Hemimean clan - Revision history

Lériendil: /* Rectified hebrew */

2026-03-01T04:51:20Z

Rectified hebrew

← Older revision		Revision as of 04:51, 1 March 2026
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	{{Main\| Rectified hebrew }}		{{Main\| Rectified hebrew }}

	Rectified hebrew (37 & 56) is derived from the [https://individual.utoronto.ca/kalendis/hebrew/rect.htm#353 calendar by the same name]. It is leap year pattern takes a stack of 18 Metonic cycle diatonic major scales and truncates the 19th one down to its generator, 11. It adds harmonic 13 through tempering out [[4394/4375]] and spliting the generator of didacus in three. Notably, it is the no-threes restriction of [[sycamore]].		Rectified hebrew (37 & 56) is derived from the [https://individual.utoronto.ca/kalendis/hebrew/rect.htm#353 calendar by the same name]. It is leap year pattern takes a stack of 18 Metonic cycle diatonic major scales and truncates the 19th one down to its generator, 11. It adds harmonic 13 through tempering out [[4394/4375]] and spliting the generator of didacus in three. Notably, it is the no-threes restriction of [[Sycamore family#Septimal sycamore\|sycamore]].

	Subgroup: 2.5.7.13		Subgroup: 2.5.7.13

Lériendil: sycamore

2026-03-01T04:50:50Z

sycamore

← Older revision		Revision as of 04:50, 1 March 2026
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	{{Main\| Rectified hebrew }}		{{Main\| Rectified hebrew }}

	Rectified hebrew (37 & 56) is derived from the [https://individual.utoronto.ca/kalendis/hebrew/rect.htm#353 calendar by the same name]. It is leap year pattern takes a stack of 18 Metonic cycle diatonic major scales and truncates the 19th one down to its generator, 11. It adds harmonic 13 through tempering out [[4394/4375]] and spliting the generator of didacus in three.		Rectified hebrew (37 & 56) is derived from the [https://individual.utoronto.ca/kalendis/hebrew/rect.htm#353 calendar by the same name]. It is leap year pattern takes a stack of 18 Metonic cycle diatonic major scales and truncates the 19th one down to its generator, 11. It adds harmonic 13 through tempering out [[4394/4375]] and spliting the generator of didacus in three. Notably, it is the no-threes restriction of [[sycamore]].

	Subgroup: 2.5.7.13		Subgroup: 2.5.7.13

Xenllium: /* Weak extensions */

2026-02-06T12:18:41Z

Weak extensions

← Older revision		Revision as of 12:18, 6 February 2026
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	== Mowglic ==		== Mowglic ==
	The mowglic temperament (19 & 161) is an extension of the [[~~Syntonic–enneadecal~~ equivalence continuum\|mowgli temperament]] which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit.		The mowglic temperament (19 & 161) is an extension of the [[Syntonic–kleismic equivalence continuum #Mowgli\|mowgli temperament]] which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Undetrita ==		== Undetrita ==
			: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Undetrita (5-limit)]].''

	The undetrita temperament (111 & 118) tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup\|twentcufo temperament]], which is no-sevens version of 111 & 118.		The undetrita temperament (111 & 118) tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup\|twentcufo temperament]], which is no-sevens version of 111 & 118.

Inthar: /* Isra */

2026-02-04T22:19:15Z

Isra

← Older revision		Revision as of 22:19, 4 February 2026
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	== Isra ==		== Isra ==
	Isra results from taking every other generator of [[septimal meantone]], or from [[didacus]] if the generator is interpreted as 9/8. It is named after the Isrāʾ ~~(''iss-RAH'')~~ night journey in the Qur'an, because it is similar to [[luna]] (septimal [[hemithirds]], a didacus extension).		Isra (''iss-RAH'') results from taking every other generator of [[septimal meantone]], or from [[didacus]] if the generator is interpreted as 9/8. It is named after the Isrāʾ night journey in the Qur'an, because it is similar to [[luna]] (septimal [[hemithirds]], a didacus extension).

	[[Subgroup]]: 2.9.5.7		[[Subgroup]]: 2.9.5.7

FloraC: Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

2025-11-27T12:30:50Z

Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

← Older revision		Revision as of 12:30, 27 November 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Hemimean clan\| ]] <!-- main article -->		[[Category:Hemimean clan\| ]] <!-- main article -->
	[[Category:Hemimean\| ]] <!-- key article -->		[[Category:Hemimean\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Overthink: /* Didacus */ + note about undecimal didacus

2025-11-23T18:41:46Z

Didacus: + note about undecimal didacus

← Older revision		Revision as of 18:41, 23 November 2025
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	== Didacus ==		== Didacus ==
	{{main\|Didacus}}		{{main\|Didacus}}

			See also its canonical extension to the 2.5.7.11 subgroup, [[#Undecimal didacus]].

	[[Subgroup]]: 2.5.7		[[Subgroup]]: 2.5.7

BudjarnLambeth at 01:13, 20 October 2025

2025-10-20T01:13:30Z

← Older revision		Revision as of 01:13, 20 October 2025
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	== Undetrita ==		== Undetrita ==
	The undetrita temperament (111 & 118) tempers out the hemimean comma (3136/3125) and [[~~skeetsma~~]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup\|twentcufo temperament]], which is no-sevens version of 111 & 118.		The undetrita temperament (111 & 118) tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup\|twentcufo temperament]], which is no-sevens version of 111 & 118.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Lériendil: /* Hemiwürschmidt */

2025-09-15T23:34:10Z

Hemiwürschmidt

← Older revision		Revision as of 23:34, 15 September 2025
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	Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.840		Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.840

	{{Optimal ET sequence\|legend=1\| 31, 99e, 130~~, 650ce~~, 811ce }}		{{Optimal ET sequence\|legend=1\| 31, 99e, 130, 811ce }}

	Badness: 0.021069		Badness: 0.021069

Lériendil: /* Quadrawürschmidt */

2025-07-08T12:12:59Z

Quadrawürschmidt

← Older revision		Revision as of 12:12, 8 July 2025
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	=== Quadrawürschmidt ===		=== Quadrawürschmidt ===
	This has been documented in Graham Breed's temperament finder as ''semihemiwürschmidt'', but ''quadrawürschmidt'' arguably makes more sense.		This has been documented in Graham Breed's temperament finder as ''semihemiwürschmidt'', but ''quadrawürschmidt'' arguably makes more sense.

			The generator of quadrawürschmidt is essentially a [[septimal meantone]] fifth. However, it is not used to represent [[3/2]], as 3/2 is found at the hemiwürschmidt position, 16 wholetones up. The small comma between the generator and 3/2 is taken to represent [[441/440]].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Lériendil: Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content"

2025-06-24T00:41:15Z

Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:41, 24 June 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Hemimean clan\| ]] <!-- main article -->		[[Category:Hemimean clan\| ]] <!-- main article -->
	[[Category:Hemimean\| ]] <!-- key article -->		[[Category:Hemimean\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]