Ploidacot/Omega-hexacot: Difference between revisions

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== Temperament interpretations ==

An obvious interpretation for omega-hexacot is [[historical]], 2.3.7/5.11/5.13/5 ~~restriction~~ of [[History (temperament)|history]], where the generator is {{nowrap|[[21/20]]~[[22/21]]}}, two of which make [[11/10]], three make [[15/13]], five make [[14/11]], six make [[4/3]], seven make [[7/5]], nine make [[20/13]], eleven make [[22/13]], sixteen make [[14/13]] above an octave. There are some extensions for full 13-limit: sextilifourths (29 & 130), marvolo (29 & 43), and nautilus (15 & 29).

An obvious interpretation for omega-hexacot is [[historical]], 2.3.7/5.11/5.13/5 [[retraction]] of [[History (temperament)|history]], where the generator is {{nowrap|[[21/20]]~[[22/21]]}}, two of which make [[11/10]], three make [[15/13]], five make [[14/11]], six make [[4/3]], seven make [[7/5]], nine make [[20/13]], eleven make [[22/13]], sixteen make [[14/13]] above an octave. There are some extensions for full 13-limit: sextilifourths (29 & 130), marvolo (29 & 43), and nautilus (15 & 29).

=== Sextilifourths ===

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In [[nautilus]], the generator is {{nowrap|[[21/20]]~[[22/21]]}}, two of which make {{nowrap|[[10/9]]~[[11/10]]}}, three make {{nowrap|[[7/6]]~[[8/7]]}}, five make [[14/11]], six make [[4/3]], seven make [[7/5]], eight make [[16/11]], and ten make [[8/5]].

~~[[Category:Ploidacots|Omega-hexacot]]~~

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 == Temperament interpretations ==
-An obvious interpretation for omega-hexacot is [[historical]], 2.3.7/5.11/5.13/5 restriction of [[History (temperament)|history]], where the generator is {{nowrap|[[21/20]]~[[22/21]]}}, two of which make [[11/10]], three make [[15/13]], five make [[14/11]], six make [[4/3]], seven make [[7/5]], nine make [[20/13]], eleven make [[22/13]], sixteen make [[14/13]] above an octave. There are some extensions for full 13-limit: sextilifourths (29 & 130), marvolo (29 & 43), and nautilus (15 & 29).
+An obvious interpretation for omega-hexacot is [[historical]], 2.3.7/5.11/5.13/5 [[retraction]] of [[History (temperament)|history]], where the generator is {{nowrap|[[21/20]]~[[22/21]]}}, two of which make [[11/10]], three make [[15/13]], five make [[14/11]], six make [[4/3]], seven make [[7/5]], nine make [[20/13]], eleven make [[22/13]], sixteen make [[14/13]] above an octave. There are some extensions for full 13-limit: sextilifourths (29 & 130), marvolo (29 & 43), and nautilus (15 & 29).
 === Sextilifourths ===
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 {{see also|Porcupine family}}
 In [[nautilus]], the generator is {{nowrap|[[21/20]]~[[22/21]]}}, two of which make {{nowrap|[[10/9]]~[[11/10]]}}, three make {{nowrap|[[7/6]]~[[8/7]]}}, five make [[14/11]], six make [[4/3]], seven make [[7/5]], eight make [[16/11]], and ten make [[8/5]].
-[[Category:Ploidacots|Omega-hexacot]]