Xenllium at 07:39, 26 January 2026

2026-01-26T07:39:59Z

Xenllium at 06:35, 26 January 2026

2026-01-26T06:35:22Z

← Older revision		Revision as of 06:35, 26 January 2026
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for gamma-hexacot is [[hemiseven]], where the generator is [[45/34]], two of which make [[7/4]], four make {{nowrap\|[[26/17]]~[[32/21]]}} above an octave, ~~and~~ six make [[4/3]] above two octaves.		An obvious interpretation for gamma-hexacot is [[hemiseven]], where the generator is [[45/34]], two of which make [[7/4]], three make [[15/13]] above an octave, four make {{nowrap\|[[26/17]]~[[32/21]]}} above an octave, six make [[4/3]] above two octaves, seven make [[30/17]] above two octaves, seventeen make [[9/5]] above six octaves, and nineteen make [[11/7]] above seven octaves.

	[[Category:Ploidacots\|Gamma-hexacot]]		[[Category:Ploidacots\|Gamma-hexacot]]

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=3|Cots=6|Pergen=[P8, ccP4/6]|Forms=17, 22, 27, 32, 37|Title=Gamma-hexacot|Wedgie=6}} '''Gamma-hexacot ''' is a temperament archetype where the generator is a grave fourth of about 482–484{{c}}, six of which make 16/3 (perfect eighteenth, two octaves above a perfect fourth), and the period is a 2/1 octave. Gamma-hexacot temperaments also include all alpha-dicot and Ploidacot/Tricot|tr..."

2026-01-26T04:14:33Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=3|Cots=6|Pergen=[P8, ccP4/6]|Forms=17, 22, 27, 32, 37|Title=Gamma-hexacot|Wedgie=6}} '''Gamma-hexacot ''' is a temperament archetype where the generator is a grave fourth of about 482–484{{c}}, six of which make 16/3 (perfect eighteenth, two octaves above a perfect fourth), and the period is a 2/1 octave. Gamma-hexacot temperaments also include all alpha-dicot and Ploidacot/Tricot|tr..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=3|Cots=6|Pergen=[P8, ccP4/6]|Forms=17, 22, 27, 32, 37|Title=Gamma-hexacot|Wedgie=6}}
'''Gamma-hexacot ''' is a temperament archetype where the generator is a grave fourth of about 482–484{{c}}, six of which make [[16/3]] (perfect eighteenth, two octaves above a perfect fourth), and the period is a [[2/1]] octave. Gamma-hexacot temperaments also include all [[Ploidacot/Alpha-dicot|alpha-dicot]] and [[Ploidacot/Tricot|tricot]] intervals. Gamma-hexacot temperaments typically generate the [[5L 7s]], [[5L 12s]], and [[5L 17s]] MOS scales.

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

{| class="wikitable"
|+ style="font-size: 105%;" | Gamma-hexacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −24
| 407.820
| E
| major third
|-
| −23
| 890.828
|
|
|-
| −22
| 173.835
|
|
|-
| −21
| 656.843
|
|
|-
| −20
| 1139.850
|
|
|-
| −19
| 422.858
|
|
|-
| −18
| 905.865
| A
| major sixth
|-
| −17
| 188.873
|
|
|-
| −16
| 671.880
|
|
|-
| −15
| 1154.888
|
|
|-
| −14
| 437.895
|
|
|-
| −13
| 920.903
|
|
|-
| −12
| 203.910
| D
| major second
|-
| −11
| 686.918
|
|
|-
| −10
| 1169.925
|
|
|-
| −9
| 452.933
|
|
|-
| −8
| 935.940
|
|
|-
| −7
| 218.948
|
|
|-
| −6
| 701.955
| G
| perfect fifth
|-
| −5
| 1184.963
|
|
|-
| −4
| 467.970
|
|
|-
| −3
| 950.978
|
|
|-
| −2
| 233.985
|
|
|-
| −1
| 716.993
|
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 483.007
|
|
|-
| 2
| 966.015
|
|
|-
| 3
| 249.022
|
|
|-
| 4
| 732.030
|
|
|-
| 5
| 15.037
|
|
|-
| 6
| 498.045
| F
| perfect fourth
|-
| 7
| 981.052
|
|
|-
| 8
| 264.060
|
|
|-
| 9
| 747.067
|
|
|-
| 10
| 30.075
|
|
|-
| 11
| 513.082
|
|
|-
| 12
| 996.090
| Bb
| minor seventh
|-
| 13
| 279.097
|
|
|-
| 14
| 762.105
|
|
|-
| 15
| 45.112
|
|
|-
| 16
| 528.120
|
|
|-
| 17
| 1011.127
|
|
|-
| 18
| 294.135
| Eb
| minor third
|-
| 19
| 777.142
|
|
|-
| 20
| 60.150
|
|
|-
| 21
| 543.157
|
|
|-
| 22
| 1026.165
|
|
|-
| 23
| 309.172
|
|
|-
| 24
| 792.180
| Ab
| minor sixth
|}

== Temperament interpretations ==
An obvious interpretation for gamma-hexacot is [[hemiseven]], where the generator is [[45/34]], two of which make [[7/4]], four make {{nowrap|[[26/17]]~[[32/21]]}} above an octave, and six make [[4/3]] above two octaves.

[[Category:Ploidacots|Gamma-hexacot]]

Ploidacot/Gamma-hexacot - Revision history

Xenllium at 07:39, 26 January 2026

Xenllium at 06:35, 26 January 2026