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| This is a collection of temperaments tempering out the [[hemimage comma]], {{monzo| 5 -7 -1 3 }} = 10976/10935. These include commatic, chromat, degrees, subfourth, bisupermajor and cotoneum, considered below, as well as the following discussed elsewhere: | | This is a collection of temperaments tempering out the [[hemimage comma]], {{monzo| 5 -7 -1 3 }} = 10976/10935. These include commatic, chromat, degrees, subfourth, and bisupermajor, considered below, as well as the following discussed elsewhere: |
| * ''[[Quasisuper]]'', {64/63, 2430/2401} → [[Archytas clan #Quasisuper|Archytas clan]] | | * ''[[Quasisuper]]'' → [[Archytas clan #Quasisuper|Archytas clan]] (+64/63) |
| * ''[[Liese]]'', {81/80, 686/675} → [[Meantone family #Liese|Meantone family]] | | * ''[[Liese]]'' → [[Meantone family #Liese|Meantone family]] (+81/80) |
| * ''[[Unicorn]]'', {126/125, 10976/10935} → [[Unicorn family #Septimal unicorn|Unicorn family]] | | * ''[[Unicorn]]'' → [[Unicorn family #Septimal unicorn|Unicorn family]] (+126/125) |
| * [[Magic]], {225/224, 245/243} → [[Magic family #Magic|Magic family]] | | * [[Magic]] → [[Magic family #Magic|Magic family]] (+225/224 or 245/243) |
| * ''[[Guiron]]'', {1029/1024, 10976/10935} → [[Gamelismic clan #Guiron|Gamelismic clan]] | | * ''[[Guiron]]'' → [[Gamelismic clan #Guiron|Gamelismic clan]] (+1029/1024) |
| * ''[[Echidna]]'', {1728/1715, 2048/2025} → [[Diaschismic family #Echidna|Diaschismic family]] | | * ''[[Echidna]]'' → [[Diaschismic family #Echidna|Diaschismic family]] (+1728/1715 or 2048/2025) |
| * [[Hemififths]], {2401/2400, 5120/5103} → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]] | | * [[Hemififths]] → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]] (+2401/2400 or 5120/5103) |
| * ''[[Dodecacot]]'', {3125/3087, 10976/10935} → [[Tetracot family #Dodecacot|Tetracot family]] | | * ''[[Dodecacot]]'' → [[Tetracot family #Dodecacot|Tetracot family]] (+3125/3087) |
| * [[Parakleismic]], {3136/3125, 4375/4374} → [[Ragismic microtemperaments #Parakleismic|Ragismic microtemperaments]] | | * [[Parakleismic]] → [[Ragismic microtemperaments #Parakleismic|Ragismic microtemperaments]] (+3136/3125 or 4375/4374) |
| * ''[[Pluto]]'', {4000/3969, 10976/10935} → [[Mirkwai clan #Pluto|Mirkwai clan]] | | * ''[[Pluto]]'' → [[Mirkwai clan #Pluto|Mirkwai clan]] (+4000/3969) |
| * ''[[Hendecatonic]]'', {6144/6125, 10976/10935} → [[Porwell temperaments #Hendecatonic|Porwell temperaments]] | | * ''[[Hendecatonic]]'' → [[Porwell temperaments #Hendecatonic|Porwell temperaments]] (+6144/6125) |
| * ''[[Marfifths]]'', {10976/10935, 15625/15552} → [[Kleismic family #Marfifths|Kleismic family]] | | * ''[[Marfifths]]'' → [[Kleismic family #Marfifths|Kleismic family]] (+15625/15552) |
| * ''[[Yarman I]]'', {10976/10935, 244140625/243045684} → [[Turkish maqam music temperaments #Yarman I|Turkish maqam music temperaments]] | | * ''[[Cotoneum]]'' → [[Garischismic clan #Cotoneum|Garischismic clan]] (+33554432/33480783) |
| | * ''[[Yarman I]]' → [[Turkish maqam music temperaments #Yarman I|Turkish maqam music temperaments]] (+244140625/243045684) |
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| == Chromat == | | == Chromat == |
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| Badness: 0.022396 | | Badness: 0.022396 |
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| == Cotoneum ==
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| {{Main| Cotoneum }}
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| The ''cotoneum'' temperament (41&217, named after the Latin for "[[Wikipedia:quince|quince]]") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41-]], [[176edo|176-]], [[217edo|217-]], and [[258edo]], and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 10976/10935, 823543/819200
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| [[Mapping]]: [{{val| 1 0 80 25 }}, {{val| 0 1 -49 -14 }}]
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| Mapping generators: ~2, ~3
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| {{Multival|legend=1| 1 -49 -14 -80 -25 105 }}
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.317
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| {{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 258, 475 }}
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| [[Badness]]: 0.105632
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 441/440, 10976/10935, 16384/16335
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| Mapping: [{{val| 1 0 80 25 -33 }}, {{val| 0 1 -49 -14 23 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.303
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| {{Optimal ET sequence|legend=1| 41, 135c, 176, 217 }}
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| Badness: 0.050966
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 364/363, 441/440, 3584/3575, 10976/10935
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| Mapping: [{{val| 1 0 80 25 -33 -93 }}, {{val| 0 1 -49 -14 23 61 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.306
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| {{Optimal ET sequence|legend=1| 41, 176, 217 }}
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| Badness: 0.036951
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262
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| Mapping: [{{val| 1 0 80 25 -33 -93 -137 }}, {{val| 0 1 -49 -14 23 61 89 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.307
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| {{Optimal ET sequence|legend=1| 41, 176, 217 }}
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| Badness: 0.029495
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| === 19-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728
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| Mapping: [{{val| 1 0 80 25 -33 -93 -137 74 }}, {{val| 0 1 -49 -14 23 61 89 -44 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.308
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| {{Optimal ET sequence|legend=1| 41, 176, 217 }}
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| Badness: 0.021811
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| == Degrees == | | == Degrees == |