Ploidacot/Omega-hexacot - Revision history

Xenllium at 11:18, 1 February 2026

2026-02-01T11:18:20Z

← Older revision		Revision as of 11:18, 1 February 2026
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	== Temperament interpretations ==		== 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 ===		=== Sextilifourths ===

Xenllium: /* Temperament interpretations */

2026-01-31T05:10:50Z

Temperament interpretations

← Older revision		Revision as of 05:10, 31 January 2026
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	== Temperament interpretations ==		== 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).

	=== Sextilifourths ===		=== Sextilifourths ===
	{{see also\|Schismatic family}}		{{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 ===		=== Marvolo ===

Xenllium at 03:22, 31 January 2026

2026-01-31T03:22:42Z

← Older revision		Revision as of 03:22, 31 January 2026
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	{{see also\|Schismatic family}}		{{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]].		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]].

			=== 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 ===		=== Nautilus ===

Xenllium at 13:05, 28 January 2026

2026-01-28T13:05:12Z

← Older revision		Revision as of 13:05, 28 January 2026
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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.		'''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 ==		== Temperament interpretations ==

			=== 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]].		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]].

			=== 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]]		[[Category:Ploidacots\|Omega-hexacot]]

ArrowHead294 at 12:30, 26 January 2026

2026-01-26T12:30:47Z

← Older revision		Revision as of 12:30, 26 January 2026
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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\|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.		'''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.

	== Intervals and notation ==		== Intervals and notation ==

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=5|Cots=6|Pergen=[P8, P4/6]|Forms=14, 15, 29|Title=Omega-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 alpha-dicot and omega-tricot intervals. Omega-hexacot temp..."

2026-01-26T07:00:17Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=5|Cots=6|Pergen=[P8, P4/6]|Forms=14, 15, 29|Title=Omega-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 alpha-dicot and omega-tricot intervals. Omega-hexacot temp..."

New page

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

== Intervals and notation ==
Due to dividing the fourth into so many steps, standard notation becomes almost useless for omega-hexacot. Regardless, notation has been provided for where omega-hexacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

{| class="wikitable"
|+ style="font-size: 105%;" | Omega-hexacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −24
| 407.820
| E
| major third
|-
| −23
| 490.828
|
|
|-
| −22
| 573.835
|
|
|-
| −21
| 656.843
|
|
|-
| −20
| 739.850
|
|
|-
| −19
| 822.858
|
|
|-
| −18
| 905.865
| A
| major sixth
|-
| −17
| 988.873
|
|
|-
| −16
| 1071.880
|
|
|-
| −15
| 1154.888
|
|
|-
| −14
| 37.895
|
|
|-
| −13
| 120.903
|
|
|-
| −12
| 203.910
| D
| major second
|-
| −11
| 286.918
|
|
|-
| −10
| 369.925
|
|
|-
| −9
| 452.933
|
|
|-
| −8
| 535.940
|
|
|-
| −7
| 618.948
|
|
|-
| −6
| 701.955
| G
| perfect fifth
|-
| −5
| 784.963
|
|
|-
| −4
| 867.970
|
|
|-
| −3
| 950.978
|
|
|-
| −2
| 1033.985
|
|
|-
| −1
| 1116.993
|
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 83.007
|
|
|-
| 2
| 166.015
|
|
|-
| 3
| 249.022
|
|
|-
| 4
| 332.030
|
|
|-
| 5
| 415.037
|
|
|-
| 6
| 498.045
| F
| perfect fourth
|-
| 7
| 581.052
|
|
|-
| 8
| 664.060
|
|
|-
| 9
| 747.067
|
|
|-
| 10
| 830.075
|
|
|-
| 11
| 913.082
|
|
|-
| 12
| 996.090
| Bb
| minor seventh
|-
| 13
| 1079.097
|
|
|-
| 14
| 1162.105
|
|
|-
| 15
| 45.112
|
|
|-
| 16
| 128.120
|
|
|-
| 17
| 211.127
|
|
|-
| 18
| 294.135
| Eb
| minor third
|-
| 19
| 377.142
|
|
|-
| 20
| 460.150
|
|
|-
| 21
| 543.157
|
|
|-
| 22
| 626.165
|
|
|-
| 23
| 709.172
|
|
|-
| 24
| 792.180
| Ab
| minor sixth
|}

== 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]].

[[Category:Ploidacots|Omega-hexacot]]