Mus 420
RHYTHM [III]
Rhythm-related procedures
Polyrhythm
Polyrhythm in the twentieth century goes well beyond the 2 against
3 and the 3 against 4 commonly found in earlier music. Some Romantic composers used
more complex polyrhytms as rhythmically free ornaments (Chopin and Bartók, for
example), while others used them in a more integral manner (Scriabin, for example).
While both ornamental and integral polyrhythms have found their way in the music
of today, some composers rely on the correct performance of polyrhythms as a fundamental
and constructive device in their work (such as Elliot Carter, Brian Ferneyhough and
George Crumb). In modern ornamental use, composers anticipate that performers will
have a foundation on which they can interpret extraordinarily complex rhythmic structures.
A polyrhythm usually contains both a ational and an irrational value. When referring
to polyrhythms over a measure, rational values are those that are contained in, or
are divisible by, or are equal divisors of the numerator of the time signature. For
example, in 4/4 (or 2/2, 2/8, or 2/16), the rational values are 1, 2, 4, 8, 16, etc.
Irrational values are 3, 5, 7, 9, etc. In 5/4 (or 5/2, 5/8, or 5/16) (or 5/2, 5/8,
or 5/16), the rational values are 1, 5, 10, 15, etc., and the irrational values are
2, 3, 4, 6, 7, 8, 9, etc.
When referring to polyrhythms smaller than a measure, rational values are those that
are contained in, or are divisible by, or are equal divisors of the denominator of
the time signaure. In all but exceptional cases found in some new scores, those numbers
are the first seven doubles of 2: 2, 4, 8, 16, 32, 64, 128.
There are several good methods of learning polyrhythms. The following approach was
first organized by Rene Longy.
Step 1 Start with the rational value
Step 2 Divide each of the rational values by the number of irrational values
Step 3 Group those divisions by the number of rational values to show where
the irrational values fall in relation to the rational ones.
(Please refer to the handout given to you in class)
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