Swetismic temperaments: Difference between revisions

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This ~~is a collection of~~ [[rank-3 temperament|rank-3]] ~~[[regular temperament|~~temperaments]] [[tempering out]] the [[swetisma]] (~~[[ratio]]: 540/539,~~ {{monzo|legend=1| 2 3 1 -2 -1 }}). For the rank-4 ~~swetismic~~ temperament, see [[Catalog of rank-4 temperaments #Swetismic (540/539)]].

This page collects [[rank-3 temperament|rank-3]] '''swetismic temperaments''', which [[tempering out|temper out]] the [[swetisma]] ({{monzo|legend=1| 2 3 1 -2 -1 }}, [[ratio]]: 540/539). For the [[rank-4 temperament]], see [[Catalog of rank-4 temperaments #Swetismic (540/539)]].

Temperaments discussed elsewhere are:

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* ''[[Gariboh]]'' (+3125/3087) → [[Gariboh family #Undecimal gariboh|Gariboh family]]

* ''[[Siebog]]'' (+3136/3125) → [[Hemimean family #Siebog|Hemimean family]]

* ''[[Laka]]'' (+5120/5103) → [[~~Hemifamity~~ family #Laka|~~Hemifamity~~ family]]

* ''[[Laka]]'' (+5120/5103) → [[Aberschismic family #Laka|Aberschismic family]]

* ''[[Jupiter]]'' (+5632/5625) → [[Porwell family #Jupiter|Porwell family]]

* ''[[Albus]]'' (+8019/8000) → [[Cataharry family #Albus|Cataharry family]]

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Comma list: 540/539, 729/728, 1375/1372

~~Mapping:~~ {{~~mapping~~| 1 0 -5 -4 5 1 | 0 1 3 3 0 3 | 0 0 5 4 -3 -4 }}

{{Mapping|legend=0| 1 0 -5 -4 5 1 | 0 1 3 3 0 3 | 0 0 5 4 -3 -4 }}

Optimal tunings:

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Comma list: 540/539, 625/624, 1375/1372

~~Mapping:~~ {{~~mapping~~| 1 0 -5 -4 5 -24 | 0 1 3 3 0 11 | 0 0 5 4 -3 20 }}

{{Mapping|legend=0| 1 0 -5 -4 5 -24 | 0 1 3 3 0 11 | 0 0 5 4 -3 20 }}

Optimal tunings:

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Comma list: 351/350, 540/539, 1375/1372

~~Mapping:~~ {{~~mapping~~| 1 0 -5 -4 5 -13 | 0 1 3 3 0 6 | 0 0 5 4 -3 14 }}

{{Mapping|legend=0| 1 0 -5 -4 5 -13 | 0 1 3 3 0 6 | 0 0 5 4 -3 14 }}

Optimal tunings:

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Comma list: 325/324, 364/363, 540/539

~~Mapping:~~ {{~~mapping~~| 1 0 0 0 2 2 | 0 1 3 3 0 -2 | 0 0 5 4 -3 -10 }}

{{Mapping|legend=0| 1 0 0 0 2 2 | 0 1 3 3 0 -2 | 0 0 5 4 -3 -10 }}

Optimal tunings:

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Comma list: 540/539, 729/728, 1575/1573

~~Mapping:~~ {{~~mapping~~| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}

{{Mapping|legend=0| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}

Optimal tunings:

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Comma list: 351/350, 364/363, 540/539

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

Optimal tunings:

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Comma list: 364/363, 540/539, 676/675

~~Mapping:~~ {{~~mapping~~| 1 0 -3 0 -1 -4 | 0 2 4 3 4 7 | 0 0 5 1 3 5 }}

{{Mapping|legend=0| 1 0 -3 0 -1 -4 | 0 2 4 3 4 7 | 0 0 5 1 3 5 }}

Optimal tunings:

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Comma list: 351/350, 540/539, 847/845

~~Mapping:~~ {{~~mapping~~| 1 0 -6 4 -12 -7 | 0 1 4 0 7 5 | 0 0 5 -3 11 7 }}

{{Mapping|legend=0| 1 0 -6 4 -12 -7 | 0 1 4 0 7 5 | 0 0 5 -3 11 7 }}

Optimal tunings:

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Comma list: 169/168, 540/539, 729/728

~~Mapping:~~ {{~~mapping~~| 1 0 0 -3 8 0 | 0 3 0 11 -13 7 | 0 0 1 0 1 0 }}

{{Mapping|legend=0| 1 0 0 -3 8 0 | 0 3 0 11 -13 7 | 0 0 1 0 1 0 }}

Optimal tunings:

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[[Category:Swetismic temperaments| ]]

[[Category:Swetismic| ]]

[[Category:Temperament collections]]

