Ploidacot/Tetracot - Revision history

Fredg999 category edits: Removing from Category:Ploidacots using Cat-a-lot

2026-07-16T06:38:50Z

Removing from Category:Ploidacots using Cat-a-lot

← Older revision		Revision as of 06:38, 16 July 2026
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	==== Monkey ====		==== Monkey ====
	Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].		Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].

	~~[[Category:Ploidacots\|Tetracot]]~~

Xenllium at 07:45, 26 January 2026

2026-01-26T07:45:58Z

← Older revision		Revision as of 07:45, 26 January 2026
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	== Intervals and notation ==		== Intervals and notation ==
	While there is no agreed-upon notation system for tetracot, the notation provided here is based on interpreting the generator as a submajor second, and produced by extending dicot notation, allowing for an ^ or v to stand for a quarter of a chromatic semitone, so {{nowrap\|Eb^^ {{=}} ~~Evv~~ {{=}} Ed}}.		While there is no agreed-upon notation system for tetracot, the notation provided here is based on interpreting the generator as a submajor second, and produced by extending dicot notation, allowing for an ^ or v to stand for a quarter of a chromatic semitone, so {{nowrap\|^^Eb {{=}} vvE {{=}} Ed}}.

	{\| class="wikitable"		{\| class="wikitable"

Xenllium at 22:12, 7 January 2026

2026-01-07T22:12:42Z

@@ Line 15: / Line 15: @@
 ! Notation
 ! Name
 |-
 | −9
@@ Line 64: / Line 84: @@
 | 0.00
 | C
-| perfect unison / perfect octave
+| perfect unison
 |-
 | 1
@@ Line 110: / Line 130: @@
 | vE
 | submajor third
 |}
@@ Line 121: / Line 161: @@
 Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].
-[[Category:Ploidacots]]
+[[Category:Ploidacots|Tetracot]]

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

2026-01-06T09:44:34Z

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

← Older revision		Revision as of 09:44, 6 January 2026
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	Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].		Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].

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

Xenllium at 22:25, 4 January 2026

2026-01-04T22:25:37Z

← Older revision		Revision as of 22:25, 4 January 2026
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	{{Breadcrumb}}		{{Breadcrumb}}
	{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13\|Title=Tetracot\|Wedgie=4}}		{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13, 20\|Title=Tetracot\|Wedgie=4}}
	'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.		'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.

	Tetracot temperaments often generate 7L 6s and 7L 13s as chromatic scales, and for particularly sharp tunings 13L 7s. More info may be found at [[Ploidacot/Tetracot/Generator tunings]].		Tetracot temperaments often generate [[7L 6s]] and [[7L 13s]] as chromatic scales, and for particularly sharp tunings [[13L 7s]]. More info may be found at [[Ploidacot/Tetracot/Generator tunings]].

	== Intervals and notation ==		== Intervals and notation ==
Line 27:		Line 27:
	\|-		\|-
	\| −7		\| −7
	\| ~~1,171~~.58		\| 1171.58
	\| vC		\| vC
	\| suboctave		\| suboctave
Line 42:		Line 42:
	\|-		\|-
	\| −4		\| −4
	\| 498.05		\| 498.04
	\| F		\| F
	\| perfect fourth		\| perfect fourth
Line 57:		Line 57:
	\|-		\|-
	\| −1		\| −1
	\| ~~1,024~~.51		\| 1024.51
	\| ^Bb		\| ^Bb
	\| supraminor seventh		\| supraminor seventh
Line 92:		Line 92:
	\|-		\|-
	\| 6		\| 6
	\| ~~1,052~~.93		\| 1052.93
	\| Bd		\| Bd
	\| neutral seventh		\| neutral seventh
Line 120:		Line 120:
	==== Monkey ====		==== Monkey ====
	Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].		Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].

			[[Category:Ploidacot]]

VectorGraphics at 00:39, 14 November 2025

2025-11-14T00:39:57Z

← Older revision		Revision as of 00:39, 14 November 2025
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	{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13\|Title=Tetracot\|Wedgie=4}}		{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13\|Title=Tetracot\|Wedgie=4}}
	'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.		'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.

			Tetracot temperaments often generate 7L 6s and 7L 13s as chromatic scales, and for particularly sharp tunings 13L 7s. More info may be found at [[Ploidacot/Tetracot/Generator tunings]].

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

VectorGraphics at 23:30, 25 October 2025

2025-10-25T23:30:15Z

← Older revision		Revision as of 23:30, 25 October 2025
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	{{Breadcrumb}}		{{Breadcrumb}}
	{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13\|Title=Tetracot}}		{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13\|Title=Tetracot\|Wedgie=4}}
	'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.		'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.

ArrowHead294 at 16:03, 9 September 2025

2025-09-09T16:03:05Z

← Older revision		Revision as of 16:03, 9 September 2025
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13\|Title=Tetracot}}'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.		{{Breadcrumb}}
			{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=4\|Pergen=[P8, P5/4]\|Forms=6, 7, 13\|Title=Tetracot}}
			'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot\|dicot]] intervals.

	== Intervals and notation ==		== Intervals and notation ==
	While there is no agreed-upon notation system for tetracot, the notation provided here is based on interpreting the generator as a submajor second, and produced by extending dicot notation, allowing for an ^ or v to stand for a quarter of a chromatic semitone. Eb^^ = Evv = Ed.		While there is no agreed-upon notation system for tetracot, the notation provided here is based on interpreting the generator as a submajor second, and produced by extending dicot notation, allowing for an ^ or v to stand for a quarter of a chromatic semitone, so {{nowrap\|Eb^^ {{=}} Evv {{=}} Ed}}.

