first each hand alone and with somewhat exaggerated accents of each group until the two relative speeds are well established in the mind. Then try to play the two hands together in a sort of semi-automatic way. Frequent correct repetition of the same figure will soon change your semi-automatic state into a conscious one, and thus train your ear to listen to and control two different rhythms or groupings at the same time.
The Two Hands Playing Different Rhythms
How should, in Chopin's Fantasy Impromptu, the four notes of the right be played to the three of the left? Is an exact division possible?
An exact division would lead to such fractions as the musician has no means of measuring and no terms for expressing. There is but one way to play unequal rhythms simultaneously in both hands; study each hand separately until you can depend upon it, and put them together without thinking of either rhythm. Think of the points where the two hands have to meet, the "dead points" of the two motions, and rely on your automatism until, by frequent hearing, you have learned to listen to two rhythms at once.
The Old Problem of Duple Time Against Triple
How should the above-quoted notes be brought in with the lower triplets?