Hewuermera comma - Revision history

Lériendil at 14:57, 4 February 2026

2026-02-04T14:57:21Z

← Older revision		Revision as of 14:57, 4 February 2026
Line 9:		Line 9:

	== Factorizations ==		== Factorizations ==
	As a generalized lopsided comma, 589824/588245 has the S-expression of (S46 = [[2116/2115]]) × (S47 = [[2209/2208]])<sup>2</sup> × (S48 = [[2304/2303]])<sup>3</sup>. Equivalent factorizations include (S48 = 2304/2303) × (S(47/2) = [[2209/2205]]) and (S46×S47×S48 = [[736/735]]) × (S47×S48 = [[1128/1127]]) × (S48 = 2304/2303).		As a generalized lopsided comma, 589824/588245 has the S-expression of (S46 = [[2116/2115]]) × (S47 = [[2209/2208]])<sup>2</sup> × (S48 = [[2304/2303]])<sup>3</sup>. Equivalent factorizations include (S48 = 2304/2303)<sup>2</sup> × (S(47/2) = [[2209/2205]]) and (S46×S47×S48 = [[736/735]]) × (S47×S48 = [[1128/1127]]) × (S48 = 2304/2303).

	The S-factorization indicates that 23 and 47 are particularly natural primes to incorporate into hewuermera temperaments (by tempering out S46, S47, and S48); in particular, three 8/7s reach a "[[1/2-comma meantone]] fifth" identified with [[70/47]][[~]][[94/63]].		The S-factorization indicates that 23 and 47 are particularly natural primes to incorporate into hewuermera temperaments (by tempering out S46, S47, and S48); in particular, three 8/7s reach a "[[1/2-comma meantone]] fifth" identified with [[70/47]][[~]][[94/63]].

Lériendil at 06:42, 15 August 2025

2025-08-15T06:42:48Z

← Older revision		Revision as of 06:42, 15 August 2025
Line 6:		Line 6:
	}}		}}

	'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount by which a stack of six [[8/7]]s exceed [[20/9]]. It can also be expressed as the difference between three intervals of {{S\|7}} = [[49/48]] and S4 = [[16/15]].		'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount by which a stack of six [[8/7]]s exceed [[20/9]]. It can also be expressed as the difference between three intervals of {{S\|7}} = [[49/48]] and S4 = [[16/15]], or as (S6/S7 = [[1728/1715]])/(S7/S8 = [[1029/1024]]).

	== Factorizations ==		== Factorizations ==

Lériendil at 06:41, 15 August 2025

2025-08-15T06:41:25Z

← Older revision		Revision as of 06:41, 15 August 2025
Line 14:		Line 14:

	== Temperaments ==		== Temperaments ==
	Tempering it out alone in the 7-limit leads to the '''hewuermera''' [[rank-3 temperament]], and in combination with another comma, to the [[hewuermera temperaments]], the most notable of which are [[hemiwürschmidt]] and [[mothra]]. For highest accuracy, this comma demands that 8/7 be tuned slightly flat, as it is in [[EDO]]s such as {{EDOs\|26, 99, and ~~161~~}}.		Tempering it out alone in the 7-limit leads to the '''hewuermera''' [[rank-3 temperament]], and in combination with another comma, to the [[hewuermera temperaments]], the most notable of which are [[hemiwürschmidt]] and [[mothra]]. For highest accuracy, this comma demands that 8/7 be tuned slightly flat, as it is in [[EDO]]s such as {{EDOs\|26, 68, and 99}}.

	== Etymology ==		== Etymology ==

Lériendil at 17:21, 14 August 2025

2025-08-14T17:21:13Z

← Older revision		Revision as of 17:21, 14 August 2025
Line 11:		Line 11:
	As a generalized lopsided comma, 589824/588245 has the S-expression of (S46 = [[2116/2115]]) × (S47 = [[2209/2208]])<sup>2</sup> × (S48 = [[2304/2303]])<sup>3</sup>. Equivalent factorizations include (S48 = 2304/2303) × (S(47/2) = [[2209/2205]]) and (S46×S47×S48 = [[736/735]]) × (S47×S48 = [[1128/1127]]) × (S48 = 2304/2303).		As a generalized lopsided comma, 589824/588245 has the S-expression of (S46 = [[2116/2115]]) × (S47 = [[2209/2208]])<sup>2</sup> × (S48 = [[2304/2303]])<sup>3</sup>. Equivalent factorizations include (S48 = 2304/2303) × (S(47/2) = [[2209/2205]]) and (S46×S47×S48 = [[736/735]]) × (S47×S48 = [[1128/1127]]) × (S48 = 2304/2303).

