Fractional-octave temperaments: Difference between revisions

Line 1:

'''Fractional-octave temperaments'''~~, when viewed from a regular~~ temperament ~~theory perspective, are temperaments~~ which have a period which corresponds to a just interval mapped to a fraction of the octave, that is one step of an [[~~EDO~~]].

'''Fractional-octave temperaments''' are [[temperament]]s which have a [[period]] which corresponds to a [[just]] [[interval]] mapped to a fraction of the [[octave]], that is one step of an [[edo]].

== Theory ==

Line 9:

The most common way to produce a fractional-octave temperament is through an excellent approximation of an interval relative to the size of the wireframe edo. For example, [[compton family]] tempers out the Pythagorean comma and maps 7 steps of 12edo to [[3/2]]. Likewise, a lot of 10th-octave temperaments have a [[13/8]] as 7\10, and 26th-octave temperaments often have a [[7/4]] for 21\26.

=== Disagreement between ~~regular~~ temperament ~~theory~~ and fractional-octave practice ===

=== Disagreement between temperament catalog strategy and fractional-octave practice ===

Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as ~~extensions~~ of a temperament with a subset period. However fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]].

Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as [[extension]]s of a temperament with a subset period. However, fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]]. This facet is reflected by the distinction of strong and weak extensions.

A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all.

@@ Line 1: / Line 1: @@
-'''Fractional-octave temperaments''', when viewed from a regular temperament theory perspective, are temperaments which have a period which corresponds to a just interval mapped to a fraction of the octave, that is one step of an [[EDO]].
+'''Fractional-octave temperaments''' are [[temperament]]s which have a [[period]] which corresponds to a [[just]] [[interval]] mapped to a fraction of the [[octave]], that is one step of an [[edo]].
 == Theory ==
@@ Line 9: / Line 9: @@
 The most common way to produce a fractional-octave temperament is through an excellent approximation of an interval relative to the size of the wireframe edo. For example, [[compton family]] tempers out the Pythagorean comma and maps 7 steps of 12edo to [[3/2]]. Likewise, a lot of 10th-octave temperaments have a [[13/8]] as 7\10, and 26th-octave temperaments often have a [[7/4]] for 21\26.
-=== Disagreement between regular temperament theory and fractional-octave practice ===
+=== Disagreement between temperament catalog strategy and fractional-octave practice ===
-Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as extensions of a temperament with a subset period. However fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]].
+Traditional regular temperament perspective on periods and generators has a shortcoming when it comes to handling fractional-octave temperaments, as it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as [[extension]]s of a temperament with a subset period. However, fractional-octave temperaments and scales are sought for being able to treat an each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]]. This facet is reflected by the distinction of strong and weak extensions.
 A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all.