46032edo - Revision history

ArrowHead294 at 14:59, 20 February 2025

2025-02-20T14:59:20Z

← Older revision		Revision as of 14:59, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	When used as an [[interval size unit]], 46032edo's step size is called a '''flu''' (from ''FLU'', "five-limit unit"), in terms of which the [[cent]] is approximately 38.36 flus. The FLU is useful when crafting irregular or [[circulating temperament]]s with twelve notes to the octave with an eye to its [[5-limit]] approximations.		When used as an [[interval size unit]], 46032edo's step size is called a '''flu''' (from ''FLU'', "five-limit unit"), in terms of which the [[cent]] is approximately 38.36 flus. The FLU is useful when crafting irregular or [[circulating temperament]]s with twelve notes to the octave with an eye to its [[5-limit]] approximations.

Fredg999: Use lowercase for "flu", external link, misc. edits

2024-07-07T22:45:40Z

Use lowercase for "flu", external link, misc. edits

← Older revision		Revision as of 22:45, 7 July 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}} This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is approximately 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.		{{EDO intro}}

	In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 ~~FLUs~~, and the Pythagorean comma, 531441/524228, to 900 ~~FLUs~~. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 ~~FLUs~~, which is the measure in ~~FLUs~~ of the schisma, 32805/32768.		When used as an [[interval size unit]], 46032edo's step size is called a '''flu''' (from ''FLU'', "five-limit unit"), in terms of which the [[cent]] is approximately 38.36 flus. The FLU is useful when crafting irregular or [[circulating temperament]]s with twelve notes to the octave with an eye to its [[5-limit]] approximations.

			== Theory ==
			In the 5-limit, the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the [[syntonic comma]], 81/80, to 825 flus, and the [[Pythagorean comma]], 531441/524228, to 900 flus. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 flus, which is the measure in flus of the schisma, 32805/32768.

	46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic\|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.		46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic\|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|46032}}		{{Harmonics in equal\|46032}}

			== External links ==
			* [http://tonalsoft.com/enc/f/flu.aspx flu] on [[Tonalsoft Encyclopedia]]

	[[Category:Atomic]]		[[Category:Atomic]]

FloraC: Adopt template: EDO intro; +prime error table; -redundant categories

2024-03-24T09:43:45Z

Adopt template: EDO intro; +prime error table; -redundant categories

← Older revision		Revision as of 09:43, 24 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''46032EDO''' is the [[~~EDO~~\|equal division of the octave]] into 46032 parts of approximately 0.02606882 cents each.~~ This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is approximately 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.		{{EDO intro}} This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is approximately 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.

	In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.		In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.
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	46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic\|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.		46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic\|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.

	~~[[Category:Equal divisions of the octave~~\|~~#####]] <!-- 5-digit number -->~~		=== Prime harmonics ===
			{{Harmonics in equal\|46032}}

	[[Category:Atomic]]		[[Category:Atomic]]

Akselai: cents value can't be exact because 137 goes into 46032, but not 5

2024-03-22T18:20:44Z

cents value can't be exact because 137 goes into 46032, but not 5

← Older revision		Revision as of 18:20, 22 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of approximately 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is ~~precisely~~ 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.		'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of approximately 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is approximately 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.

	In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.		In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.

Akselai: cent value can46032

2024-03-22T18:19:41Z

cent value can46032

← Older revision		Revision as of 18:19, 22 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of ~~exactly~~ 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.		'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of approximately 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.

	In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.		In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo\| 161 -84 -12 }} as well as {{monzo\| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.

BudjarnLambeth at 07:17, 9 July 2023

2023-07-09T07:17:12Z

← Older revision		Revision as of 07:17, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.		'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.

BudjarnLambeth at 04:07, 9 July 2023

2023-07-09T04:07:26Z

← Older revision		Revision as of 04:07, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.		'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.

Plumtree: Infobox ET added

2022-10-04T22:28:30Z

Infobox ET added

← Older revision		Revision as of 22:28, 4 October 2022
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			{{Infobox ET}}
	'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.		'''46032EDO''' is the [[EDO\|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.

Fredg999 category edits: Sort key

2022-07-04T01:45:18Z

Sort key

← Older revision		Revision as of 01:45, 4 July 2022
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	46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic\|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.		46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic\|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->
	[[Category:Atomic]]		[[Category:Atomic]]

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

2022-02-26T16:48:53Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 16:48, 26 February 2022
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	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	~~[[Category:Theory]]~~
	[[Category:Atomic]]		[[Category:Atomic]]