Semicathartismic clan: Difference between revisions

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The '''~~semicanousmic~~ clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[~~semicanousma~~]] ({{monzo|legend=1| -2 -6 -1 0 4 }}, [[ratio]]: 14641/14580).

The '''semicathartismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[semicathartisma]] ({{monzo|legend=1| -2 -6 -1 0 4 }}, [[ratio]]: 14641/14580).

For the rank-4 ~~semicanousmic~~ temperament, see [[Catalog of rank-4 temperaments #~~Semicanousmic~~ (14641/14580)]].

For the rank-4 semicathartismic temperament, see [[Catalog of rank-4 temperaments #Semicathartismic (14641/14580)]].

== Deuteromere ==

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[[Comma list]]: 14641/14580

: mapping generators: ~2, ~3, ~11/9

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* ''[[Urania]]'' (+81/80 or 121/120) → [[Rastmic rank-3 clan #Urania|Rastmic rank-3 clan]]

* ''[[Triglav]]'' (+3025/3024 or 3136/3125) → [[Hemimean family #Triglav|Hemimean family]]

* ''[[~~Semicanou~~]]'' (+9801/9800) → [[~~Canou~~ family #~~Semicanou~~|~~Canou~~ family]]

* ''[[Semicathart]]'' (+9801/9800) → [[Cathartic family #Semicathart|Cathartic family]]

Considered below are syndeute and hemireiwa, in addition to the add-17 extension of deuteromere.

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Comma list: 1573/1568, 2080/2079, 14641/14580

~~Mapping:~~ {{~~mapping~~| 1 0 -2 -8 0 -11 | 0 1 2 7 2 10 | 0 0 4 -1 1 -4 }}

{{Mapping|legend=0| 1 0 -2 -8 0 -11 | 0 1 2 7 2 10 | 0 0 4 -1 1 -4 }}

Optimal tunings:

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Comma list: 442/441, 561/560, 715/714, 14641/14580

~~Mapping:~~ {{~~mapping~~| 1 0 -2 -8 0 -11 -6 | 0 1 2 7 2 10 6 | 0 0 4 -1 1 -4 2 }}

{{Mapping|legend=0| 1 0 -2 -8 0 -11 -6 | 0 1 2 7 2 10 6 | 0 0 4 -1 1 -4 2 }}

Optimal tunings:

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Comma list: 442/441, 561/560, 715/714, 1216/1215, 1445/1444

~~Mapping:~~ {{~~mapping~~| 1 0 -2 -8 0 -11 -6 -8 | 0 1 2 7 2 10 6 7 | 0 0 4 -1 1 -4 2 4 }}

{{Mapping|legend=0| 1 0 -2 -8 0 -11 -6 -8 | 0 1 2 7 2 10 6 7 | 0 0 4 -1 1 -4 2 4 }}

Optimal tunings:

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== Hemireiwa ==

Hemireiwa is in a certain sense dual to [[~~semicanou~~]]. It splits the perfect twelfth into two, whereas ~~semicanou~~ splits the octave.

Hemireiwa is in a certain sense dual to [[semicathart]]. It splits the perfect twelfth into two, whereas semicathart splits the octave.

[[Subgroup]]: 2.3.5.7.11

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Comma list: 676/675, 1001/1000, 14641/14580

~~Mapping:~~ {{~~mapping~~| 1 0 2 7 1 1 | 0 2 0 -6 3 3 | 0 0 4 7 1 4 }}

Optimal tuning:

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Comma list: 676/675, 715/714, 1001/1000, 14641/14580

~~Mapping:~~ {{~~mapping~~| 1 0 2 7 1 1 -4 | 0 2 0 -6 3 3 10 | 0 0 4 7 1 4 2 }}

{{Mapping|legend=0| 1 0 2 7 1 1 -4 | 0 2 0 -6 3 3 10 | 0 0 4 7 1 4 2 }}

Optimal tuning:

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Comma list: 676/675, 715/714, 1001/1000, 1216/1215, 1445/1444

~~Mapping:~~ {{~~mapping~~| 1 0 2 7 1 1 -4 -4 | 0 2 0 -6 3 3 10 10 | 0 0 4 7 1 4 2 4 }}

{{Mapping|legend=0| 1 0 2 7 1 1 -4 -4 | 0 2 0 -6 3 3 10 10 | 0 0 4 7 1 4 2 4 }}

Optimal tuning:

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Comma list: 1089/1088, 14641/14580

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 0 -2 0 -6 | 0 1 2 2 6 | 0 0 4 1 2 }}

Optimal tunings:

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Comma list: 1089/1088, 1216/1215, 1445/1444

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 0 -2 0 -6 -8 | 0 1 2 2 6 7 | 0 0 4 1 2 4 }}

{{Mapping|legend=2| 1 0 -2 0 -6 -8 | 0 1 2 2 6 7 | 0 0 4 1 2 4 }}

Optimal tunings:

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Badness (Sintel): 0.630

[[Category:Semicathartismic clan| ]]

[[Category:Temperament clans]]

[[Category:~~Semicanousmic clan| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-3 temperaments]]

~~[[Category:Rank~~ 3]]

