Cataharry temperaments: Difference between revisions

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-'''Cataharry temperaments''' temper out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} = 19683/19600.
+{{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:
+* [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]
+* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
+* ''[[Unicorn]]'' (+126/125) → [[Unicorn family #Septimal unicorn|Unicorn family]]
+* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]]
+* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
+* ''[[Buzzard]]'' (+1728/1715) → [[Hemifamity temperaments #Buzzard|Hemifamity temperaments]]
+* [[Harry]] (+2401/2400) → [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
+* [[Hamity]] (+2430/2401) → [[Amity family #Hamity|Amity family]]
+* ''[[Subpental]]'' (+3136/3125) → [[Hemimean clan #Subpental|Hemimean clan]]
+* ''[[Hemischis]]'' (+6144/6125) → [[Porwell temperaments #Hemischis|Porwell temperaments]]
+* ''[[Mirkat]]'' (+16875/16807) → [[Mirkwai clan #Mirkat|Mirkwai clan]]
+* ''[[Hours]]'' (+33075/32768) → [[Compton family #Hours|Compton family]]
+* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
+* ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]
-= Swetneus =
+== Swetneus ==
 The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.
-Commas: 19683/19600, 50421/50000
+[[Subgroup]]: 2.3.5.7
-POTE generator: ~49/45 = 144.956
+[[Comma list]]: 19683/19600, 50421/50000
-Map: [|1 4 8 8&gt;, |0 -20 -47 -43&gt;]
+{{Mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}
-Wedgie: &lt;&lt;20 47 43 28 12 -32||
-{{EDOs|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 144.956
-Badness: 0.1332
+{{Optimal ET sequence|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}
-== 11-limit ==
+[[Badness]]: 0.133168
-Commas: 441/440, 3388/3375, 19683/19600
-POTE generator: ~49/45 = 144.941
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Map: [|1 4 8 8 13&gt;, |0 -20 -47 -43 -79&gt;]
+Comma list: 441/440, 3388/3375, 19683/19600
-{{EDOs|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}
+Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}
-Badness: 0.0552
+Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941
-== 13-limit ==
+{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}
-Commas: 351/350, 441/440, 676/675, 847/845
-POTE generator: ~49/45 = 144.939
+Badness: 0.055163
-Map: [|1 4 8 8 13 13&gt;, |0 -20 -47 -43 -79 -77&gt;]
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-{{EDOs|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}
+Comma list: 351/350, 441/440, 676/675, 847/845
-Badness: 0.0289
+Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}
-[[Category:Theory]]
+Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.939
-[[Category:Temperament]]
-[[Category:Cataharry]]
+{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}
+Badness: 0.028876
+== Majvamoid ==
+The ''majvamoid'' temperament (149 &amp; 183) is an extension of the [[Subgroup temperaments #No-sevens subgroup|majvam]] temperament which tempers out the cataharry comma and the quasiorwellisma (29360128/29296875, sazoquinbigu) in the 7-limit.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 19683/19600, 29360128/29296875
+{{Mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}
+[[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
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 5632/5625, 19683/19600
+Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}
+Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027
+{{Optimal ET sequence|legend=1| 34d, 149, 183, 332e, 515e, 698e }}
+Badness: 0.065874
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 351/350, 676/675, 1573/1568, 4225/4224
+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 ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef }}
+Badness: 0.034696
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224
+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 ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef, 698ef }}
+Badness: 0.023302
+[[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Cataharry temperaments| ]] <!-- main article -->
+[[Category:Cataharry| ]] <!-- key article -->
 [[Category:Rank 2]]