	The S-factorization indicates that 23 and 47 are particularly natural primes to incorporate into hewuermera temperaments (by tempering out S46, S47, and S48); in particular, three 8/7s reach a "[[~~half~~-comma meantone]] fifth" identified with [[70/47]][[~]][[94/63]].		The S-factorization indicates that 23 and 47 are particularly natural primes to incorporate into hewuermera temperaments (by tempering out S46, S47, and S48); in particular, three 8/7s reach a "[[1/2-comma meantone]] fifth" identified with [[70/47]][[~]][[94/63]].

	== Temperaments ==		== Temperaments ==

Lériendil: unstubbed the article

2025-08-14T17:21:02Z

unstubbed the article

← Older revision		Revision as of 17:21, 14 August 2025
Line 6:		Line 6:
	}}		}}

	'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount, by which a stack of six [[8/7]]s exceed [[20/9]]. Tempering it out leads to the [[hewuermera temperaments]]. The comma was named by [[User:Xenllium\|Xenllium]] in 2021.		'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount by which a stack of six [[8/7]]s exceed [[20/9]]. It can also be expressed as the difference between three intervals of {{S\|7}} = [[49/48]] and S4 = [[16/15]].

			== Factorizations ==
			As a generalized lopsided comma, 589824/588245 has the S-expression of (S46 = [[2116/2115]]) × (S47 = [[2209/2208]])<sup>2</sup> × (S48 = [[2304/2303]])<sup>3</sup>. Equivalent factorizations include (S48 = 2304/2303) × (S(47/2) = [[2209/2205]]) and (S46×S47×S48 = [[736/735]]) × (S47×S48 = [[1128/1127]]) × (S48 = 2304/2303).

			The S-factorization indicates that 23 and 47 are particularly natural primes to incorporate into hewuermera temperaments (by tempering out S46, S47, and S48); in particular, three 8/7s reach a "[[half-comma meantone]] fifth" identified with [[70/47]][[~]][[94/63]].

			== Temperaments ==
			Tempering it out alone in the 7-limit leads to the '''hewuermera''' [[rank-3 temperament]], and in combination with another comma, to the [[hewuermera temperaments]], the most notable of which are [[hemiwürschmidt]] and [[mothra]]. For highest accuracy, this comma demands that 8/7 be tuned slightly flat, as it is in [[EDO]]s such as {{EDOs\|26, 99, and 161}}.

			== Etymology ==
			The comma was named by [[User:Xenllium\|Xenllium]] in 2021, from a combination of hemiwürschmidt and [[gamera]], two 7-limit temperaments that share this tempered comma.

			[[Category:Commas named by combining multiple temperament names]]
			[[Category:Commas named after other creatives]]
			[[Category:Commas named after compositions]]

BudjarnLambeth: Ratio

2024-02-19T04:38:35Z

Ratio

← Older revision		Revision as of 04:38, 19 February 2024
Line 2:		Line 2:
	\|Name = Hewuermera comma		\|Name = Hewuermera comma
	\|Color name = sr<sup>6</sup>g-3, satribiru-agu negative 3rd		\|Color name = sr<sup>6</sup>g-3, satribiru-agu negative 3rd
			\|Ratio = 589824/588245
	\|Comma = yes		\|Comma = yes
	}}		}}

	'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount, by which a stack of six [[8/7]]s exceed [[20/9]]. Tempering it out leads to the [[hewuermera temperaments]]. The comma was named by [[User:Xenllium\|Xenllium]] in 2021.		'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount, by which a stack of six [[8/7]]s exceed [[20/9]]. Tempering it out leads to the [[hewuermera temperaments]]. The comma was named by [[User:Xenllium\|Xenllium]] in 2021.

BudjarnLambeth: BudjarnLambeth moved page 589824/588245 to Hewuermera comma over redirect: Big comma number

2024-02-19T04:26:48Z

BudjarnLambeth moved page 589824/588245 to Hewuermera comma over redirect: Big comma number

← Older revision	Revision as of 04:26, 19 February 2024
(No difference)

Francium: Created page with "{{Infobox Interval |Name = Hewuermera comma |Color name = sr⁶g-3, satribiru-agu negative 3rd |Comma = yes }} '''589824/588245''', the '''hewuermera comma''', is a..."

2023-11-05T17:44:13Z

Created page with "{{Infobox Interval |Name = Hewuermera comma |Color name = sr<sup>6</sup>g-3, satribiru-agu negative 3rd |Comma = yes }} '''589824/588245''', the '''hewuermera comma''', is a..."

New page

{{Infobox Interval
|Name = Hewuermera comma
|Color name = sr<sup>6</sup>g-3, satribiru-agu negative 3rd
|Comma = yes
}}

'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount, by which a stack of six [[8/7]]s exceed [[20/9]]. Tempering it out leads to the [[hewuermera temperaments]]. The comma was named by [[User:Xenllium|Xenllium]] in 2021.