Ploidacot/Omega-hexacot: Difference between revisions

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{{Infobox ploidacot|Ploids=1|Shears=5|Cots=6|Pergen=[P8, P4/6]|Forms=14, 15, 29|Title=Omega-hexacot|Wedgie=6}}

{{Infobox ploidacot|Ploids=1|Shears=5|Cots=6|Pergen=[P8, P4/6]|Forms=14, 15, 29|Title=Omega-hexacot (epsilon-hexacot)|Wedgie=6}}

'''Omega-hexacot''' is a temperament archetype where the generator is a small semitone of about 82–84{{c}}, six of which make a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-hexacot temperaments also include all [[Ploidacot/Alpha-dicot|alpha-dicot]] and [[Ploidacot/Omega-tricot|omega-tricot]] intervals. Omega-hexacot temperaments typically generate the [[14L 1s]] and [[14L 15s]] MOS scales.

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== Temperament interpretations ==

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]].

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 ===

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 ===

In [[marvolo]], 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]], ten make [[13/8]], eleven make [[22/13]], and sixteen make {{nowrap|[[13/12]]~[[14/13]]}}.

=== Nautilus ===

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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 {{Breadcrumb}}
-{{Infobox ploidacot|Ploids=1|Shears=5|Cots=6|Pergen=[P8, P4/6]|Forms=14, 15, 29|Title=Omega-hexacot|Wedgie=6}}
+{{Infobox ploidacot|Ploids=1|Shears=5|Cots=6|Pergen=[P8, P4/6]|Forms=14, 15, 29|Title=Omega-hexacot (epsilon-hexacot)|Wedgie=6}}
 '''Omega-hexacot''' is a temperament archetype where the generator is a small semitone of about 82–84{{c}}, six of which make a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-hexacot temperaments also include all [[Ploidacot/Alpha-dicot|alpha-dicot]] and [[Ploidacot/Omega-tricot|omega-tricot]] intervals. Omega-hexacot temperaments typically generate the [[14L&nbsp;1s]] and [[14L&nbsp;15s]] MOS scales.
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 == Temperament interpretations ==
-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]].
+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}}
+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 ===
+{{see also|Marvel temperaments}}
+In [[marvolo]], 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]], ten make [[13/8]], eleven make [[22/13]], and sixteen make {{nowrap|[[13/12]]~[[14/13]]}}.
+=== Nautilus ===
+{{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]]