Blare comma - Revision history

FloraC: Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

2025-06-06T16:39:21Z

Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

← Older revision		Revision as of 16:39, 6 June 2025
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	{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs\|254860}}[-9]		{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs\|254860}}[-9]

	[[Badness]] (~~Dirichlet~~): 0.78992		[[Badness]] (Sintel): 0.78992

	=== Blazen ===		=== Blazen ===

BudjarnLambeth at 00:06, 4 November 2024

2024-11-04T00:06:05Z

← Older revision		Revision as of 00:06, 4 November 2024
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	=== Blare ===		=== Blare ===
	Tempering out this interval in the full [[11-limit]] leads to the '''blare family'''.		Tempering out this interval in the full [[11-limit]] leads to the '''blare family'''.

			[[Category:Commas named for their regular temperament properties]]

Akselai: the rank 2 temperament is useless for 2.9.7.11. also write monzos in subgroup instead of in full p-limit. also use dirichlet badness (this temp is actually really really bad).

2024-04-28T10:03:18Z

the rank 2 temperament is useless for 2.9.7.11. also write monzos in subgroup instead of in full p-limit. also use dirichlet badness (this temp is actually really really bad).

← Older revision		Revision as of 10:03, 28 April 2024
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	== Temperaments ==		== Temperaments ==
			=== Loudspeaker ===
	Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.		Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.

	=== Rank-3 ===		==== Rank-3 ====
	==== Loudspeaker ====		===== Loudspeaker =====
	[[Subgroup]]: 2.9.7.11		[[Subgroup]]: 2.9.7.11

	[[Comma list]]: {{monzo\| -51 -~~24 0~~ 12 16 }}		[[Comma list]]: {{monzo\| -51 -12 12 16 }}

	{{Mapping\|legend=2\| 4 12 13 12 \| 0 1 1 0 \| 0 0 -4 3 }}		{{Mapping\|legend=2\| 4 12 13 12 \| 0 1 1 0 \| 0 0 -4 3 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~{{monzo\| 13 ~~6 0~~ -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo\| 16 ~~8 0~~ -4 -5 }} = 183.772		* [[CTE]]: ~{{monzo\| 13 3 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo\| 16 4 -4 -5 }} = 183.772

	{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs\|254860}}[-9]		{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs\|254860}}[-9]

	[[Badness]] (~~Smith~~): ~~7 × 10<sup>-6</sup>~~		[[Badness]] (Dirichlet): 0.78992

	=== ~~Rank-2~~ ===		=== Blazen ===
	~~==== Microphone ====~~		Tempering out this interval in the no-fives [[11-limit]] (2.3.7.11 subgroup) leads to the '''blazen family'''.
	~~{{see also\| 44th~~-~~octave temperaments}}~~

	~~This temperament additionally tempers out the parismina [1 -26 0 2 10⟩, which is even smaller than the blare comma. Surprisingly, this temperament admits an optimal generator very close to [[3/2]].~~		=== Blare ===
			Tempering out this interval in the full [[11-limit]] leads to the '''blare family'''.
	~~[[Subgroup]]: 2.9.7.11~~

	~~[[Comma list]]: {{monzo\| -52 2 0 10 6 }}, {{monzo\| 1 -26 0 2 10 }}~~

	~~{{Mapping\|legend~~=~~2\| 44 88 175 75 \| 0 2 -2 3 }}~~

	~~[[Optimal tuning]]s:~~
	* [[CTE]]: ~64/63 = ~~1\44~~ = ~~27.273, ~{{monzo\| 25 0 0 -5 -3 }}~~ = ~~701.953~~

	~~{{Optimal ET sequence\|legend~~=~~1\| 176, 484, 660, 836, 1012, 1848, 4708, 6556, 11264, 17820, 29084, 46904, 75988, 122892}}~~

	[[~~Badness~~]] ~~(Smith): 2~~.~~466 × 10<sup>-3</sup>~~

Akselai: /* Temperaments */

2024-04-24T12:50:51Z

Temperaments

← Older revision		Revision as of 12:50, 24 April 2024
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	Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.		Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.

