OPTIC-Equivalence
Glossary
Set Theory
Octave + Permutation + Transposition + Involution + Cardinality Equivalence or OPTIC-Equivalence treats musical objects the same if they are transpositions and/or involutions of the same unordered collection of notes (see OPC-equivalence); that is, if they share the same forte number.
OPTC-Equivalent objects share a transposition-equivalent (rotationally-equivalent) pattern of intervals such that the order of the intervals cannot be involuted and remain OPTC-equivalent. Objects are OPTIC-Equivalent when they are OPTC-Equivalent and/or related by involution.
See Grouping Clocks for more details about set classes, prime forms, and black and white clocks, and flipping clocks.
So for example, under OPTIC-Equivalence, these six patterns of intervals are one forte number, 3-11, containing all transpositions of the major triad and the minor triad:
- major third + minor third + perfect fourth
- minor third + perfect fourth + major third
- perfect fourth + major third + minor third
- minor third + major third + perfect fourth
- major third + perfect fourth + minor third
- perfect fourth + minor third + major third
See Equivalence Groups for a tutorial that runs through some examples.
Set Theory
Octave + Permutation + Transposition + Involution + Cardinality Equivalence or OPTIC-Equivalence treats musical objects the same if they are transpositions and/or involutions of the same unordered collection of notes (see OPC-equivalence); that is, if they share the same forte number.
OPTC-Equivalent objects share a transposition-equivalent (rotationally-equivalent) pattern of intervals such that the order of the intervals cannot be involuted and remain OPTC-equivalent. Objects are OPTIC-Equivalent when they are OPTC-Equivalent and/or related by involution.
See Grouping Clocks for more details about set classes, prime forms, and black and white clocks, and flipping clocks.
So for example, under OPTIC-Equivalence, these six patterns of intervals are one forte number, 3-11, containing all transpositions of the major triad and the minor triad:
- major third + minor third + perfect fourth
- minor third + perfect fourth + major third
- perfect fourth + major third + minor third
- minor third + major third + perfect fourth
- major third + perfect fourth + minor third
- perfect fourth + minor third + major third
See Equivalence Groups for a tutorial that runs through some examples.