Glossary
OPTIC/K-Equivalence
Glossary
Set Theory
Octave + Permutation + Transposition + Involution + Cardinality + Complementarity Equivalence or OPTIC/K-Equivalence treats musical objects the same if they are OPTIC-Equivalent and/or complements; that is, if they share the same row of the set classes table. (The K for Complementarity is not standard terminology, it is just used here to make a working acronym.)
Since Allen Forte numbered complementary set classes with matching values for their second components, OPTIC/K-Equivalent objects share a row in the set classes tables. For example the triads (3-11) and their complements (nine-note scales, 9-11) line up as one row of OPTIC/K-Equivalent objects.
See Equivalence Groups for a tutorial that runs through some examples.
See Lewin-Quinn FC-components for more on why OPTIC + Complementarity Equivalence matters musically, and the meaning of FC1 through FC6 columns in the tables.
Set Theory
Octave + Permutation + Transposition + Involution + Cardinality + Complementarity Equivalence or OPTIC/K-Equivalence treats musical objects the same if they are OPTIC-Equivalent and/or complements; that is, if they share the same row of the set classes table. (The K for Complementarity is not standard terminology, it is just used here to make a working acronym.)
Since Allen Forte numbered complementary set classes with matching values for their second components, OPTIC/K-Equivalent objects share a row in the set classes tables. For example the triads (3-11) and their complements (nine-note scales, 9-11) line up as one row of OPTIC/K-Equivalent objects.
See Equivalence Groups for a tutorial that runs through some examples.
See Lewin-Quinn FC-components for more on why OPTIC + Complementarity Equivalence matters musically, and the meaning of FC1 through FC6 columns in the tables.