Glossary
OC-Equivalence
Glossary
Set Theory
In Harmonious, Octave + Cardinality-Equivalence, or OC-Equivalence, refers to when two or more scales or chords have the same notes present (pitch classes) and the same root note, but each note may appear in different registers or a different number of times (but at least once in each chord or scale).
For chords, two OC-equivalent objects are considered the same inversion (permutation) or the same named chord with the same function, but may be played differently; for example on piano, with one hand instead of two, or on guitar, in a different position (see CAGED System) but with the same root (not Permutation-Equivalent—order matters).
For modes, two modes are considered OC-equivalent if they start and end on the same note (or emphasize that root rhythmically), and contain the same notes in the same order.
Set Theory
In Harmonious, Octave + Cardinality-Equivalence, or OC-Equivalence, refers to when two or more scales or chords have the same notes present (pitch classes) and the same root note, but each note may appear in different registers or a different number of times (but at least once in each chord or scale).
For chords, two OC-equivalent objects are considered the same inversion (permutation) or the same named chord with the same function, but may be played differently; for example on piano, with one hand instead of two, or on guitar, in a different position (see CAGED System) but with the same root (not Permutation-Equivalent—order matters).
For modes, two modes are considered OC-equivalent if they start and end on the same note (or emphasize that root rhythmically), and contain the same notes in the same order.