Symmetries for Orchestra
1982, 10:30
Symmetries owes its name to the features of the structure formula that serves as input to a computer program for composition generating the material for this work. In this formula, the composer defines a syntactic deep structure in terms of the degrees of order & disorder that characterizes essential musical parameters, thus encoding a compositional plan. The formula employs 7 degrees of change, from 7 (highest degree of constancy) to 1 (highest degree of change), made explicit in four movements, A to D as follows:
The piece is based on two tendencies of parametrical counterpoint:
- increasing sense of meter and dynamic grouping;
- decreasing sense of pitch centeredness and tone color grouping, with register distribution deviating from both.
A compromise between these tendencies is reached in the second part of section B. In semantic terms, the movements can be characterized as follows:
A. Introduction: increasing in tempo to the midpoint, and returning to the initial tempo.
B. Contrasting middle part pairing an Adagio and an Allegro Vivace.
C. Third movement showing increasing tone color mixture, in tempo growing from slow to fast.
D. Final movement that reaches a plateau of slow movement, then increasing in speed until the end