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. | Temperaments involving larger splits include [[#Sqrtphi|sqrtphi]], [[#Quartkeenlig|quartkeenlig]], [[#Novemkleismic|novemkleismic]]. Those split the kleismic structure into five to nine parts. | ||
==== | ==== 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]]} }}. | 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]]} }}. | ||
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== Subgroup extensions == | == 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 === | === Kleismic (2.3.5.13) a.k.a. cata === | ||
Subgroup: 2.3.5.13 | Subgroup: 2.3.5.13 | ||