University of South Carolina
School of Music

BAIN MUSC 525
Post-Tonal Music Theory

Sets and Equivalence Classes

Equivalence classes have traditionally been formed under the following equivalence relations, as well as many others. The number of distinct sets formed under each relation is indicated in parentheses.
  1. Cardinality (4096 unordered pc sets)
    • Rahn 1980 defines the following thirteen cardinality types: 0-null set, 1-monad, 2-dyad, 3-trichord, 4-tetrachord, 5-pentachord, 6-hexachord, 7-septachord, 8-octachord, 9-nonachord, 10-decachord, 11-undecachord, 12-aggregate.
  2. Rahn Tn-type (364 set classes formed under Tn)
  3. Rahn Tn/TnI-type and Straus "set class," (224 set classes formed under Tn or TnI)
  4. Forte Z-relation (201 set classes formed under Tn, TnI and Z)
  5. M-equivalence, Castine 1994 (158)
  6. Complement relation (literal/abstract)
  7. Subset relation (literal/abstract)
  8. Superset relation (literal/abstract)
  9. among many others...

According to Rahn 1980 (p. 75), equivalence classes must meet the following two criteria:

  1. exhaustivity
  2. exclusivity

Sources: Rahn 1980 and Castine 1994 (pp. 61-66).

Updated: November 11, 2003