Basic Set Theory : Pitch-Class, Integer Notation, and Modulus

Abstract

Pitch Class, Integer Notation, and Modulo 12 are basic concepts of
set theory.A pitch class is not any notes or pitches on the staff, but
each one relates to one another by octave—same letter name—including
enharmonic equivalences. All pitch classes are represented by integer notation,
0-11. Moreover, modulo 12 is applied for
the pitch class relationship. These numeral symbols seem to be perfect
for explaining twentieth-century compositions. It is not, however, only
onesystem or condition to describe all compositions in the century,
or even betterthan the common practice In some cases, analyzing music by usingset theory accompanied with traditional harmony can more clearly explain twentieth-century compositions.