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

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 {{Technical data page}}
-This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out]] the [[swetisma]] ([[ratio]]: 540/539, {{monzo|legend=1| 2 3 1 -2 -1 }}). For the rank-4 swetismic temperament, see [[Catalog of rank-4 temperaments #Swetismic (540/539)]].
+This page collects [[rank-3 temperament|rank-3]] '''swetismic temperaments''', which [[tempering out|temper out]] the [[swetisma]] ({{monzo|legend=1| 2 3 1 -2 -1 }}, [[ratio]]: 540/539). For the [[rank-4 temperament]], see [[Catalog of rank-4 temperaments #Swetismic (540/539)]].
 Temperaments discussed elsewhere are:
@@ Line 16: / Line 16: @@
 * ''[[Gariboh]]'' (+3125/3087) → [[Gariboh family #Undecimal gariboh|Gariboh family]]
 * ''[[Siebog]]'' (+3136/3125) → [[Hemimean family #Siebog|Hemimean family]]
-* ''[[Laka]]'' (+5120/5103) → [[Hemifamity family #Laka|Hemifamity family]]
+* ''[[Laka]]'' (+5120/5103) → [[Aberschismic family #Laka|Aberschismic family]]
 * ''[[Jupiter]]'' (+5632/5625) → [[Porwell family #Jupiter|Porwell family]]
 * ''[[Albus]]'' (+8019/8000) → [[Cataharry family #Albus|Cataharry family]]
@@ Line 63: / Line 63: @@
 Comma list: 540/539, 729/728, 1375/1372
-Mapping: {{mapping| 1 0 -5 -4 5 1 | 0 1 3 3 0 3 | 0 0 5 4 -3 -4 }}
+{{Mapping|legend=0| 1 0 -5 -4 5 1 | 0 1 3 3 0 3 | 0 0 5 4 -3 -4 }}
 Optimal tunings:
@@ Line 78: / Line 78: @@
 Comma list: 540/539, 625/624, 1375/1372
-Mapping: {{mapping| 1 0 -5 -4 5 -24 | 0 1 3 3 0 11 | 0 0 5 4 -3 20 }}
+{{Mapping|legend=0| 1 0 -5 -4 5 -24 | 0 1 3 3 0 11 | 0 0 5 4 -3 20 }}
 Optimal tunings:
@@ Line 101: / Line 101: @@
 Comma list: 351/350, 540/539, 1375/1372
-Mapping: {{mapping| 1 0 -5 -4 5 -13 | 0 1 3 3 0 6 | 0 0 5 4 -3 14 }}
+{{Mapping|legend=0| 1 0 -5 -4 5 -13 | 0 1 3 3 0 6 | 0 0 5 4 -3 14 }}
 Optimal tunings:
@@ Line 116: / Line 116: @@
 Comma list: 325/324, 364/363, 540/539
-Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 3 3 0 -2 | 0 0 5 4 -3 -10 }}
+{{Mapping|legend=0| 1 0 0 0 2 2 | 0 1 3 3 0 -2 | 0 0 5 4 -3 -10 }}
 Optimal tunings:
@@ Line 151: / Line 151: @@
 Comma list: 540/539, 729/728, 1575/1573
-Mapping: {{mapping| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}
+{{Mapping|legend=0| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}
 Optimal tunings:
@@ Line 166: / Line 166: @@
 Comma list: 351/350, 364/363, 540/539
-Mapping: {{mapping| 2 1 0 2 3 1 | 0 3 0 5 -1 -4 | 0 0 1 0 1 2 }}
+{{Mapping|legend=0| 2 1 0 2 3 1 | 0 3 0 5 -1 -4 | 0 0 1 0 1 2 }}
 Optimal tunings:
@@ Line 201: / Line 201: @@
 Comma list: 364/363, 540/539, 676/675
-Mapping: {{mapping| 1 0 -3 0 -1 -4 | 0 2 4 3 4 7 | 0 0 5 1 3 5 }}
+{{Mapping|legend=0| 1 0 -3 0 -1 -4 | 0 2 4 3 4 7 | 0 0 5 1 3 5 }}
 Optimal tunings:
@@ Line 234: / Line 234: @@
 Comma list: 351/350, 540/539, 847/845
-Mapping: {{mapping| 1 0 -6 4 -12 -7 | 0 1 4 0 7 5 | 0 0 5 -3 11 7 }}
+{{Mapping|legend=0| 1 0 -6 4 -12 -7 | 0 1 4 0 7 5 | 0 0 5 -3 11 7 }}
 Optimal tunings:
@@ Line 267: / Line 267: @@
 Comma list: 169/168, 540/539, 729/728
-Mapping: {{mapping| 1 0 0 -3 8 0 | 0 3 0 11 -13 7 | 0 0 1 0 1 0 }}
+{{Mapping|legend=0| 1 0 0 -3 8 0 | 0 3 0 11 -13 7 | 0 0 1 0 1 0 }}
 Optimal tunings:
@@ Line 278: / Line 278: @@
 [[Category:Swetismic temperaments| ]] <!-- main article -->
+[[Category:Swetismic| ]] <!-- key article -->
 [[Category:Temperament collections]]
 [[Category:Catalogs of rank-3 temperaments]]

Swetismic temperaments: Difference between revisions

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