1225/1224 - Revision history

FloraC: /* Temperaments */ + relation to the breed temperament

2026-03-25T10:25:46Z

Temperaments: + relation to the breed temperament

← Older revision		Revision as of 10:25, 25 March 2026
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.		[[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.

			Since 1225/1224 factors as (2401/2400)⋅(2500/2499), it would make sense to temper them both out, so noellic can be further tempered to a simple extension of [[breed (temperament)\|breed]] that adds prime 17, though it loses accuracy when compared to breed.

	=== Noellic ===		=== Noellic ===

FloraC: Update data

2026-03-25T10:20:25Z

Update data

← Older revision		Revision as of 10:20, 25 March 2026
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	: mapping generators: ~2, ~3, ~5, ~7		: mapping generators: ~2, ~3, ~5, ~7

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = ~~702~~.~~0440~~{{c}}, ~5/4 = 386.~~1228~~{{c}}, ~7/4 = 968.~~5468~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0477{{c}}, ~3/2 = 701.9872{{c}}, ~5/4 = 386.0466{{c}}, ~7/4 = 968.4796{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9993{{c}}, ~5/4 = 386.0746{{c}}, ~7/4 = 968.4911{{c}}

	{{Optimal ET sequence\|legend=1\| ~~19g,~~ 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}		{{Optimal ET sequence\|legend=1\| 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}

			[[Badness]] (Sintel): 0.0985

	=== Noellismic ===		=== Noellismic ===
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	: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = ~~702~~.~~0440~~{{c}}, ~5/4 = 386.~~1228~~{{c}}, ~7/4 = 968.~~5468~~{{c}}, ~11/8 = 551.~~3179~~{{c}}, ~13/8 = 840.~~5277~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0477{{c}}, ~3/2 = 701.9872{{c}}, ~5/4 = 386.0466{{c}}, ~7/4 = 968.4796{{c}}, ~11/8 = 551.1747{{c}}, ~13/8 = 840.3844{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9993{{c}}, ~5/4 = 386.0746{{c}}, ~7/4 = 968.4911{{c}}, ~11/8 = 551.2309{{c}}, ~13/8 = 840.4346{{c}}

			{{Optimal ET sequence\|legend=1\| 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}

	~~{{Optimal ET sequence\|legend=1\| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}~~		[[Badness]] (Sintel): 0.578

	== Etymology ==		== Etymology ==

FloraC: Expand with some ways to pump it

2026-03-25T10:13:58Z

Expand with some ways to pump it

← Older revision		Revision as of 10:13, 25 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''1225/1224''', the '''noellisma''', is a [[17-limit]] (also 2.3.5.7.17 subgroup) [[comma]] measuring about 1.41 [[cent]]s. It is the difference between [[35/34]] and [[36/35]], and between [[49/48]] and [[51/50]].		'''1225/1224''', the '''noellisma''', is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] (also 2.3.5.7.17-[[subgroup]]) [[comma]] measuring about 1.41 [[cent]]s. It is the amount by which a stack of two [[7/6]] subminor thirds exceeds [[34/25]], and the amount by which a stack of two [[35/24]] subfifths exceeds [[17/8]], one octave above [[17/16]]. It is also the difference between [[35/34]] and [[36/35]], and between [[49/48]] and [[51/50]].

	== Commatic relations ==		== Commatic relations ==
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit results in the rank-6 '''noellismic ~~temperament~~''', or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic ~~temperament~~'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.		[[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.

	=== Noellic ===		=== Noellic ===
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	{{Mapping\|legend=2\| 1 0 0 0 -3 \| 0 1 0 0 -2 \| 0 0 1 0 2 \| 0 0 0 1 2 }}		{{Mapping\|legend=2\| 1 0 0 0 -3 \| 0 1 0 0 -2 \| 0 0 1 0 2 \| 0 0 0 1 2 }}
			: mapping generators: ~2, ~3, ~5, ~7

	~~: sval mapping generators: ~2, ~3, ~5, ~7~~		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0440{{c}}, ~5/4 = 386.1228{{c}}, ~7/4 = 968.5468{{c}}

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

	{{Optimal ET sequence\|legend=1\| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}		{{Optimal ET sequence\|legend=1\| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
	\|}		\|}

	: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0440{{c}}, ~5/4 = 386.1228{{c}}, ~7/4 = 968.5468{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5277{{c}}

	{{Optimal ET sequence\|legend=1\| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}		{{Optimal ET sequence\|legend=1\| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
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	== See also ==		== See also ==
	* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Noellismic]]		[[Category:Noellismic]]
	[[Category:Commas referencing a famous use of a number]]		[[Category:Commas referencing a famous use of a number]]

BudjarnLambeth at 01:56, 16 November 2024

2024-11-16T01:56:29Z

← Older revision		Revision as of 01:56, 16 November 2024
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	[[Category:Noellismic]]		[[Category:Noellismic]]
			[[Category:Commas referencing a famous use of a number]]

FloraC: /* Temperaments */ swap them to impress the reader of the "simpler" temp first

