Ploidacot/Enneacot - Revision history

Xenllium at 10:33, 8 January 2026

2026-01-08T10:33:21Z

← Older revision		Revision as of 10:33, 8 January 2026
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	{{Breadcrumb}}		{{Breadcrumb}}
	{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=9\|Pergen=[P8, P5/9]\|Forms=15, 16, 31\|Title=Enneacot\|Wedgie=9}}		{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=9\|Pergen=[P8, P5/9]\|Forms=15, 16, 31\|Title=Enneacot\|Wedgie=9}}
	'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three.		'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[Ploidacot/Tricot\|tricot]] intervals, as the tricot generator is split further into three.

	Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.		Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.
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	[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].		[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].

	[[Category:Ploidacots]]		[[Category:Ploidacots\|Enneacot]]

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

2026-01-06T09:43:59Z

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

← Older revision		Revision as of 09:43, 6 January 2026
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	[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].		[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].

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

Xenllium at 09:41, 4 January 2026

2026-01-04T09:41:19Z

← Older revision		Revision as of 09:41, 4 January 2026
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			{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=9\|Pergen=[P8, P5/9]\|Forms=15, 16, 31\|Title=Enneacot\|Wedgie=9}}
	'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three.		'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three.

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	=== Valentine ===		=== Valentine ===
	[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].		[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].

			[[Category:Ploidacot]]

Overthink: add trailing zeros

2025-12-22T20:53:03Z

add trailing zeros

← Older revision		Revision as of 20:53, 22 December 2025
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	\|-		\|-
	\| −8		\| −8
	\| 576.04		\| 576.040
	\|		\|
	\|		\|
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	\|-		\|-
	\| −6		\| −6
	\| 732.03		\| 732.030
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	\|		\|
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	\| −4		\| −4
	\| 888.02		\| 888.020
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	\|		\|
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	\| −2		\| −2
	\| 1044.01		\| 1044.010
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	\|		\|
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	\| 0		\| 0
	\| 0		\| 0.000
	\| C		\| C
	\| perfect unison		\| perfect unison
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	\| 2		\| 2
	\| 155.99		\| 155.990
	\|		\|
	\|		\|
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	\| 4		\| 4
	\| 311.98		\| 311.980
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	=== Valentine ===		=== Valentine ===
	[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].		[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].

	~~{{Todo\| unify precision }}~~

ArrowHead294 at 16:04, 9 September 2025

2025-09-09T16:04:50Z

← Older revision		Revision as of 16:04, 9 September 2025
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	'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three.		'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three.

	Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.		Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.

	== Intervals and notation ==		== Intervals and notation ==
	Due to dividing the fifth into so many steps, standard notation becomes almost useless for enneacot. Regardless, notation has been provided for where [[Ploidacot/Monocot\|monocot]] intervals appear in this system.		Due to dividing the fifth into so many steps, standard notation becomes almost useless for enneacot. Regardless, notation has been provided for where [[Ploidacot/Monocot\|monocot]] intervals appear in this system.

