Generator: Difference between revisions

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The term '''generator''' has multiple senses.

== Generators in ~~MOS~~ ==

== Generators in MOSes ==

In MOS and rank-2 temperament contexts, the '''generator''' of a MOS or a rank-2 temperament is an interval that you stack up and reduce by the [[period]] of the MOS to construct the MOS pattern within each period. Along with the [[period]], it is one of two defining intervals of the [[MOS]]. For example:

In [[MOS]] and rank-2 temperament contexts, the '''generator''' of a MOS or a rank-2 temperament is an interval that you stack up and reduce by the [[period]] of the MOS to construct the MOS pattern within each period. Along with the [[period]], it is one of two defining intervals of the [[MOS]]. For example:

* In [[meantone]], the (flattened) perfect fifth is a generator: stacking 6 fifths up from the tonic and reducing by the octave produces the pattern LLLsLLs, the Lydian mode. Note that the perfect fourth and the perfect twelfth are also generators.

* One example for a MOS with multiple periods per octave: for [[pajara]], the perfect fifth (a tempered [[3/2]]) is a generator and the half-octave is the period.

@@ Line 1: / Line 1: @@
 The term '''generator''' has multiple senses.
-== Generators in MOS ==
+== Generators in MOSes ==
-In MOS and rank-2 temperament contexts, the '''generator''' of a MOS or a rank-2 temperament is an interval that you stack up and reduce by the [[period]] of the MOS to construct the MOS pattern within each period. Along with the [[period]], it is one of two defining intervals of the [[MOS]]. For example:
+In [[MOS]] and rank-2 temperament contexts, the '''generator''' of a MOS or a rank-2 temperament is an interval that you stack up and reduce by the [[period]] of the MOS to construct the MOS pattern within each period. Along with the [[period]], it is one of two defining intervals of the [[MOS]]. For example:
 * In [[meantone]], the (flattened) perfect fifth is a generator: stacking 6 fifths up from the tonic and reducing by the octave produces the pattern LLLsLLs, the Lydian mode. Note that the perfect fourth and the perfect twelfth are also generators.
 * One example for a MOS with multiple periods per octave: for [[pajara]], the perfect fifth (a tempered [[3/2]]) is a generator and the half-octave is the period.