Ploidacot/Omega-tricot - Revision history

Xenllium at 11:08, 7 January 2026

2026-01-07T11:08:05Z

← Older revision		Revision as of 11:08, 7 January 2026
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	'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.		'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.

	== ~~Notation~~ ==		== Intervals and notation ==
	While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^C and vC# are enharmonic.		While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^C and vC# are enharmonic.

Xenllium at 11:04, 7 January 2026

2026-01-07T11:04:13Z

← Older revision		Revision as of 11:04, 7 January 2026
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	== Notation ==		== Notation ==
	While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic.		While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^C and vC# are enharmonic.

	{\| class="wikitable"		{\| class="wikitable"
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	In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.		In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

	[[Category:Ploidacots]]		[[Category:Ploidacots\|Omega-tricot]]

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

2026-01-06T09:43:19Z

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

← Older revision		Revision as of 09:43, 6 January 2026
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	In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.		In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

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

Xenllium at 06:53, 4 January 2026

2026-01-04T06:53:13Z

← Older revision		Revision as of 06:53, 4 January 2026
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=3\|Pergen=[P8, P4/3]\|Forms=7, 8, 15\|Title=Omega-tricot\|Wedgie=3}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=3\|Pergen=[P8, P4/3]\|Forms=7, 8, 15, 22\|Title=Omega-tricot (beta-tricot)\|Wedgie=3}}
	'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.		'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.

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	{\| class="wikitable"		{\| class="wikitable"
			\|+ style="font-size: 105%;" \| Omega-tricot intervals (assuming pure fifth and octave)
	\|-		\|-
	! #		! #
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	\| 0		\| 0
	\| C		\| C
	\| perfect unison ~~/ perfect octave~~		\| perfect unison
	\|-		\|-
	\| 1		\| 1
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	In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.		In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

	~~{{Todo\| unify precision }}~~		[[Category:Ploidacot]]

VectorGraphics at 23:30, 25 October 2025

2025-10-25T23:30:04Z

← Older revision		Revision as of 23:30, 25 October 2025
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=3\|Pergen=[P8, P4/3]\|Forms=7, 8, 15\|Title=Omega-tricot}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=3\|Pergen=[P8, P4/3]\|Forms=7, 8, 15\|Title=Omega-tricot\|Wedgie=3}}
	'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.		'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.

Lériendil: /* Superpine */

2025-09-12T06:04:11Z

Superpine

← Older revision		Revision as of 06:04, 12 September 2025
Line 113:		Line 113:

	=== Superpine ===		=== Superpine ===
	In [[superpine]], the generator is mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.		In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

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

Lériendil: /* Temperament interpretations */

2025-09-12T06:04:02Z

Temperament interpretations

← Older revision		Revision as of 06:04, 12 September 2025
Line 113:		Line 113:

	=== Superpine ===		=== Superpine ===
	In [[superpine]], the generator is mapped to 11/10, and the mapping for 5 is as in meantone, so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.		In [[superpine]], the generator is mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

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

Lériendil: /* Superpine */

2025-09-12T06:03:16Z

Superpine

← Older revision		Revision as of 06:03, 12 September 2025
Line 113:		Line 113:

	=== Superpine ===		=== Superpine ===
	In [[superpine]], the ~~subminor seventh (C–vBb, 13 generators up)~~ is mapped to 7/4, and the ~~mappings~~ for ~~3 and~~ 5 ~~are~~ as in meantone, so −3 generators is [[3/2]] ~~and −12~~ generators is [[5/4]]. It is best tuned with a slightly sharp generator of about 168{{c}}.		In [[superpine]], the generator is mapped to 11/10, and the mapping for 5 is as in meantone, so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

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

ArrowHead294 at 16:01, 9 September 2025

2025-09-09T16:01:12Z

Show changes

VectorGraphics at 00:23, 2 September 2025

2025-09-02T00:23:02Z

← Older revision		Revision as of 00:23, 2 September 2025
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	{{Breadcrumb}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=3\|Pergen=[P8, P4/3]\|Forms=7, 8, 15\|Title=Omega-tricot}}'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.

	'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.

	== Notation ==		== Notation ==