Musical
set theory
While
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.
- Important theorists:
John Rahn: Basic Atonal Theory (ASIN 0028731603); Larry Solomon, 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
External
links
