Keemic temperaments: Difference between revisions
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These temper out the keema, |-5 -3 3 1 | These temper out the keema, {{monzo| -5 -3 3 1 }} = [[875/864]]. Keemic temperaments include [[Magic family #Magic|magic]], [[Kleismic family #Keemun|keemun]], [[Meantone family #Flattone|flattone]], [[Porcupine family #Porcupine|porcupine]], [[Jubilismic clan #Doublewide|doublewide]], [[Gamelismic clan #Superkleismic|superkleismic]], [[Sycamore family #Sycamore|sycamore]] and quasitemp. | ||
=Quasitemp= | = Quasitemp = | ||
Comma: 6103515625/5804752896 | Comma: 6103515625/5804752896 | ||
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Map: [<1 5 5|, <0 -14 -11|] | Map: [<1 5 5|, <0 -14 -11|] | ||
EDOs: 4, 37, 41, 78 | EDOs: {{EDOs| 4, 37, 41, 78 }} | ||
Badness: 0.7678 | Badness: 0.7678 | ||
==7-limit== | == 7-limit == | ||
Commas: 875/864, 2401/2400 | Commas: 875/864, 2401/2400 | ||
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Wedgie: <<14 11 9 -15 -25 -10|| | Wedgie: <<14 11 9 -15 -25 -10|| | ||
EDOs: 4, 37, 41, 78 | EDOs: {{EDOs| 4, 37, 41, 78 }} | ||
Badness: 0.0603 | Badness: 0.0603 | ||
==11-limit== | == 11-limit == | ||
Commas: 100/99, 385/384, 1375/1372 | Commas: 100/99, 385/384, 1375/1372 | ||
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Map: [<1 5 5 5 2|, <0 -14 -11 -9 6|] | Map: [<1 5 5 5 2|, <0 -14 -11 -9 6|] | ||
EDOs: 4, 37, 41, 78, 119 | EDOs: {{EDOs| 4, 37, 41, 78, 119 }} | ||
Badness: 0.0432 | Badness: 0.0432 | ||
==13-limit== | === 13-limit === | ||
Commas: 100/99, 196/195, 275/273, 385/384 | Commas: 100/99, 196/195, 275/273, 385/384 | ||
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Map: [<1 5 5 5 2 2|, <0 -14 -11 -9 6 7|] | Map: [<1 5 5 5 2 2|, <0 -14 -11 -9 6 7|] | ||
EDOs: 4, 37, 41, 78, 119f | EDOs: {{EDOs| 4, 37, 41, 78, 119f }} | ||
Badness: 0.0329 | Badness: 0.0329 | ||
==Quato== | == Quato == | ||
Commas: 243/242, 441/440, 625/616 | Commas: 243/242, 441/440, 625/616 | ||
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Map: [<1 5 5 5 12|, <0 -14 -11 -9 -35|] | Map: [<1 5 5 5 12|, <0 -14 -11 -9 -35|] | ||
EDOs: 41, 127cd, 168cd | EDOs: {{EDOs| 41, 127cd, 168cd }} | ||
Badness: 0.0412 | Badness: 0.0412 | ||
===13-limit=== | === 13-limit === | ||
Commas: 105/104, 243/242, 275/273, 325/324 | Commas: 105/104, 243/242, 275/273, 325/324 | ||
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Map: [<1 5 5 5 12 12|, <0 -14 -11 -9 -35 -34|] | Map: [<1 5 5 5 12 12|, <0 -14 -11 -9 -35 -34|] | ||
EDOs: 41, 86ce, 127cd | EDOs: {{EDOs| 41, 86ce, 127cd }} | ||
Badness: 0.0301 | Badness: 0.0301 | ||
=Barbad= | = Barbad = | ||
Commas: 875/864, 16875/16807 | Commas: 875/864, 16875/16807 | ||
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Wedgie: <<19 12 21 -25 -20 15|| | Wedgie: <<19 12 21 -25 -20 15|| | ||
EDOs: 18, 23d, 41 | EDOs: {{EDOs| 18, 23d, 41 }} | ||
Badness: 0.1104 | Badness: 0.1104 | ||
==11-limit== | == 11-limit == | ||
Commas: 245/242, 540/539, 625/616 | Commas: 245/242, 540/539, 625/616 | ||
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Map: [<1 9 7 11 14|, <0 -19 -12 -21 -27|] | Map: [<1 9 7 11 14|, <0 -19 -12 -21 -27|] | ||
EDOs: 41, | EDOs: {{EDOs| 18e, 23de, 41, 228ccdd }} | ||
Badness: 0.0501 | Badness: 0.0501 | ||
==13-limit== | == 13-limit == | ||
Commas: 144/143, 196/195, 245/242, 275/273 | Commas: 144/143, 196/195, 245/242, 275/273 | ||
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Map: [<1 9 7 11 14 8|, <0 -19 -12 -21 -27 -11|] | Map: [<1 9 7 11 14 8|, <0 -19 -12 -21 -27 -11|] | ||
EDOs: 41 | EDOs: {{EDOs| 18e, 23de, 41 }} | ||
Badness: 0.0392 | Badness: 0.0392 | ||
[[Category:Theory]] | |||
[[Category:Temperament]] | |||
[[Category:Keemic]] | |||
[[Category:Rank 2]] | |||
Revision as of 17:07, 20 November 2020
These temper out the keema, [-5 -3 3 1⟩ = 875/864. Keemic temperaments include magic, keemun, flattone, porcupine, doublewide, superkleismic, sycamore and quasitemp.
Quasitemp
Comma: 6103515625/5804752896
POTE generator: ~3125/2592 = 292.702
Map: [<1 5 5|, <0 -14 -11|]
Badness: 0.7678
7-limit
Commas: 875/864, 2401/2400
POTE generator ~25/21 = 292.710
Map: [<1 5 5 5|, <0 -14 -11 -9|]
Wedgie: <<14 11 9 -15 -25 -10||
Badness: 0.0603
11-limit
Commas: 100/99, 385/384, 1375/1372
POTE generator: ~25/21 = 292.547
Map: [<1 5 5 5 2|, <0 -14 -11 -9 6|]
Badness: 0.0432
13-limit
Commas: 100/99, 196/195, 275/273, 385/384
POTE generator: ~13/11 = 292.457
Map: [<1 5 5 5 2 2|, <0 -14 -11 -9 6 7|]
Badness: 0.0329
Quato
Commas: 243/242, 441/440, 625/616
POTE generator: ~25/21 = 292.851
Map: [<1 5 5 5 12|, <0 -14 -11 -9 -35|]
Badness: 0.0412
13-limit
Commas: 105/104, 243/242, 275/273, 325/324
POTE generator: ~13/11 = 292.928
Map: [<1 5 5 5 12 12|, <0 -14 -11 -9 -35 -34|]
Badness: 0.0301
Barbad
Commas: 875/864, 16875/16807
POTE generator: ~75/49 = 468.331
Map: [<1 9 7 11|, <0 -19 -12 -21|]
Wedgie: <<19 12 21 -25 -20 15||
Badness: 0.1104
11-limit
Commas: 245/242, 540/539, 625/616
POTE generator: ~98/75 = 468.367
Map: [<1 9 7 11 14|, <0 -19 -12 -21 -27|]
Badness: 0.0501
13-limit
Commas: 144/143, 196/195, 245/242, 275/273
POTE generator: ~13/10 = 468.270
Map: [<1 9 7 11 14 8|, <0 -19 -12 -21 -27 -11|]
Badness: 0.0392