Werckismic temperaments: Difference between revisions

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: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #History]].''

History splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].

History, named by [[Graham Breed]] some time before 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96550.html#96556 Yahoo! Tuning Group | ''Madagascar<nowiki>[</nowiki>19<nowiki>]</nowiki>'']</ref>, splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].

[[Subgroup]]: 2.3.5.7.11

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Comma list: 364/363, 441/440, 676/675

~~Mapping:~~ {{~~mapping~~| 1 2 0 0 1 2 | 0 -6 0 7 2 -9 | 0 0 1 1 1 1 }}

Optimal tunings:

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Badness (Sintel): 0.505

~~Complexity spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7~~

== Varuna ==

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Comma list: 351/350, 364/363, 441/440

~~Mapping:~~ {{~~mapping~~| 2 0 0 9 12 11 | 0 1 0 -4 -6 -7 | 0 0 1 2 3 4 }}

{{Mapping|legend=0| 2 0 0 9 12 11 | 0 1 0 -4 -6 -7 | 0 0 1 2 3 4 }}

Optimal tunings:

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Comma list: 196/195, 352/351, 1001/1000

~~Mapping:~~ {{~~mapping~~| 1 -1 0 1 -3 5 | 0 5 0 -1 8 -7 | 0 0 1 1 1 1 }}

{{Mapping|legend=0| 1 -1 0 1 -3 5 | 0 5 0 -1 8 -7 | 0 0 1 1 1 1 }}

Optimal tunings:

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Comma list: 441/440, 676/675, 847/845

~~Mapping:~~ {{~~mapping~~| 1 -6 0 2 -11 -10 | 0 10 0 -2 16 15 | 0 0 1 1 1 1 }}

{{Mapping|legend=0| 1 -6 0 2 -11 -10 | 0 10 0 -2 16 15 | 0 0 1 1 1 1 }}

: mapping generators: ~2, ~22/13, ~5

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Comma list: 441/440, 847/845, 1001/1000

~~Mapping:~~ {{~~mapping~~| 1 5 0 -2 3 2 | 0 -11 0 8 -6 -2 | 0 0 1 1 1 1 }}

{{Mapping|legend=0| 1 5 0 -2 3 2 | 0 -11 0 8 -6 -2 | 0 0 1 1 1 1 }}

Optimal tunings:

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Comma list: 170/169, 221/220, 441/440, 847/845

~~Mapping:~~ {{~~mapping~~| 1 5 0 -2 3 2 3 | 0 -11 0 8 -6 -2 -4 | 0 0 1 1 1 1 1 }}

{{Mapping|legend=0| 1 5 0 -2 3 2 3 | 0 -11 0 8 -6 -2 -4 | 0 0 1 1 1 1 1 }}

Optimal tunings:

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Comma list: 441/440, 833/832, 847/845, 1001/1000

~~Mapping:~~ {{~~mapping~~| 1 5 0 -2 3 2 12 | 0 -11 0 8 -6 -2 -18 | 0 0 1 1 1 1 -1 }}

{{Mapping|legend=0| 1 5 0 -2 3 2 12 | 0 -11 0 8 -6 -2 -18 | 0 0 1 1 1 1 -1 }}

Optimal tunings:

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Badness (Sintel): 1.284

== References ==

[[Category:Werckismic temperaments| ]]

[[Category:Temperament collections]]

[[Category:~~Werckismic temperaments| ]] <!~~-~~- main article -->~~

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

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

~~[[Category:Varuna]]~~

~~[[Category:Trimyna~~]]

@@ Line 26: / Line 26: @@
 : ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #History]].''
-History splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].
+History, named by [[Graham Breed]] some time before 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96550.html#96556 Yahoo! Tuning Group | ''Madagascar<nowiki>[</nowiki>19<nowiki>]</nowiki>'']</ref>, splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].
 [[Subgroup]]: 2.3.5.7.11
@@ Line 55: / Line 55: @@
 Comma list: 364/363, 441/440, 676/675
-Mapping: {{mapping| 1 2 0 0 1 2 | 0 -6 0 7 2 -9 | 0 0 1 1 1 1 }}
+{{Mapping|legend=0| 1 2 0 0 1 2 | 0 -6 0 7 2 -9 | 0 0 1 1 1 1 }}
 Optimal tunings:
@@ Line 69: / Line 69: @@
 Badness (Sintel): 0.505
-Complexity spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7
 == Varuna ==
@@ Line 97: / Line 95: @@
 Comma list: 351/350, 364/363, 441/440
-Mapping: {{mapping| 2 0 0 9 12 11 | 0 1 0 -4 -6 -7 | 0 0 1 2 3 4 }}
+{{Mapping|legend=0| 2 0 0 9 12 11 | 0 1 0 -4 -6 -7 | 0 0 1 2 3 4 }}
 Optimal tunings:
@@ Line 134: / Line 132: @@
 Comma list: 196/195, 352/351, 1001/1000
-Mapping: {{mapping| 1 -1 0 1 -3 5 | 0 5 0 -1 8 -7 | 0 0 1 1 1 1 }}
+{{Mapping|legend=0| 1 -1 0 1 -3 5 | 0 5 0 -1 8 -7 | 0 0 1 1 1 1 }}
 Optimal tunings:
@@ Line 149: / Line 147: @@
 Comma list: 441/440, 676/675, 847/845
-Mapping: {{mapping| 1 -6 0 2 -11 -10 | 0 10 0 -2 16 15 | 0 0 1 1 1 1 }}
+{{Mapping|legend=0| 1 -6 0 2 -11 -10 | 0 10 0 -2 16 15 | 0 0 1 1 1 1 }}
 : mapping generators: ~2, ~22/13, ~5
@@ Line 187: / Line 185: @@
 Comma list: 441/440, 847/845, 1001/1000
-Mapping: {{mapping| 1 5 0 -2 3 2 | 0 -11 0 8 -6 -2 | 0 0 1 1 1 1 }}
+{{Mapping|legend=0| 1 5 0 -2 3 2 | 0 -11 0 8 -6 -2 | 0 0 1 1 1 1 }}
 Optimal tunings:
@@ Line 202: / Line 200: @@
 Comma list: 170/169, 221/220, 441/440, 847/845
-Mapping: {{mapping| 1 5 0 -2 3 2 3 | 0 -11 0 8 -6 -2 -4 | 0 0 1 1 1 1 1 }}
+{{Mapping|legend=0| 1 5 0 -2 3 2 3 | 0 -11 0 8 -6 -2 -4 | 0 0 1 1 1 1 1 }}
 Optimal tunings:
@@ Line 217: / Line 215: @@
 Comma list: 441/440, 833/832, 847/845, 1001/1000
-Mapping: {{mapping| 1 5 0 -2 3 2 12 | 0 -11 0 8 -6 -2 -18 | 0 0 1 1 1 1 -1 }}
+{{Mapping|legend=0| 1 5 0 -2 3 2 12 | 0 -11 0 8 -6 -2 -18 | 0 0 1 1 1 1 -1 }}
 Optimal tunings:
@@ Line 227: / Line 225: @@
 Badness (Sintel): 1.284
+== References ==
+[[Category:Werckismic temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Werckismic temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]
-[[Category:Varuna]]
-[[Category:Trimyna]]