Xenharmonic Wiki

Meantone family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Undo. The sequence was simply done on TE. Revision needs to be discussed at Talk: Optimal ET sequence
Tag: Undo
Template for mappings (1/2); +descriptions to some diamond tradeoff ranges
Line 14: Line 14:
[[Comma list]]: 81/80
[[Comma list]]: 81/80


[[Mapping]]: [{{val| 1 0 -4 }}, {{val| 0 1 4 }}]
{{Mapping|legend=1| 1 0 -4 | 0 1 4 }}


: mapping generators: ~2, ~3
: mapping generators: ~2, ~3
Line 28: Line 28:
[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 720.000] (4\7 to 3\5)
* 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 720.000] (4\7 to 3\5)
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955]
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955] (1/3-comma to Pyth.)
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]


Line 60: Line 60:
[[Comma list]]: 81/80, 121/120
[[Comma list]]: 81/80, 121/120


[[Sval]] [[mapping]]: [{{val| 1 1 0 2 }}, {{val| 0 2 8 5 }}]
{{Mapping|legend=2| 1 1 0 2 | 0 2 8 5 }}


: sval mapping generators: ~2, ~11/9
: sval mapping generators: ~2, ~11/9


[[Gencom]] [[mapping]]: [{{val| 1 1 0 0 2 }}, {{val| 0 2 8 0 5 }}]
{{Mapping|legend=3| 1 1 0 0 2 | 0 2 8 0 5 }}


: gencom: [2 11/9; 81/80 121/120]
: gencom: [2 11/9; 81/80 121/120]
Line 79: Line 79:
Comma list: 66/65, 81/80, 121/120
Comma list: 66/65, 81/80, 121/120


Sval mapping: [{{val| 1 1 0 2 4 }}, {{val| 0 2 8 5 -1 }}]
Sval mapping: {{mapping| 1 1 0 2 4| 0 2 8 5 -1 }}


: sval mapping generators: ~2, ~11/9
: sval mapping generators: ~2, ~11/9


Gencom mapping: [{{val| 1 1 0 0 2 4 }}, {{val| 0 2 8 0 5 -1 }}]
Gencom mapping: {{mapping| 1 1 0 0 2 4 | 0 2 8 0 5 -1 }}


: gencom: [2 11/9; 66/65 81/80 121/120]
: gencom: [2 11/9; 66/65 81/80 121/120]
Line 104: Line 104:
[[Comma list]]: 81/80, 126/125
[[Comma list]]: 81/80, 126/125


[[Mapping]]: [{{val| 1 0 -4 -13 }}, {{val| 0 1 4 10 }}]
{{Mapping|legend=1| 1 0 -4 -13 | 0 1 4 10 }}


{{Multival|legend=1| 1 4 10 4 13 12 }}
{{Multival|legend=1| 1 4 10 4 13 12 }}
Line 112: Line 112:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~3/2 = {{monzo| 0 0 1/4 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~3/2 = {{monzo| 0 0 1/4 }}
: [{{Monzo| 1 0 0 0 }}, {{monzo| 1 0 1/4 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| -3 0 5/2 0 }}]
: {{Monzo list| 1 0 0 0 | 1 0 1/4 0 | 0 0 1 0 | -3 0 5/2 0 }}
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [694.737, 700.000] (11\19 to 7\12)
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [694.737, 700.000] (11\19 to 7\12)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955] (1/3-comma to Pyth.)
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)
* 7-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 700.000]
* 7-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 700.000]
* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]
* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]
Line 135: Line 135:
Comma list: 81/80, 99/98, 126/125
Comma list: 81/80, 99/98, 126/125


Mapping: [{{val| 1 0 -4 -13 -25 }}, {{val| 0 1 4 10 18 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.1676
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.1676


