GROUP STRUCTURE AND EQUIVALENCE CLASSES IN EXTENDED TWELVE-TONE OPERATIONS
Tuukka Ilomôki · University of Michigan Library Repository · 2005
The classic set of pitch-class and row operations – transposition, inversion and retrograde – has been extended with new types of operations: first by Moperation and rotation, and more recently by a family of operations known as alpha, beta, gamma and delta. For a better understanding of these new operations, group theory enables us to find canonical forms that derive them, and to calculate the number of set-classes and row classes by tracking the invariances of the sets and rows under the operations.