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 [[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 ===

~~An obvious interpretation for omega-hexacot is~~ [[sextilifourths]], ~~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, 48 make [[10/1|tenth harmonic]], 50 make [[11/1|eleventh harmonic]], and 55 make [[14/1|fourteenth harmonic]].

In [[sextilifourths]], 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, 48 make [[10/1|tenth harmonic]], 50 make [[11/1|eleventh harmonic]], and 55 make [[14/1|fourteenth harmonic]].

=== Marvolo ===

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 == Temperament interpretations ==
+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 ===
 {{see also|Schismatic family}}
-An obvious interpretation for omega-hexacot is [[sextilifourths]], 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, 48 make [[10/1|tenth harmonic]], 50 make [[11/1|eleventh harmonic]], and 55 make [[14/1|fourteenth harmonic]].
+In [[sextilifourths]], 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, 48 make [[10/1|tenth harmonic]], 50 make [[11/1|eleventh harmonic]], and 55 make [[14/1|fourteenth harmonic]].
 === Marvolo ===