Bisector (music)

In diatonic set theory, a bisector divides the octave approximately in half and may be used in place of a generator to derive collections for which structure implies multiplicity is not true such as the ascending melodic minor, harmonic minor, and octatonic scales. Well formed generated collections generators and bisectors coincide, such as in the diatonic collection. The term was introduced by Jay Rahn (1977), who considers any division between one and two thirds as approximately half and who applied the term only the equally spaced collections. Clough and Johnson both adapt the term to apply to generic scale steps. Rahn also uses aliquant bisector for bisectors which may be used to generate every note in a collection, in which case the bisector and the number of notes must be coprime. Bisectors may be used to produce the diatonic, harmonic minor, and ascending melodic minor collections. (Johnson 2003, p.97, 101, 158n10-12)

References

Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1-930190-80-8.
Rahn, Jay (1977). "Some Recurrent Features of Scales", In Theory Only 2, no. 11-12: 43-52

Musical set theory

All-interval tetrachord Complement Forte number Identity Interval class Interval vector Multiplication Permutation Pitch class Pitch interval Pitch-interval class Set List Similarity relation Transformation Z-relation

Diatonic set theory	Bisector Cardinality equals variety Common tone Diatonic scale Deep scale property Generated collection Generic interval Maximal evenness Myhill's property Rothenberg propriety Specific interval Structure implies multiplicity

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