Glossary
OPC-Equivalence
Glossary
Set Theory
Octave + Permutation + Cardinality Equivalence or OPC-Equivalence treats musical objects the same if they have the same note names or pitch classes even if the notes come in a different order, in different octave registers, or if the pitch classes occur just once or many times.
In OC-equivalence, permutation or order still matters, especially which note is on the bottom (the root). In OPC-equivalence the notes are treated as an unordered collection. A simple example of OPC-Equivalent objects are the inversions of the C major triad—in this case we would not care which note is on the bottom, just which notes are present at all (and not their order).
See Equivalence Groups for a tutorial that runs through some examples.
Set Theory
Octave + Permutation + Cardinality Equivalence or OPC-Equivalence treats musical objects the same if they have the same note names or pitch classes even if the notes come in a different order, in different octave registers, or if the pitch classes occur just once or many times.
In OC-equivalence, permutation or order still matters, especially which note is on the bottom (the root). In OPC-equivalence the notes are treated as an unordered collection. A simple example of OPC-Equivalent objects are the inversions of the C major triad—in this case we would not care which note is on the bottom, just which notes are present at all (and not their order).
See Equivalence Groups for a tutorial that runs through some examples.