Canousmic temperaments: Difference between revisions
Move satin here since this is a simpler comma |
+Semiluna temperament |
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* [[Hemifamity temperaments #Septiquarter|Septiquarter]] | * [[Hemifamity temperaments #Septiquarter|Septiquarter]] | ||
* [[Schismatic family #Kleischismic|Kleischismic]] | * [[Schismatic family #Kleischismic|Kleischismic]] | ||
Discussed below are satin and semiluna. | |||
= Satin = | = Satin = | ||
| Line 87: | Line 89: | ||
Badness: 0.0122 | Badness: 0.0122 | ||
= Semiluna = | |||
{{see also|Luna family #Semiluna}} | |||
Commas: 4802000/4782969, 95703125/95551488 | |||
POTE generator: ~2187/1960 = 193.1725 | |||
Map: [<2 8 4 23|, <0 -15 2 -54|] | |||
EDOs: {{EDOs|56d, 118, 292, 410}} | |||
Badness: 0.1922 | |||
== 11-limit == | |||
Commas: 5632/5625, 9801/9800, 14641/14580 | |||
POTE generator: ~121/108 = 193.1732 | |||
Map: [<2 8 4 23 14|, <0 -15 2 -54 -22|] | |||
EDOs: {{EDOs|56d, 118, 292, 410}} | |||
Badness: 0.0678 | |||
== 13-limit == | |||
Commas: 352/351, 625/624, 9801/9800, 14641/14580 | |||
POTE generator: ~121/108 = 193.1550 | |||
Map: [<2 8 4 23 14 0|, <0 -15 2 -54 -22 23|] | |||
EDOs: {{EDOs|56d, 118, 174d, 292}} | |||
Badness: 0.0620 | |||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Canou]] | [[Category:Canou]] | ||
Revision as of 12:57, 16 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:
Discussed below are satin and semiluna.
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
Semiluna
Commas: 4802000/4782969, 95703125/95551488
POTE generator: ~2187/1960 = 193.1725
Map: [<2 8 4 23|, <0 -15 2 -54|]
Badness: 0.1922
11-limit
Commas: 5632/5625, 9801/9800, 14641/14580
POTE generator: ~121/108 = 193.1732
Map: [<2 8 4 23 14|, <0 -15 2 -54 -22|]
Badness: 0.0678
13-limit
Commas: 352/351, 625/624, 9801/9800, 14641/14580
POTE generator: ~121/108 = 193.1550
Map: [<2 8 4 23 14 0|, <0 -15 2 -54 -22 23|]
Badness: 0.0620