	=== Loudspeaker ===		=== Rank-3 ===
			==== Loudspeaker ====
	[[Subgroup]]: 2.9.7.11		[[Subgroup]]: 2.9.7.11

	[[Comma list]]: {{monzo\| 51 -24 0 12 16 }}		[[Comma list]]: {{monzo\| -51 -24 0 12 16 }}

	{{Mapping\|legend=1\| 4 12 13 12 \| 0 1 1 0 \| 0 0 -4 3 }}		{{Mapping\|legend=2\| 4 12 13 12 \| 0 1 1 0 \| 0 0 -4 3 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~{{monzo\| 13 6 0 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo\| 16 8 0 -4 -5 }} = 183.772		* [[CTE]]: ~{{monzo\| 13 6 0 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo\| 16 8 0 -4 -5 }} = 183.772

	{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012}}		{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs\|254860}}[-9]

	[[Badness]]: 7 × 10<sup>-6</sup>		[[Badness]] (Smith): 7 × 10<sup>-6</sup>

			=== Rank-2 ===
			==== Microphone ====
			{{see also\| 44th-octave temperaments}}

			This temperament additionally tempers out the parismina [1 -26 0 2 10⟩, which is even smaller than the blare comma. Surprisingly, this temperament admits an optimal generator very close to [[3/2]].

			[[Subgroup]]: 2.9.7.11

			[[Comma list]]: {{monzo\| -52 2 0 10 6 }}, {{monzo\| 1 -26 0 2 10 }}

			{{Mapping\|legend=2\| 44 88 175 75 \| 0 2 -2 3 }}

			[[Optimal tuning]]s:
			* [[CTE]]: ~64/63 = 1\44 = 27.273, ~{{monzo\| 25 0 0 -5 -3 }} = 701.953

			{{Optimal ET sequence\|legend=1\| 176, 484, 660, 836, 1012, 1848, 4708, 6556, 11264, 17820, 29084, 46904, 75988, 122892}}

			[[Badness]] (Smith): 2.466 × 10<sup>-3</sup>

FloraC: Internalize internal links (as it should). Template-ize monzo notation. Bold the neologism; +links

2024-04-22T15:30:29Z

Internalize internal links (as it should). Template-ize monzo notation. Bold the neologism; +links

← Older revision		Revision as of 15:30, 22 April 2024
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	}}		}}

	The '''blare comma''' is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] comma in the 2.9.7.11 subgroup, with a size of only 0.078 [[cent]]s. It is the interval in which twelve [[9/7]] septimal major thirds plus three octaves fall short by sixteen [[11/8]] undecimal major fourths.		The '''blare comma''' is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] in the 2.9.7.11 [[subgroup]], with a size of only 0.078 [[cent]]s. It is the interval in which twelve [[9/7]] septimal major thirds plus three octaves fall short by sixteen [[11/8]] undecimal major fourths.

	It is named in analogy with the industrial theme of [~~https://en.xen.wiki/w/Subgroup_temperaments~~#2.9.7.~~11_subgroup~~ 2.9.7.11 subgroup temperaments], "blare" being a word used to describe the loud and piercing noise of machines.		It is named in analogy with the industrial theme of [[Subgroup temperaments #2.9.7.11 subgroup\|2.9.7.11 subgroup temperaments]], "blare" being a word used to describe the loud and piercing noise of machines.

	Tempering out this interval leads to the loudspeaker family of microtemperaments.		== Temperaments ==
			Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.
	~~== Related temperaments ==~~

	=== Loudspeaker ===		=== Loudspeaker ===

	[[Subgroup]]: 2.9.7.11		[[Subgroup]]: 2.9.7.11

	[[Comma list]]: [51 -24 0 12 ~~16⟩~~		[[Comma list]]: {{monzo\| 51 -24 0 12 16 }}

	{{Mapping\|legend=1\| 4 12 13 12 \| 0 1 1 0 \| 0 0 -4 3 }}		{{Mapping\|legend=1\| 4 12 13 12 \| 0 1 1 0 \| 0 0 -4 3 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~[13 6 0 -3 -4⟩ = 1\4 = 300.000, ~9/8 = 203.912, ~[16 8 0 -4 -5⟩ = 183.772		* [[CTE]]: ~{{monzo\| 13 6 0 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo\| 16 8 0 -4 -5 }} = 183.772

	{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012}}		{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012}}

