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| == Rank-2 temperaments == | | == Rank-2 temperaments == |
| Rank two temperaments tempering out 676/675 include the 13-limit versions of [[Ragismic microtemperaments #Hemiennealimmal|hemiennealimmal]], [[Breedsmic temperaments #Harry|harry]], [[Kleismic family #Tritikleismic|tritikleismic]], [[Kleismic family #Catakleismic|catakleimsic]], [[Marvel temperaments #Negri|negri]], [[Hemifamity temperaments #Mystery|mystery]], [[Hemifamity temperaments #Buzzard|buzzard]], [[Kleismic family #Quadritikleismic|quadritikleismic]]. | | Rank-2 temperaments tempering out 676/675 include the 13-limit versions of [[semaphoresmic clan #Negri|negri]], [[buzzardsmic clan #Buzzard|buzzard]], [[kleismic family #Catakleismic|catakleismic]], [[gravity family #Harry|harry]], [[kleismic family #Tritikleismic|tritikleismic]], [[quintosec family #Decoid|decoid]], [[kleismic family #Quadritikleismic|quadritikleismic]], [[landscape microtemperaments #Avicenna|avicenna]], [[septiennealimmal clan #Hemiennealimmal|hemiennealimmal]], [[wizmic microtemperaments #Tertiathirds|tertiathirds]], and [[aberschismic temperaments #Mystery|mystery]]. |
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| It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to [[29edo]] alone. | | It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 2 in negri, 2 in buzzard, 3 in catakleismic, 6 in harry, 9 in tritikleismic, 10 in decoid, 12 in quadritikleismic, 12 in avicenna, 18 in hemiennealimmal, 26 in tertiathirds. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to [[29edo]] alone. |
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| === Decitonic aka decoid ===
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| {{see also| Breedsmic temperaments #Decoid}}
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| Subgroup: 2.3.5.7.11.13
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| [[Comma list]]: 676/675, 1001/1000, 1716/1715, 4096/4095
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| [[Mapping]]: [{{val| 10 0 47 36 98 37 }}, {{val| 0 2 -3 -1 -8 0 }}]
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| [[POTE generator]]: ~15/13 = 248.917
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| {{Optimal ET sequence|legend=1| 130, 270, 940, 1210f }}
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| [[Badness]]: 0.013475
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| === Avicenna ===
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| {{see also| Landscape microtemperaments #Avicenna }}
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| Subgroup: 2.3.5.7.11.13
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| [[Comma list]]: 676/675, 1001/1000, 3025/3024, 4096/4095
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| [[Mapping]]: [{{val| 3 2 8 16 9 8 }}, {{val| 0 8 -3 -22 4 9 }}]
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| [[CTE|CTE generator]]: ~13/12 = 137.777
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| [[POTE generator]]: ~13/12 = 137.777
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| {{Optimal ET sequence|legend=1| 87, 183, 270 }}
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| [[Badness]]: 0.015557
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| === Tertiathirds ===
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| {{see also| Wizmic microtemperaments #Tertiathirds }}
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| Subgroup: 2.3.5.7.11.13
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| [[Comma list]]: 676/675, 1716/1715, 3025/3024, 4225/4224
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| [[Mapping]]: [{{val| 1 -4 2 -6 -9 -5 }}, {{val| 0 52 3 82 116 81 }}]
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| [[POTE generator]]: ~14/13 = 128.8902
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| {{Optimal ET sequence|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
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| [[Badness]]: 0.019494
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224
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| Mapping: [{{val| 1 -4 2 -6 -9 -5 -3 }}, {{val| 0 52 3 82 116 81 66 }}]
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| POTE generator: ~14/13 = 128.8912
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| {{Optimal ET sequence|legend=1| 121, 149, 270 }}
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| Badness: 0.019107
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| == Subgroup temperaments == | | == Subgroup temperaments == |