Generator: Difference between revisions

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

== 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.

* In diatonic (LLLsLLs), the 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.

* One example for a MOS with multiple periods per octave: for [[pajara[10] (ssLssssLss), the perfect fifth (a tempered [[3/2]]) is a generator and the half-octave is the period.

== Generators in math ==

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 The term '''generator''' has multiple senses.
 == 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.
+* In diatonic (LLLsLLs), the 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.
+* One example for a MOS with multiple periods per octave: for [[pajara[10] (ssLssssLss), the perfect fifth (a tempered [[3/2]]) is a generator and the half-octave is the period.
 == Generators in math ==