Kleismic family: Difference between revisions

Eufalesio (talk | contribs)
Added and redescribed many things
Restore subsection of the overview; - no-11 countercata (no viable alternative 11-limit extension)
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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.
==== Subgroup extensions ====
Kleismic lends itself to a natural extension to the [[2.3.5.13 subgroup]], as the hemitwelfth, reached by three generator steps, can be interpreted as [[26/15]]. This is discussed immediately below.


=== 2.3.5.13 subgroup (cata) ===
=== 2.3.5.13 subgroup (cata) ===
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[[Badness]] (Sintel): 1.32
[[Badness]] (Sintel): 1.32
==== 2.3.5.7.13 subgroup ====
Subgroup: 2.3.5.7.13
Comma list: 169/168, 225/224, 325/324
Subgroup-val mapping: {{mapping| 1 0 1 11 0 | 0 6 5 -31 14 }}
Optimal tunings:
* WE: ~2 = 1199.981{{c}}, ~6/5 = 317.124{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.129{{c}}
{{Optimal ET sequence|legend=0|TBA}}
Badness (Sintel): 0.675


=== 11-limit ===
=== 11-limit ===