	{\| class="wikitable"		{\| class="wikitable"
	\|+Tetracot intervals (assuming pure fifth and octave)		\|+ style="font-size: 105%;" \| Tetracot intervals (assuming pure fifth and octave)
	!#		\|-
	!Cents		! #
	!Notation		! Cents
	!Name		! Notation
			! Name
	\|-		\|-
	\| -9		\| −9
	\|820.60		\| 820.60
	\|^Ab		\| ^Ab
	\|supraminor sixth		\| supraminor sixth
	\|-		\|-
	\| -8		\| −8
	\|996.09		\| 996.09
	\|Bb		\| Bb
	\|minor seventh		\| minor seventh
	\|-		\|-
	\| -7		\| −7
	\|1,171.58		\| 1,171.58
	\|vC		\| vC
	\|suboctave		\| suboctave
	\|-		\|-
	\| -6		\| −6
	\|147.07		\| 147.07
	\|Dd		\| Dd
	\|neutral second		\| neutral second
	\|-		\|-
	\| -5		\| −5
	\|322.56		\| 322.56
	\|^Eb		\| ^Eb
	\|supraminor third		\| supraminor third
	\|-		\|-
	\| -4		\| −4
	\|498.05		\| 498.05
	\|F		\| F
	\|perfect fourth		\| perfect fourth
	\|-		\|-
	\| -3		\| −3
	\|673.53		\| 673.53
	\|vG		\| vG
	\|subfifth		\| subfifth
	\|-		\|-
	\| -2		\| −2
	\|849.02		\| 849.02
	\|Ad		\| Ad
	\|neutral sixth		\| neutral sixth
	\|-		\|-
	\| -1		\| −1
	\|1,024.51		\| 1,024.51
	\|^Bb		\| ^Bb
	\|supraminor seventh		\| supraminor seventh
	\|-		\|-
	\|0		\| 0
	\|0.00		\| 0.00
	\|C		\| C
	\|perfect unison / perfect octave		\| perfect unison / perfect octave
	\|-		\|-
	\|1		\| 1
	\|175.49		\| 175.49
	\|vD		\| vD
	\|submajor second		\| submajor second
	\|-		\|-
	\|2		\| 2
	\|350.98		\| 350.98
	\|Ed		\| Ed
	\|neutral third		\| neutral third
	\|-		\|-
	\|3		\| 3
	\|526.47		\| 526.47
	\|^F		\| ^F
	\|superfourth		\| superfourth
	\|-		\|-
	\|4		\| 4
	\|701.96		\| 701.96
	\|G		\| G
	\|perfect fifth		\| perfect fifth
	\|-		\|-
	\|5		\| 5
	\|877.44		\| 877.44
	\|vA		\| vA
	\|submajor sixth		\| submajor sixth
	\|-		\|-
	\|6		\| 6
	\|1,052.93		\| 1,052.93
	\|Bd		\| Bd
	\|neutral seventh		\| neutral seventh
	\|-		\|-
	\|7		\| 7
	\|28.42		\| 28.42
	\|^C		\| ^C
	\|superunison		\| superunison
	\|-		\|-
	\|8		\| 8
	\|203.91		\| 203.91
	\|D		\| D
	\|major second		\| major second
	\|-		\|-
	\|9		\| 9
	\|379.40		\| 379.40
	\|vE		\| vE
	\|submajor third		\| submajor third
	\|}		\|}

	A notable feature of tetracot is the small diesis encountered after 7 steps. This makes tetracot scales cluster around 7edo.		A notable feature of tetracot is the small diesis encountered after 7 steps. This makes tetracot scales cluster around 7edo.

	== Temperament interpretations ==		== Temperament interpretations ==

	=== Tetracot ===		=== Tetracot ===
	The temperament named "tetracot" is one of the simplest 5-limit interpretations. The step is interpreted as [[10/9]], meaning the submajor third is interpreted as [[5/4]], and extends to include prime 11 by mapping the neutral third to [[11/9]] (so that the step stands for both 10/9 and [[11/10]]). It is best tuned with a sharpened generator of around 176 ~~cents~~.		The temperament named "tetracot" is one of the simplest 5-limit interpretations. The step is interpreted as [[10/9]], meaning the submajor third is interpreted as [[5/4]], and extends to include prime 11 by mapping the neutral third to [[11/9]] (so that the step stands for both 10/9 and [[11/10]]). It is best tuned with a sharpened generator of around 176{{c}}.

	==== Monkey ====		==== Monkey ====
	Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].		Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].

Lériendil: /* Temperament interpretations */

2025-09-09T06:44:26Z

Temperament interpretations

← Older revision		Revision as of 06:44, 9 September 2025
Line 112:		Line 112:
	The temperament named "tetracot" is one of the simplest 5-limit interpretations. The step is interpreted as [[10/9]], meaning the submajor third is interpreted as [[5/4]], and extends to include prime 11 by mapping the neutral third to [[11/9]] (so that the step stands for both 10/9 and [[11/10]]). It is best tuned with a sharpened generator of around 176 cents.		The temperament named "tetracot" is one of the simplest 5-limit interpretations. The step is interpreted as [[10/9]], meaning the submajor third is interpreted as [[5/4]], and extends to include prime 11 by mapping the neutral third to [[11/9]] (so that the step stands for both 10/9 and [[11/10]]). It is best tuned with a sharpened generator of around 176 cents.

	=== Monkey ===		==== Monkey ====
	Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].		Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].

Lériendil: /* Temperament interpretations */

2025-09-09T06:42:55Z

Temperament interpretations

← Older revision		Revision as of 06:42, 9 September 2025
Line 113:		Line 113:

	=== Monkey ===		=== Monkey ===
	Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh.		Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh. In monkey, the 7-step diesis represents both [[64/63]] and [[81/80]].