Kleismic family: Difference between revisions

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Temperaments involving larger splits include [[#Sqrtphi|sqrtphi]], [[#Quartkeenlig|quartkeenlig]], [[#Novemkleismic|novemkleismic]]. Those split the kleismic structure into five to nine parts.

The ~~kleismic family boasts~~ a very remarkable extension to the [[2.3.5.13 subgroup]], ~~which has further extensions with higher primes~~. ~~These are listed at~~ the ~~bottom of this page~~, in [[~~#Subgroup extensions~~]].

==== Other subgroup extensions ====

The main extension of note is a very remarkable extension to the [[2.3.5.13 subgroup]], as the hemitwelfth, reached by three generator steps, can be interpreted as [[26/15]]. Notice 15625/15552 = ([[325/324]])⋅([[625/624]]) and 325/324 = (625/624)⋅([[676/675]]). The [[S-expression]]-based comma list of the temperament is {{nowrap| {[[325/324|S10/S12 = S25⋅S26]], ([[625/624|S25]]), [[676/675|S13/S15 = S26]]} }}.

~~====~~ Subgroup extensions ~~====~~

See [[#Subgroup extensions]].

== Catakleismic ==

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== Subgroup extensions ==

For the high-limit version of cata with a 1\5 period, see [[thunderclysmic]].

=== Kleismic (2.3.5.13) a.k.a. cata ===

Hanson lends itself nicely to this extension in the 2.3.5.13 subgroup, as the hemitwelfth, reached by three generator steps, can be interpreted as [[26/15]]. Notice 15625/15552 = ([[325/324]])⋅([[625/624]]) and 325/324 = (625/624)⋅([[676/675]]). The [[S-expression]]-based comma list of the temperament is {[[325/324|S10/S12 = S25⋅S26]], ([[625/624|S25]]), [[676/675|S13/S15 = S26]]}. For the high-limit version of cata with a 1\5 period, see [[thunderclysmic]].

Subgroup: 2.3.5.13

@@ Line 36: / Line 36: @@
 Temperaments involving larger splits include [[#Sqrtphi|sqrtphi]], [[#Quartkeenlig|quartkeenlig]], [[#Novemkleismic|novemkleismic]]. Those split the kleismic structure into five to nine parts.
-The kleismic family boasts a very remarkable extension to the [[2.3.5.13 subgroup]], which has further extensions with higher primes. These are listed at the bottom of this page, in [[#Subgroup extensions]].
+==== Other subgroup extensions ====
+The main extension of note is a very remarkable extension to the [[2.3.5.13 subgroup]], as the hemitwelfth, reached by three generator steps, can be interpreted as [[26/15]]. Notice 15625/15552 = ([[325/324]])⋅([[625/624]]) and 325/324 = (625/624)⋅([[676/675]]). The [[S-expression]]-based comma list of the temperament is {{nowrap| {[[325/324|S10/S12 = S25⋅S26]], ([[625/624|S25]]), [[676/675|S13/S15 = S26]]} }}.
-==== Subgroup extensions ====
+See [[#Subgroup extensions]].
 == Catakleismic ==
@@ Line 1,231: / Line 1,232: @@
 == Subgroup extensions ==
+For the high-limit version of cata with a 1\5 period, see [[thunderclysmic]].
 === Kleismic (2.3.5.13) a.k.a. cata ===
-Hanson lends itself nicely to this extension in the 2.3.5.13 subgroup, as the hemitwelfth, reached by three generator steps, can be interpreted as [[26/15]]. Notice 15625/15552 = ([[325/324]])⋅([[625/624]]) and 325/324 = (625/624)⋅([[676/675]]). The [[S-expression]]-based comma list of the temperament is {[[325/324|S10/S12 = S25⋅S26]], ([[625/624|S25]]), [[676/675|S13/S15 = S26]]}. For the high-limit version of cata with a 1\5 period, see [[thunderclysmic]].
 Subgroup: 2.3.5.13