Boulez's Rhythm
System
Messiaen
Mode de valeurs et d'intensite
(1949)
- introduced nonordered
12-member sets of numerous parameters (pitch, rhythm, dynamics, density,
attack, register)
- sets not used serially;
extended Messiaen's already established pitch modes
Boulez
- took Webern as point
of departure
Structures Ia (1952)
- divided into three
pieces; each concentrates on specific elements: a-pitch and duration; b-attack;
c-dynamics
- adapts one of Messiaen's
pitch modes from Mode de valeurs
- limits rhythmic vocabulary
according to 12 values from thirty-second to dotted quarter; assigns a rhythmic
duration to each pitch in the series
- the key problem:
upon transposition, the rhythmic series loses its relationship, as invariant
intervallic relationships don't correspond to new placement of durational
values: every permutation of the series assumes a new series of durational
values