Cataharry temperaments: Difference between revisions

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This is a collection of rank-2 temperaments tempering out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} = 19683/19600. ~~These include swetneus~~, ~~considered below, as well as others discussed~~ elsewhere:

This is a collection of [[rank-2 temperament|rank-2]] '''cataharry temperaments''', which [[tempering out|temper out]] the [[cataharry comma]] ({{monzo|legend=1| -4 9 -2 -2 }}, [[ratio]]: 19683/19600). For the family of [[rank-3 temperament]]s, see [[Cataharry family]].

Discussed elsewhere are:

* [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]

* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]

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* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]

* ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]

Considered below is swetneus and majvamoid, in the order of increasing [[badness]].

== Swetneus ==

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[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 144.956{{c}}

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~49/45 = 144.956

{{Optimal ET sequence|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}

[[Badness]]: 0.133168

[[Badness]] (Smith): 0.133168

=== 11-limit ===

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Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~49/45 = 144.941

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/45 = 144.941{{c}}

{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}

{{Optimal ET sequence|legend=0| 58, 149, 207, 356e, 563cde, 919bcde }}

Badness: 0.055163

Badness (Smith): 0.055163

=== 13-limit ===

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Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~49/45 = 144.939

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/45 = 144.939{{c}}

{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}

{{Optimal ET sequence|legend=0| 58, 149, 207, 356e, 563cde, 919bcdef }}

Badness: 0.028876

Badness (Smith): 0.028876

== Majvamoid ==

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[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~125/96 = 459.031{{c}}

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~125/96 = 459.031

{{Optimal ET sequence|legend=1| 34d, 115d, 149, 183, 332, 515, 847, 1362bc }}

[[Badness]]: 0.207280

[[Badness]] (Smith): 0.207280

=== 11-limit ===

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Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~125/96 = 459.027

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.027{{c}}

{{Optimal ET sequence|legend=1| 34d, 149, 183, 332e, 515e, 698e }}

{{Optimal ET sequence|legend=0| 34d, 149, 183, 332e, 515e, 698e }}

Badness: 0.065874

Badness (Smith): 0.065874

=== 13-limit ===

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Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~125/96 = 459.028

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.028{{c}}

Badness: 0.034696

Badness (Smith): 0.034696

=== 17-limit ===

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Mapping: {{mapping| 1 10 5 38 31 19 6 | 0 -22 -7 -92 -72 -40 -5 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~125/96 = 459.027

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.027{{c}}

{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef, 698ef }}

{{Optimal ET sequence|legend=0| 34d, 149, 183, 332ef, 515ef, 698ef }}

Badness: 0.023302

Badness (Smith): 0.023302

[[Category:Cataharry temperaments| ]]

[[Category:Temperament collections]]

~~[[Category:Cataharry temperaments| ]] ~~

~~[[Category:Cataharry| ]] ~~

[[Category:Rank 2]]

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 {{Technical data page}}
-This is a collection of rank-2 temperaments tempering out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:
+This is a collection of [[rank-2 temperament|rank-2]] '''cataharry temperaments''', which [[tempering out|temper out]] the [[cataharry comma]] ({{monzo|legend=1| -4 9 -2 -2 }}, [[ratio]]: 19683/19600). For the family of [[rank-3 temperament]]s, see [[Cataharry family]].
+Discussed elsewhere are:
 * [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]
 * ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
@@ Line 15: / Line 17: @@
 * ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
 * ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]
+Considered below is swetneus and majvamoid, in the order of increasing [[badness]].
 == Swetneus ==
@@ Line 25: / Line 29: @@
 {{Mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 144.956{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 144.956
 {{Optimal ET sequence|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}
-[[Badness]]: 0.133168
+[[Badness]] (Smith): 0.133168
 === 11-limit ===
@@ Line 39: / Line 42: @@
 Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}
-Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/45 = 144.941{{c}}
-{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}
+{{Optimal ET sequence|legend=0| 58, 149, 207, 356e, 563cde, 919bcde }}
-Badness: 0.055163
+Badness (Smith): 0.055163
 === 13-limit ===
@@ Line 52: / Line 55: @@
 Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}
-Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.939
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/45 = 144.939{{c}}
-{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}
+{{Optimal ET sequence|legend=0| 58, 149, 207, 356e, 563cde, 919bcdef }}
-Badness: 0.028876
+Badness (Smith): 0.028876
 == Majvamoid ==
@@ Line 67: / Line 70: @@
 {{Mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~125/96 = 459.031{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 459.031
 {{Optimal ET sequence|legend=1| 34d, 115d, 149, 183, 332, 515, 847, 1362bc }}
-[[Badness]]: 0.207280
+[[Badness]] (Smith): 0.207280
 === 11-limit ===
@@ Line 81: / Line 83: @@
 Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}
-Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.027{{c}}
-{{Optimal ET sequence|legend=1| 34d, 149, 183, 332e, 515e, 698e }}
+{{Optimal ET sequence|legend=0| 34d, 149, 183, 332e, 515e, 698e }}
-Badness: 0.065874
+Badness (Smith): 0.065874
 === 13-limit ===
@@ Line 94: / Line 96: @@
 Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}
-Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.028
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.028{{c}}
-{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef }}
+{{Optimal ET sequence|legend=0| 34d, 149, 183, 332ef, 515ef }}
-Badness: 0.034696
+Badness (Smith): 0.034696
 === 17-limit ===
@@ Line 107: / Line 109: @@
 Mapping: {{mapping| 1 10 5 38 31 19 6 | 0 -22 -7 -92 -72 -40 -5 }}
-Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.027{{c}}
-{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef, 698ef }}
+{{Optimal ET sequence|legend=0| 34d, 149, 183, 332ef, 515ef, 698ef }}
-Badness: 0.023302
+Badness (Smith): 0.023302
+[[Category:Cataharry temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Cataharry temperaments| ]] <!-- main article -->
-[[Category:Cataharry| ]] <!-- key article -->
 [[Category:Rank 2]]