Hemimean clan: Difference between revisions

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* ''[[Passion]]'' (+64/63 or 3125/3087) → [[Passion family #Septimal passion|Passion family]]

* [[Meantone]] (+81/80, 126/125, 225/224) → [[Meantone family #Septimal meantone|Meantone family]]

* ''[[Mohavila]]'' (+135/128 or 1323/1250) → [[~~Pelogic~~ family #Mohavila|~~Pelogic~~ family]]

* ''[[Mohavila]]'' (+135/128 or 1323/1250) → [[Mavila family #Mohavila|Mavila family]]

* ''[[Cohemimabila]]'' (+65536/64827) → [[Mabila family #Cohemimabila|Mabila family]]

* ''[[Sycamore]]'' (+686/675 or 875/864) → [[Sycamore family #Septimal sycamore|Sycamore family]]

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* ''[[Bischismic]]'' (+32805/32768) → [[Schismatic family #Bischismic|Schismatic family]]

* ''[[Clyde]]'' (+245/243) → [[Kleismic family #Clyde|Kleismic family]]

* [[Parakleismic]] (+4375/4374) → [[~~Ragismic microtemperaments~~ #Parakleismic|~~Ragismic microtemperaments~~]]

* [[Parakleismic]] (+4375/4374) → [[Parakleismic family #Parakleismic|Parakleismic family]]

* ''[[Arch]]'' (+5250987/5242880) → [[Escapade family #Arch|Escapade family]]

* ''[[Subpental]]'' (+19683/19600) → [[Sensipent family #Sensipent|Sensipent family]]

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== Didacus ==

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

[[Subgroup]]: 2.5.7

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Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.840

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

Badness: 0.021069

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=== Quadrawürschmidt ===

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

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* [[7-odd-limit]]: ~28/25 = {{monzo| 1/10 -1/20 0 1/20 }}

: {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 11/5 -1/10 0 1/10 | 5/2 -1/4 0 1/4 }}

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/3

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3

* [[9-odd-limit]]: ~28/25 = {{monzo| 6/35 -2/35 0 1/35 }}

: {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 82/35 -4/35 0 2/35 | 20/7 -2/7 0 1/7 }}

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/7

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7

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== 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

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== 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.

: ''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.

[[Subgroup]]: 2.3.5.7

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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 family#Septimal sycamore|sycamore]].

Subgroup: 2.5.7.13

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== 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

@@ Line 11: / Line 11: @@
 * ''[[Passion]]'' (+64/63 or 3125/3087) → [[Passion family #Septimal passion|Passion family]]
 * [[Meantone]] (+81/80, 126/125, 225/224) → [[Meantone family #Septimal meantone|Meantone family]]
-* ''[[Mohavila]]'' (+135/128 or 1323/1250) → [[Pelogic family #Mohavila|Pelogic family]]
+* ''[[Mohavila]]'' (+135/128 or 1323/1250) → [[Mavila family #Mohavila|Mavila family]]
 * ''[[Cohemimabila]]'' (+65536/64827) → [[Mabila family #Cohemimabila|Mabila family]]
 * ''[[Sycamore]]'' (+686/675 or 875/864) → [[Sycamore family #Septimal sycamore|Sycamore family]]
@@ Line 19: / Line 19: @@
 * ''[[Bischismic]]'' (+32805/32768) → [[Schismatic family #Bischismic|Schismatic family]]
 * ''[[Clyde]]'' (+245/243) → [[Kleismic family #Clyde|Kleismic family]]
-* [[Parakleismic]] (+4375/4374) → [[Ragismic microtemperaments #Parakleismic|Ragismic microtemperaments]]
+* [[Parakleismic]] (+4375/4374) → [[Parakleismic family #Parakleismic|Parakleismic family]]
 * ''[[Arch]]'' (+5250987/5242880) → [[Escapade family #Arch|Escapade family]]
 * ''[[Subpental]]'' (+19683/19600) → [[Sensipent family #Sensipent|Sensipent family]]
@@ Line 30: / Line 30: @@
 == Didacus ==
 {{main|Didacus}}
+See also its canonical extension to the 2.5.7.11 subgroup, [[#Undecimal didacus]].
 [[Subgroup]]: 2.5.7
@@ Line 114: / Line 116: @@
 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
@@ Line 185: / Line 187: @@
 === Quadrawürschmidt ===
 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
@@ Line 296: / Line 300: @@
 * [[7-odd-limit]]: ~28/25 = {{monzo| 1/10 -1/20 0 1/20 }}
 : {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 11/5 -1/10 0 1/10 | 5/2 -1/4 0 1/4 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3
 * [[9-odd-limit]]: ~28/25 = {{monzo| 6/35 -2/35 0 1/35 }}
 : {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 82/35 -4/35 0 2/35 | 20/7 -2/7 0 1/7 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
 {{Optimal ET sequence|legend=1| 25, 31, 87, 118 }}
@@ Line 682: / Line 686: @@
 == Mowglic ==
-The mowglic temperament (19 &amp; 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 &amp; 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
@@ Line 856: / Line 860: @@
 == Undetrita ==
-The undetrita temperament (111 &amp; 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 &amp; 118.
+: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Undetrita (5-limit)]].''
+The undetrita temperament (111 &amp; 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 &amp; 118.
 [[Subgroup]]: 2.3.5.7
@@ Line 994: / Line 1,000: @@
 {{Main| Rectified hebrew }}
-Rectified hebrew (37 &amp; 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 &amp; 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
@@ Line 1,009: / Line 1,015: @@
 == 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