Canousmic temperaments: Difference between revisions
+Semiluna temperament |
Corrections of edos for satin |
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| Line 13: | Line 13: | ||
= Satin = | = Satin = | ||
Comma: |104 -70 3 | Comma: {{monzo|104 -70 3}} | ||
[[POTE_tuning|POTE generator]]: ~|-34 23 -1 | [[POTE_tuning|POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907 | ||
Map: [<1 2 12|, <0 -3 -70|] | Map: [<1 2 12|, <0 -3 -70|] | ||
EDOs: 94 | EDOs: {{EDOs|94, 217, 528, 745, 1273}} | ||
Badness: 2.8530 | Badness: 2.8530 | ||
| Line 30: | Line 30: | ||
Map: [<1 2 12 -3|, <0 -3 -70 42|] | Map: [<1 2 12 -3|, <0 -3 -70 42|] | ||
EDOs: 94 | EDOs: {{EDOs|94, 217, 311, 839, 1150}} | ||
Badness: 0.1972 | Badness: 0.1972 | ||
| Line 41: | Line 41: | ||
Map: [<1 2 12 -3 13|, <0 -3 -70 42 -69|] | Map: [<1 2 12 -3 13|, <0 -3 -70 42 -69|] | ||
EDOs: 94 | EDOs: {{EDOs|94, 217, 311}} | ||
Badness: 0.0580 | Badness: 0.0580 | ||
| Line 52: | Line 52: | ||
Map: [<1 2 12 -3 13 -1|, <0 -3 -70 42 -69 34|] | Map: [<1 2 12 -3 13 -1|, <0 -3 -70 42 -69 34|] | ||
EDOs: 94 | EDOs: {{EDOs|94, 217, 311, 839e, 1150e}} | ||
Badness: 0.0303 | Badness: 0.0303 | ||
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Map: [<1 2 12 -3 13 -1 11|, <0 -3 -70 42 -69 34 -50|] | Map: [<1 2 12 -3 13 -1 11|, <0 -3 -70 42 -69 34 -50|] | ||
EDOs: 94 | EDOs: {{EDOs|94, 217, 311, 839e, 1150eg}} | ||
Badness: 0.0200 | Badness: 0.0200 | ||
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Map: [<1 2 12 -3 13 -1 11 16|, <0 -3 -70 42 -69 34 -50 -85|] | Map: [<1 2 12 -3 13 -1 11 16|, <0 -3 -70 42 -69 34 -50 -85|] | ||
EDOs: 94 | EDOs: {{EDOs|94, 217, 311, 839e, 1150eg}} | ||
Badness: 0.0145 | Badness: 0.0145 | ||
| Line 85: | Line 85: | ||
Map: [<1 2 12 -3 13 -1 11 16 16|, <0 -3 -70 42 -69 34 -50 -85 -83|] | Map: [<1 2 12 -3 13 -1 11 16 16|, <0 -3 -70 42 -69 34 -50 -85 -83|] | ||
EDOs: 94, 217, 311, | EDOs: {{EDOs|94, 217, 311, 839ei, 1150egi}} | ||
Badness: 0.0122 | Badness: 0.0122 | ||
Revision as of 10:00, 18 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|]
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|]
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|]
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, 217, 311, 839e, 1150e
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, 217, 311, 839e, 1150eg
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, 217, 311, 839e, 1150eg
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, 839ei, 1150egi
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