Musical set theory
Although musical set theory
may be considered the application of mathematical set theory
to music, there is often little coincidence between the terminology and possibly the methods of the two. Both theories make use of sets, but in the mathematical theory a set is an unordered
collection of things, while in music theory what is called a set is, in the mathematical theory, a sequence, an ordered
collection of things. Musical set theory also uses the terms linear and nonlinear for ordered and unordered sets. Allen Forte's book, The Structure of Atonal Music
(ISBN 0300021208), one of the primary developments in musical set theory, is sometimes criticised for its supposedly faulty calculations and terminology. Musical set theory may, however, be considered as an unrelated field from mathematical set theory that, at the most, adapted some techniques from mathematical set theory for its own uses.
In addition to octave and enharmonic equivalency assumed in twelve tone theory, set theory also makes use of inversionalal and transpositional equivalency. However, many theorists question or do not use inversional equivalency while Solomon simply adds a distinction to the end of the Forte prime form number of any sets which would be considered inversionally equivalent in his own Solomon Prime form number.
Set theory, like the twelve tone technique, makes use of integer notation and modulo 12.
Theorists and Books
- John Rahn: Basic Atonal Theory (ASIN 0028731603)
- Allen Forte: Structure of Atonal Music (ISBN 0300021208)
- David Lewin: Musical Form and Transformation: 4 Analytic Essays (ASIN 0300056869), Generalized Musical Intervals and Transformations (ASIN 0300034938)
- Joseph N. Straus: Introduction to Post-Tonal Theory (ISBN 0130143316)
- Important terms: pitch (music), pitch class, (pitch class) set, Z-relation, interval vector, transposition, inversion (music), rotation, permutation