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 {{Technical data page}}
-The '''semicanousmic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[semicanousma]] ({{monzo|legend=1| -2 -6 -1 0 4 }}, [[ratio]]: 14641/14580).
+The '''semicathartismic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[semicathartisma]] ({{monzo|legend=1| -2 -6 -1 0 4 }}, [[ratio]]: 14641/14580).
-For the rank-4 semicanousmic temperament, see [[Catalog of rank-4 temperaments #Semicanousmic (14641/14580)]].
+For the rank-4 semicathartismic temperament, see [[Catalog of rank-4 temperaments #Semicathartismic (14641/14580)]].
 == Deuteromere ==
@@ Line 12: / Line 12: @@
 [[Comma list]]: 14641/14580
-{{Mapping|legend=2| 1 0 -2 0 | 0 1 2 2 | 0 0 4 1 }}
+{{Mapping|legend=3| 1 0 -2 0 | 0 1 2 2 | 0 0 4 1 }}
 : mapping generators: ~2, ~3, ~11/9
@@ Line 29: / Line 29: @@
 * ''[[Urania]]'' (+81/80 or 121/120) → [[Rastmic rank-3 clan #Urania|Rastmic rank-3 clan]]
 * ''[[Triglav]]'' (+3025/3024 or 3136/3125) → [[Hemimean family #Triglav|Hemimean family]]
-* ''[[Semicanou]]'' (+9801/9800) → [[Canou family #Semicanou|Canou family]]
+* ''[[Semicathart]]'' (+9801/9800) → [[Cathartic family #Semicathart|Cathartic family]]
 Considered below are syndeute and hemireiwa, in addition to the add-17 extension of deuteromere.
@@ Line 55: / Line 55: @@
 Comma list: 1573/1568, 2080/2079, 14641/14580
-Mapping: {{mapping| 1 0 -2 -8 0 -11 | 0 1 2 7 2 10 | 0 0 4 -1 1 -4 }}
+{{Mapping|legend=0| 1 0 -2 -8 0 -11 | 0 1 2 7 2 10 | 0 0 4 -1 1 -4 }}
 Optimal tunings:
@@ Line 70: / Line 70: @@
 Comma list: 442/441, 561/560, 715/714, 14641/14580
-Mapping: {{mapping| 1 0 -2 -8 0 -11 -6 | 0 1 2 7 2 10 6 | 0 0 4 -1 1 -4 2 }}
+{{Mapping|legend=0| 1 0 -2 -8 0 -11 -6 | 0 1 2 7 2 10 6 | 0 0 4 -1 1 -4 2 }}
 Optimal tunings:
@@ Line 85: / Line 85: @@
 Comma list: 442/441, 561/560, 715/714, 1216/1215, 1445/1444
-Mapping: {{mapping| 1 0 -2 -8 0 -11 -6 -8 | 0 1 2 7 2 10 6 7 | 0 0 4 -1 1 -4 2 4 }}
+{{Mapping|legend=0| 1 0 -2 -8 0 -11 -6 -8 | 0 1 2 7 2 10 6 7 | 0 0 4 -1 1 -4 2 4 }}
 Optimal tunings:
@@ Line 96: / Line 96: @@
 == Hemireiwa ==
-Hemireiwa is in a certain sense dual to [[semicanou]]. It splits the perfect twelfth into two, whereas semicanou splits the octave.
+Hemireiwa is in a certain sense dual to [[semicathart]]. It splits the perfect twelfth into two, whereas semicathart splits the octave.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 120: / Line 120: @@
 Comma list: 676/675, 1001/1000, 14641/14580
-Mapping: {{mapping| 1 0 2 7 1 1 | 0 2 0 -6 3 3 | 0 0 4 7 1 4 }}
+{{Mapping|legend=0| 1 0 2 7 1 1 | 0 2 0 -6 3 3 | 0 0 4 7 1 4 }}
 Optimal tuning:
@@ Line 135: / Line 135: @@
 Comma list: 676/675, 715/714, 1001/1000, 14641/14580
-Mapping: {{mapping| 1 0 2 7 1 1 -4 | 0 2 0 -6 3 3 10 | 0 0 4 7 1 4 2 }}
+{{Mapping|legend=0| 1 0 2 7 1 1 -4 | 0 2 0 -6 3 3 10 | 0 0 4 7 1 4 2 }}
 Optimal tuning:
@@ Line 150: / Line 150: @@
 Comma list: 676/675, 715/714, 1001/1000, 1216/1215, 1445/1444
-Mapping: {{mapping| 1 0 2 7 1 1 -4 -4 | 0 2 0 -6 3 3 10 10 | 0 0 4 7 1 4 2 4 }}
+{{Mapping|legend=0| 1 0 2 7 1 1 -4 -4 | 0 2 0 -6 3 3 10 10 | 0 0 4 7 1 4 2 4 }}
 Optimal tuning:
@@ Line 166: / Line 166: @@
 Comma list: 1089/1088, 14641/14580
-Subgroup-val mapping: {{mapping| 1 0 -2 0 -6 | 0 1 2 2 6 | 0 0 4 1 2 }}
+{{Mapping|legend=2| 1 0 -2 0 -6 | 0 1 2 2 6 | 0 0 4 1 2 }}
 Optimal tunings:
@@ Line 181: / Line 181: @@
 Comma list: 1089/1088, 1216/1215, 1445/1444
-Subgroup-val mapping: {{mapping| 1 0 -2 0 -6 -8 | 0 1 2 2 6 7 | 0 0 4 1 2 4 }}
+{{Mapping|legend=2| 1 0 -2 0 -6 -8 | 0 1 2 2 6 7 | 0 0 4 1 2 4 }}
 Optimal tunings:
@@ Line 191: / Line 191: @@
 Badness (Sintel): 0.630
+[[Category:Semicathartismic clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Semicanousmic clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]