	{\| class="wikitable"		{\| class="wikitable"
	\|+Enneacot intervals (assuming pure fifth and octave)		\|+ style="font-size: 105%;" \| Enneacot intervals (assuming pure fifth and octave)
	!#		\|-
	!Cents		! #
	!Notation		! Cents
	!Name		! Notation
			! Name
	\|-		\|-
	\| -9		\| −9
	\|498.045		\| 498.045
	\|F		\| F
	\|perfect fourth		\| perfect fourth
	\|-		\|-
	\| -8		\| −8
	\|576.04		\| 576.04
	\|		\|
	\|		\|
	\|-		\|-
	\| -7		\| −7
	\|654.035		\| 654.035
	\|		\|
	\|		\|
	\|-		\|-
	\| -6		\| −6
	\|732.03		\| 732.03
	\|		\|
	\|		\|
	\|-		\|-
	\| -5		\| −5
	\|810.025		\| 810.025
	\|		\|
	\|		\|
	\|-		\|-
	\| -4		\| −4
	\|888.02		\| 888.02
	\|		\|
	\|		\|
	\|-		\|-
	\| -3		\| −3
	\|966.015		\| 966.015
	\|		\|
	\|		\|
	\|-		\|-
	\| -2		\| −2
	\|1044.01		\| 1044.01
	\|		\|
	\|		\|
	\|-		\|-
	\| -1		\| −1
	\|1122.005		\| 1122.005
	\|		\|
	\|		\|
	\|-		\|-
	\|0		\| 0
	\|0		\| 0
	\|C		\| C
	\|perfect unison		\| perfect unison
	\|-		\|-
	\|1		\| 1
	\|77.995		\| 77.995
	\|		\|
	\|		\|
	\|-		\|-
	\|2		\| 2
	\|155.99		\| 155.99
	\|		\|
	\|		\|
	\|-		\|-
	\|3		\| 3
	\|233.985		\| 233.985
	\|		\|
	\|		\|
	\|-		\|-
	\|4		\| 4
	\|311.98		\| 311.98
	\|		\|
	\|		\|
	\|-		\|-
	\|5		\| 5
	\|389.975		\| 389.975
	\|		\|
	\|		\|
	\|-		\|-
	\|6		\| 6
	\|467.97		\| 467.97
	\|		\|
	\|		\|
	\|-		\|-
	\|7		\| 7
	\|545.965		\| 545.965
	\|		\|
	\|		\|
	\|-		\|-
	\|8		\| 8
	\|623.96		\| 623.96
	\|		\|
	\|		\|
	\|-		\|-
	\|9		\| 9
	\|701.955		\| 701.955
	\|G		\| G
	\|perfect fifth		\| perfect fifth
	\|}		\|}

	== Temperament interpretations ==		== Temperament interpretations ==
			=== Valentine ===
			[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].

	~~=== Valentine ===~~
	[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].
	{{Todo\| unify precision }}		{{Todo\| unify precision }}

Lériendil at 03:17, 6 September 2025

2025-09-06T03:17:46Z

← Older revision		Revision as of 03:17, 6 September 2025
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	{{Breadcrumb}}		{{Breadcrumb}}

	'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave.		'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three.

	Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.		Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.

Lériendil at 03:15, 6 September 2025

2025-09-06T03:15:45Z

← Older revision		Revision as of 03:15, 6 September 2025
Line 113:		Line 113:

	=== Valentine ===		=== Valentine ===
	[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is 5/4, 4 is 6/5, and 3 is 8/7. It can be extended to the 11-limit by setting 7 steps to 11/8; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to 32/13.		[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].
	{{Todo\| unify precision }}		{{Todo\| unify precision }}

Lériendil at 03:15, 6 September 2025

2025-09-06T03:15:07Z

← Older revision		Revision as of 03:15, 6 September 2025
Line 113:		Line 113:

	=== Valentine ===		=== Valentine ===
	Valentine is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is 5/4, 4 is 6/5, and 3 is 8/7. It can be extended to the 11-limit by setting 7 steps to 11/8, ~~and to~~ the ~~13-limit by setting 11 steps~~ to 13/8.		[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is 5/4, 4 is 6/5, and 3 is 8/7. It can be extended to the 11-limit by setting 7 steps to 11/8; [[Valentine extensions\|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to 32/13.

	{{Todo\| unify precision }}		{{Todo\| unify precision }}

FloraC: Todo

2025-09-01T09:31:05Z

Todo

← Older revision		Revision as of 09:31, 1 September 2025
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	=== Valentine ===		=== Valentine ===
	Valentine is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is 5/4, 4 is 6/5, and 3 is 8/7. It can be extended to the 11-limit by setting 7 steps to 11/8, and to the 13-limit by setting 11 steps to 13/8.		Valentine is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is 5/4, 4 is 6/5, and 3 is 8/7. It can be extended to the 11-limit by setting 7 steps to 11/8, and to the 13-limit by setting 11 steps to 13/8.

			{{Todo\| unify precision }}

VectorGraphics at 05:21, 1 September 2025

2025-09-01T05:21:46Z

← Older revision		Revision as of 05:21, 1 September 2025
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			{{Breadcrumb}}

	'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave.		'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave.