Ploidacot/Alpha-tetracot - Revision history

Xenllium at 22:15, 7 January 2026

2026-01-07T22:15:58Z

← Older revision		Revision as of 22:15, 7 January 2026
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	{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=4\|Pergen=[P8, P12/4]\|Forms=33, 38, 43, 48, 53\|Title=Alpha-tetracot\|Wedgie=4}}		{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=4\|Pergen=[P8, P12/4]\|Forms=13, 18, 23, 28, 33\|Title=Alpha-tetracot\|Wedgie=4}}
	'''Alpha-tetracot''' is a temperament archetype where the generator is a sub-fourth, four of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Alpha-tetracot temperaments typically generate the [[5L 3s]], [[5L 8s]], [[5L 13s]], and [[5L 18s]] MOS scales, and they split the diatonic semitone into four equal parts, creating "supermajor", "interseptal", and "subminor" intervals and containing all [[Ploidacot/Alpha-dicot\|alpha-dicot]] intervals.		'''Alpha-tetracot''' is a temperament archetype where the generator is a sub-fourth, four of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Alpha-tetracot temperaments typically generate the [[5L 3s]], [[5L 8s]], [[5L 13s]], and [[5L 18s]] MOS scales, and they split the diatonic semitone into four equal parts, creating "supermajor", "interseptal", and "subminor" intervals and containing all [[Ploidacot/Alpha-dicot\|alpha-dicot]] intervals.

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	An obvious interpretation for alpha-tetracot is [[Buzzard\|buzzardsmic]], a 2.3.7 subgroup temperament, where the generator is [[21/16]] and four of them make a perfect twelfth. There are some extensions for full 7-limit: buzzard (53 & 58), subfourth (58 & 63), and lemongrass (63 & 68).		An obvious interpretation for alpha-tetracot is [[Buzzard\|buzzardsmic]], a 2.3.7 subgroup temperament, where the generator is [[21/16]] and four of them make a perfect twelfth. There are some extensions for full 7-limit: buzzard (53 & 58), subfourth (58 & 63), and lemongrass (63 & 68).

	[[Category:Ploidacots]]		[[Category:Ploidacots\|Alpha-tetracot]]

FloraC: Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

2026-01-06T09:44:27Z

Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

← Older revision		Revision as of 09:44, 6 January 2026
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	An obvious interpretation for alpha-tetracot is [[Buzzard\|buzzardsmic]], a 2.3.7 subgroup temperament, where the generator is [[21/16]] and four of them make a perfect twelfth. There are some extensions for full 7-limit: buzzard (53 & 58), subfourth (58 & 63), and lemongrass (63 & 68).		An obvious interpretation for alpha-tetracot is [[Buzzard\|buzzardsmic]], a 2.3.7 subgroup temperament, where the generator is [[21/16]] and four of them make a perfect twelfth. There are some extensions for full 7-limit: buzzard (53 & 58), subfourth (58 & 63), and lemongrass (63 & 68).

	[[Category:~~Ploidacot~~]]		[[Category:Ploidacots]]

Xenllium: /* Intervals and notation */Fixed typo

2026-01-05T03:53:55Z

Intervals and notation: Fixed typo

← Older revision		Revision as of 03:53, 5 January 2026
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	\|		\|
	\|-		\|-
	\| 8		\| 12
	\| 905.87		\| 905.87
	\| A		\| A
	\| major ~~second~~		\| major sixth
	\|}		\|}

Xenllium at 03:47, 5 January 2026

2026-01-05T03:47:21Z

@@ Line 15: / Line 15: @@
 ! Notation
 ! Name
 |-
 | −9
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 | vG
+|
 |}

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=1|Cots=4|Pergen=[P8, P12/4]|Forms=33, 38, 43, 48, 53|Title=Alpha-tetracot|Wedgie=4}} '''Alpha-tetracot''' is a temperament archetype where the generator is a sub-fourth, four of which make a perfect twelfth of 3/1, and the period is a 2/1 octave. Alpha-tetracot temperaments typically generate the 5L 3s, 5L 8s, 5L 13s, and 5L 18s MOS scales, and they split the diatonic semitone..."

2026-01-04T23:53:42Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=1|Cots=4|Pergen=[P8, P12/4]|Forms=33, 38, 43, 48, 53|Title=Alpha-tetracot|Wedgie=4}} '''Alpha-tetracot''' is a temperament archetype where the generator is a sub-fourth, four of which make a perfect twelfth of 3/1, and the period is a 2/1 octave. Alpha-tetracot temperaments typically generate the 5L 3s, 5L 8s, 5L 13s, and 5L 18s MOS scales, and they split the diatonic semitone..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=1|Cots=4|Pergen=[P8, P12/4]|Forms=33, 38, 43, 48, 53|Title=Alpha-tetracot|Wedgie=4}}
'''Alpha-tetracot''' is a temperament archetype where the generator is a sub-fourth, four of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Alpha-tetracot temperaments typically generate the [[5L 3s]], [[5L 8s]], [[5L 13s]], and [[5L 18s]] MOS scales, and they split the diatonic semitone into four equal parts, creating "supermajor", "interseptal", and "subminor" intervals and containing all [[Ploidacot/Alpha-dicot|alpha-dicot]] intervals.

Alpha-tetracot temperaments often generate 5L 23s and 5L 28s as chromatic scales, and for particularly sharp tunings 23L 5s or 28L 5s.

== Intervals and notation ==
While there is no agreed-upon notation system for alpha-tetracot, the notation provided here is based on interpreting the generator as a sub-fourth, and allowing for an ^ or v to stand for a quarter of a diatonic semitone, so ^^C and vvDb are enharmonic.

{| class="wikitable"
|+ style="font-size: 105%;" | Alpha-tetracot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −9
| 520.60
| ^F
|
|-
| −8
| 996.09
| Bb
| minor seventh
|-
| −7
| 271.58
| vEb
|
|-
| −6
| 747.07
| ^^G/vvAb
|
|-
| −5
| 22.56
| ^C
|
|-
| −4
| 498.04
| F
| perfect fourth
|-
| −3
| 973.53
| vBb
|
|-
| −2
| 249.02
| ^^D/vvEb
|
|-
| −1
| 724.51
| ^G
|
|-
| 0
| 0.00
| C
| perfect unison
|-
| 1
| 475.49
| vF
|
|-
| 2
| 950.98
| ^^A/vvBb
|
|-
| 3
| 226.47
| ^D
|
|-
| 4
| 701.96
| G
| perfect fifth
|-
| 5
| 1177.44
| vC
|
|-
| 6
| 452.93
| ^^E/vvF
|
|-
| 7
| 928.42
| ^A
|
|-
| 8
| 203.91
| D
| major second
|-
| 9
| 679.40
| vG
|
|}

== Temperament interpretations ==
An obvious interpretation for alpha-tetracot is [[Buzzard|buzzardsmic]], a 2.3.7 subgroup temperament, where the generator is [[21/16]] and four of them make a perfect twelfth. There are some extensions for full 7-limit: buzzard (53 & 58), subfourth (58 & 63), and lemongrass (63 & 68).

[[Category:Ploidacot]]