Canousmic temperaments: Difference between revisions
Created page with "These are rank-2 temperaments that temper out the canousma, 4802000/4782969 = {{monzo|4 -14 3 4}}. For the rank-3 temperament, see Canou family. Note that 4802000/47..." |
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* [[Hemifamity temperaments #Septiquarter|Septiquarter]] | * [[Hemifamity temperaments #Septiquarter|Septiquarter]] | ||
* [[Schismatic family #Kleischismic|Kleischismic]] | * [[Schismatic family #Kleischismic|Kleischismic]] | ||
= Satin = | |||
Comma: |104 -70 3> | |||
[[POTE_tuning|POTE generator]]: ~|-34 23 -1> = 165.907 | |||
Map: [<1 2 12|, <0 -3 -70|] | |||
EDOs: 94, 123, 217, 311, 405, 528, 745 | |||
Badness: 2.8530 | |||
==7-limit== | |||
Commas: 2100875/2097152, 4802000/4782969 | |||
POTE generator: ~8575/7776 = 165.913 | |||
Map: [<1 2 12 -3|, <0 -3 -70 42|] | |||
EDOs: 94, 123, 217, 311, 405, 528 | |||
Badness: 0.1972 | |||
==11-limit== | |||
Commas: 4000/3993, 19712/19683, 41503/41472 | |||
POTE generator: ~11/10 = 165.915 | |||
Map: [<1 2 12 -3 13|, <0 -3 -70 42 -69|] | |||
EDOs: 94, 123, 217, 311, 405, 528 | |||
Badness: 0.0580 | |||
==13-limit== | |||
Commas: 1575/1573, 2080/2079, 4096/4095, 13720/13689 | |||
POTE generator: ~11/10 = 165.914 | |||
Map: [<1 2 12 -3 13 -1|, <0 -3 -70 42 -69 34|] | |||
EDOs: 94, 123, 217, 311, 405, 528 | |||
Badness: 0.0303 | |||
==17-limit== | |||
Commas: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095 | |||
POTE generator: ~11/10 = 165.913 | |||
Map: [<1 2 12 -3 13 -1 11|, <0 -3 -70 42 -69 34 -50|] | |||
EDOs: 94, 123, 217, 311, 405, 528 | |||
Badness: 0.0200 | |||
==19-limit== | |||
Commas: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573 | |||
POTE generator: ~11/10 = 165.913 | |||
Map: [<1 2 12 -3 13 -1 11 16|, <0 -3 -70 42 -69 34 -50 -85|] | |||
EDOs: 94, 123h, 217, 311, 405, 528 | |||
Badness: 0.0145 | |||
==23-limit== | |||
Commas: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155 | |||
POTE generator: ~11/10 = 165.914 | |||
Map: [<1 2 12 -3 13 -1 11 16 16|, <0 -3 -70 42 -69 34 -50 -85 -83|] | |||
EDOs: 94, 217, 311, 405 | |||
Badness: 0.0122 | |||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Canou]] | [[Category:Canou]] | ||
Revision as of 12:34, 12 October 2020
These are rank-2 temperaments that temper out the canousma, 4802000/4782969 = [4 -14 3 4⟩. For the rank-3 temperament, see Canou family.
Note that 4802000/4782969 = 2×(10/9)3/(9/7)4, these intervals tend to have lower complexity.
Temperaments not dicussed here include godzilla (a trivial case) and these:
Satin
Comma: |104 -70 3>
POTE generator: ~|-34 23 -1> = 165.907
Map: [<1 2 12|, <0 -3 -70|]
EDOs: 94, 123, 217, 311, 405, 528, 745
Badness: 2.8530
7-limit
Commas: 2100875/2097152, 4802000/4782969
POTE generator: ~8575/7776 = 165.913
Map: [<1 2 12 -3|, <0 -3 -70 42|]
EDOs: 94, 123, 217, 311, 405, 528
Badness: 0.1972
11-limit
Commas: 4000/3993, 19712/19683, 41503/41472
POTE generator: ~11/10 = 165.915
Map: [<1 2 12 -3 13|, <0 -3 -70 42 -69|]
EDOs: 94, 123, 217, 311, 405, 528
Badness: 0.0580
13-limit
Commas: 1575/1573, 2080/2079, 4096/4095, 13720/13689
POTE generator: ~11/10 = 165.914
Map: [<1 2 12 -3 13 -1|, <0 -3 -70 42 -69 34|]
EDOs: 94, 123, 217, 311, 405, 528
Badness: 0.0303
17-limit
Commas: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095
POTE generator: ~11/10 = 165.913
Map: [<1 2 12 -3 13 -1 11|, <0 -3 -70 42 -69 34 -50|]
EDOs: 94, 123, 217, 311, 405, 528
Badness: 0.0200
19-limit
Commas: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573
POTE generator: ~11/10 = 165.913
Map: [<1 2 12 -3 13 -1 11 16|, <0 -3 -70 42 -69 34 -50 -85|]
EDOs: 94, 123h, 217, 311, 405, 528
Badness: 0.0145
23-limit
Commas: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155
POTE generator: ~11/10 = 165.914
Map: [<1 2 12 -3 13 -1 11 16 16|, <0 -3 -70 42 -69 34 -50 -85 -83|]
EDOs: 94, 217, 311, 405
Badness: 0.0122