2024-03-28T10:28:56Z

Temperaments: swap them to impress the reader of the "simpler" temp first

@@ Line 26: / Line 26: @@
 == Temperaments ==
 Tempering out this comma in the 17-limit results in the rank-6 '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.
 === Noellismic ===
@@ Line 51: / Line 62: @@
 {{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
 == Etymology ==

FloraC: /* Temperaments */ formatting

2023-07-19T12:34:03Z

Temperaments: formatting

← Older revision		Revision as of 12:34, 19 July 2023
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	[[Subgroup]]: 2.3.5.7.11.13.17		[[Subgroup]]: 2.3.5.7.11.13.17

	[[Mapping]]:		[[Mapping]]: <br>
	<br>[~~{{val~~\| 1 0 0 0 0 0 -3 }}		{\| class="right-all"
	~~<br>{{val~~\| 0 1 0 0 0 0 -2 }}		\|-
	~~<br>{{val~~\| 0 0 1 0 0 0 2 }}		\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| -3 \|\| ],
	~~<br>{{val~~\| 0 0 0 1 0 0 2 }}		\|-
	~~<br>{{val~~\| 0 0 0 0 1 0 0 }}		\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| -2 \|\| ],
	~~<br>{{val~~\| 0 0 0 0 0 1 0 }}		\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 2 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 2 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
			\|}

	~~Mapping~~ generators: ~2, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277
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	[[Subgroup]]: 2.3.5.7.17		[[Subgroup]]: 2.3.5.7.17

	~~[[Sval]] [[mapping]]:~~		{{Mapping\|legend=2\| 1 0 0 0 -3 \| 0 1 0 0 -2 \| 0 0 1 0 2 \| 0 0 0 1 2 }}
	~~<br>[~~{{~~val~~\| 1 0 0 0 -3 }}
	~~<br>{{val~~\| 0 1 0 0 -2 }}
	~~<br>{{val~~\| 0 0 1 0 2 }}
	~~<br>{{val~~\| 0 0 0 1 2 }}

	~~Sval~~ mapping generators: ~2, ~3, ~5, ~7		: sval mapping generators: ~2, ~3, ~5, ~7

	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:35:30Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:35, 7 May 2023
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	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277

	{{~~Val list~~\|legend=1\| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}		{{Optimal ET sequence\|legend=1\| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}

	=== Noellic ===		=== Noellic ===
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	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

	{{~~Val list~~\|legend=1\| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}		{{Optimal ET sequence\|legend=1\| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}

	== Etymology ==		== Etymology ==

FloraC: /* Temperaments */ note on the ranks

2023-02-17T08:10:36Z

Temperaments: note on the ranks

← Older revision		Revision as of 08:10, 17 February 2023
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit results in the '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.		Tempering out this comma in the 17-limit results in the rank-6 '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.

	=== Noellismic ===		=== Noellismic ===
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	=== Noellic ===		=== Noellic ===
	Subgroup: 2.3.5.7.17		[[Subgroup]]: 2.3.5.7.17

	Sval mapping:		[[Sval]] [[mapping]]:
	<br>[{{val\| 1 0 0 0 -3 }}		<br>[{{val\| 1 0 0 0 -3 }}
	<br>{{val\| 0 1 0 0 -2 }}		<br>{{val\| 0 1 0 0 -2 }}
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	Sval mapping generators: ~2, ~3, ~5, ~7		Sval mapping generators: ~2, ~3, ~5, ~7

	Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

	~~Optimal GPV sequence:~~ {{~~val~~ list\| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}		{{Val list\|legend=1\| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}

	== Etymology ==		== Etymology ==

FloraC: Date

2023-02-10T15:19:46Z

Date

← Older revision		Revision as of 15:19, 10 February 2023
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	== Commatic relations ==		== Commatic relations ==
	~~In terms of commas, it~~ is the difference between the following superparticular pairs:		This comma is the difference between the following superparticular pairs:
	* [[273/272]] and [[351/350]]		* [[273/272]] and [[351/350]]
	* [[325/324]] and [[442/441]]		* [[325/324]] and [[442/441]]
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	== Etymology ==		== Etymology ==
	The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.		The noellisma was named by [[Flora Canou]] in 2022. The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.

	== See also ==		== See also ==

FloraC: /* Temperaments */ +subgroup temp

2023-02-10T15:14:57Z

Temperaments: +subgroup temp

← Older revision		Revision as of 15:14, 10 February 2023
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit results in the '''noellismic temperament''', ~~where~~ [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support ~~this temperament~~ below.		Tempering out this comma in the 17-limit results in the '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.

			=== Noellismic ===
	[[Subgroup]]: 2.3.5.7.11.13.17		[[Subgroup]]: 2.3.5.7.11.13.17

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	Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13		Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

			[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277

	{{Val list\|legend=1\| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}		{{Val list\|legend=1\| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}

			=== Noellic ===
			Subgroup: 2.3.5.7.17

			Sval mapping:
			<br>[{{val\| 1 0 0 0 -3 }}
			<br>{{val\| 0 1 0 0 -2 }}
			<br>{{val\| 0 0 1 0 2 }}
			<br>{{val\| 0 0 0 1 2 }}

			Sval mapping generators: ~2, ~3, ~5, ~7

			Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

			Optimal GPV sequence: {{val list\| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}

	== Etymology ==		== Etymology ==