	[[Badness]]: 7 × 10<sup>-6</sup>		[[Badness]]: 7 × 10<sup>-6</sup>

Akselai at 14:53, 22 April 2024

2024-04-22T14:53:05Z

← Older revision		Revision as of 14:53, 22 April 2024
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~[13 6 0 -3 -4⟩ = ~1\4 = 300.000, ~9/8 = 203.912, ~[16 8 0 -4 -5⟩ = 183.772		* [[CTE]]: ~[13 6 0 -3 -4⟩ = 1\4 = 300.000, ~9/8 = 203.912, ~[16 8 0 -4 -5⟩ = 183.772

	{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012}}		{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012}}

	[[Badness]]: 7 × 10<sup>-6</sup>		[[Badness]]: 7 × 10<sup>-6</sup>

Akselai: my bad, forgot to add this temperament

2024-04-22T14:36:43Z

my bad, forgot to add this temperament

← Older revision		Revision as of 14:36, 22 April 2024
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	It is named in analogy with the industrial theme of [https://en.xen.wiki/w/Subgroup_temperaments#2.9.7.11_subgroup 2.9.7.11 subgroup temperaments], "blare" being a word used to describe the loud and piercing noise of machines.		It is named in analogy with the industrial theme of [https://en.xen.wiki/w/Subgroup_temperaments#2.9.7.11_subgroup 2.9.7.11 subgroup temperaments], "blare" being a word used to describe the loud and piercing noise of machines.

			Tempering out this interval leads to the loudspeaker family of microtemperaments.

			== Related temperaments ==

			=== Loudspeaker ===

			[[Subgroup]]: 2.9.7.11

			[[Comma list]]: [51 -24 0 12 16⟩

			{{Mapping\|legend=1\| 4 12 13 12 \| 0 1 1 0 \| 0 0 -4 3 }}

			[[Optimal tuning]]s:
			* [[CTE]]: ~[13 6 0 -3 -4⟩ = ~1\4 = 300.000, ~9/8 = 203.912, ~[16 8 0 -4 -5⟩ = 183.772

			{{Optimal ET sequence\|legend=1\| 20, 32}}[+9], {{EDOs\|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012}}

			[[Badness]]: 7 × 10<sup>-6</sup>

Sintel: 'loudspeaker' not attested anywhere

2024-04-22T13:31:16Z

'loudspeaker' not attested anywhere

← Older revision		Revision as of 13:31, 22 April 2024
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	It is named in analogy with the industrial theme of [https://en.xen.wiki/w/Subgroup_temperaments#2.9.7.11_subgroup 2.9.7.11 subgroup temperaments], "blare" being a word used to describe the loud and piercing noise of machines.		It is named in analogy with the industrial theme of [https://en.xen.wiki/w/Subgroup_temperaments#2.9.7.11_subgroup 2.9.7.11 subgroup temperaments], "blare" being a word used to describe the loud and piercing noise of machines.

	~~Tempering out this interval leads to the [[loudspeaker family]] of microtemperaments.~~

Akselai: delete nonstandard fjs notation

2024-03-27T13:38:55Z

delete nonstandard fjs notation

← Older revision		Revision as of 13:38, 27 March 2024
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	\| Monzo = -51 -24 0 12 16		\| Monzo = -51 -24 0 12 16
	\| Name = blare comma		\| Name = blare comma
	\| FJS name = ~~9d4^{7^{12}, 11^{16} }~~		\| FJS name = -
	\| Color name = Laquadquadlo-aquadtrizo comma		\| Color name = Laquadquadlo-aquadtrizo comma
	\| Comma = yes		\| Comma = yes

Akselai: corrected infobox

2024-02-01T23:19:21Z

corrected infobox

← Older revision		Revision as of 23:19, 1 February 2024
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	{{Infobox Interval		{{Infobox Interval
	\| ~~Ratio~~ = ~~1542511279331105/1542441841901568~~		\| Monzo = -51 -24 0 12 16
	\| Name = blare comma		\| Name = blare comma
			\| FJS name = 9d4^{7^{12}, 11^{16} }
	\| Color name = Laquadquadlo-aquadtrizo comma		\| Color name = Laquadquadlo-aquadtrizo comma
	\| Comma = yes		\| Comma = yes