Composers on Mathematical Music
Subtext 2493183


The Seasons . . . commissioned by the Ballet Society, is an attempt to express the traditional Indian view of the seasons as quiescence (winter), creation (spring), preservation (summer), and destruction (fall). It concludes with the Prelude to Winter with which it begins. The rhythmic structure is 2, 2, 1, 3, 2, 4, 1, 3, 1. It was written for the ballet by Merce Cunningham. The sounds are a gamut (variously orchestrated) of single tones, intervals and aggregates.

The scenario given me by Mr. Cunningham was the basis for a study of numbers with which I find it congenial to begin a musical composition. His remark, “the fullness and stillness of a summer day,” suggested that Summer would be the longest section; that, together with his desire that each season would be developed by continuous invention and preceded by a short formal prelude (formal by means of exact repetitions), and that the entire work would be cyclical and concise, brought about the following numerical situation: 2,2; 1,3; 2,4; 1,3; 1. The number, 4, represents Summer, since it is the largest number (it is also the smallest number which could be the largest number in this situation); the first 3 is Spring, the second, Fall (3’s are, like these seasons, asymmetrical, un-static): they suggest both the approach to and away from 4. The second 2 is Winter, for 2 suggests the place between two 3’s, opposite a 4. The other numbers are the Preludes. Summer (4) has a Prelude of 2 (fittingly, the longest). Spring and Fall have Preludes of 1. Winter has a Prelude of 2 which is actually 1 repeated.

. . . The entire series of numbers occurs throughout the ballet, not only with respect to the length of sections, but, as is my custom in works for percussion and “prepared” piano, also with respect to phraseology. Thus within each 1, the series given above occurs as the determinant of breathing. Within the 4 of Summer, it occurs 4 times, etc. The tempo changes the actual number of measures as it changes: actual time length being the basis of this plan. Naturally, a plan like this is made not only to be followed, but also that it may be broken. Yet the pleasure of breaking a law can only exist if the law is existent. The question arises whether one can know this rhythmic structure from a first hearing. The answer clearly is: No.

John Cage



Composers on Mathematical Music: A Subtext Poem

Other Work by John Greschak

Public Domain