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~3/2 = {{Monzo| 9/16 -1/8 0 0 1/16 }}
* 11-odd-limit: ~3/2 = {{monzo| 9/16 -1/8 0 0 1/16 }}
: [{{Monzo| 1 0 0 0 0 }}, {{monzo| 25/16 -1/8 0 0 1/16 }}, {{monzo| 9/4 -1/2 0 0 1/4 }}, {{monzo| 21/8 -5/4 0 0 5/8 }}, {{monzo| 25/8 -9/4 0 0 9/8 }}]
: [{{Monzo| 1 0 0 0 0 }}, {{monzo| 25/16 -1/8 0 0 1/16 }}, {{monzo| 9/4 -1/2 0 0 1/4 }}, {{monzo| 21/8 -5/4 0 0 5/8 }}, {{monzo| 25/8 -9/4 0 0 9/8 }}]
: Eigenmonzo (unchanged-interval) basis: 2.11/9
: Eigenmonzo (unchanged-interval) basis: 2.11/9
Line 146: Line 146:
Tuning ranges:  
Tuning ranges:  
* 11-odd-limit diamond monotone: ~3/2 = [696.774, 700.000] (18\31 to 7\12)
* 11-odd-limit diamond monotone: ~3/2 = [696.774, 700.000] (18\31 to 7\12)
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 700.000]


Line 163: Line 163:
Comma list: 66/65, 81/80, 99/98, 105/104
Comma list: 66/65, 81/80, 99/98, 105/104


Mapping: [{{val| 1 0 -4 -13 -25 -20 }}, {{val| 0 1 4 10 18 15 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8552
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8552
Line 180: Line 180:
Comma list: 66/65, 81/80, 99/98, 105/104, 121/119
Comma list: 66/65, 81/80, 99/98, 105/104, 121/119


Mapping: [{{val| 1 0 -4 -13 -25 -20 -37 }}, {{val| 0 1 4 10 18 15 26 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 | 0 1 4 10 18 15 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486
Line 193: Line 193:
Comma list: 66/65, 77/76, 81/80, 99/98, 105/104, 121/119
Comma list: 66/65, 77/76, 81/80, 99/98, 105/104, 121/119


Mapping: [{{val| 1 0 -4 -13 -25 -20 -37 -40 }}, {{val| 0 1 4 10 18 15 26 28 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 -40 | 0 1 4 10 18 15 26 28 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551
Line 206: Line 206:
Comma list: 51/50, 66/65, 81/80, 85/84, 99/98
Comma list: 51/50, 66/65, 81/80, 85/84, 99/98


Mapping: [{{val| 1 0 -4 -13 -25 -20 -7 }}, {{val| 0 1 4 10 18 15 7 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 | 0 1 4 10 18 15 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0360
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0360
Line 219: Line 219:
Comma list: 51/50, 57/56, 66/65, 81/80, 85/84, 99/98
Comma list: 51/50, 57/56, 66/65, 81/80, 85/84, 99/98


Mapping: [{{val| 1 0 -4 -13 -25 -20 -7 -10 }}, {{val| 0 1 4 10 18 15 7 9 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 -10 | 0 1 4 10 18 15 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2161
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2161
Line 232: Line 232:
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119


Mapping: [{{val| 1 0 -4 -13 -25 -20 12 }}, {{val| 0 1 4 10 18 15 -5 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9080
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9080
Line 245: Line 245:
Comma list: 66/65, 81/80, 96/95, 99/98, 105/104, 120/119
Comma list: 66/65, 81/80, 96/95, 99/98, 105/104, 120/119


Mapping: [{{val| 1 0 -4 -13 -25 -20 12 9 }}, {{val| 0 1 4 10 18 15 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9308
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9308
Line 258: Line 258:
Comma list: 81/80, 99/98, 126/125, 144/143
Comma list: 81/80, 99/98, 126/125, 144/143


Mapping: [{{val| 1 0 -4 -13 -25 29 }}, {{val| 0 1 4 10 18 -16 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2582
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2582
Line 268: Line 268:
Tuning ranges:  
Tuning ranges:  
* 13- and 15-odd-limit diamond monotone: ~3/2 = [696.774, 697.674] (18\31 to 25\43)
* 13- and 15-odd-limit diamond monotone: ~3/2 = [696.774, 697.674] (18\31 to 25\43)
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]


Line 280: Line 280:
Comma list: 81/80, 99/98, 120/119, 126/125, 144/143
Comma list: 81/80, 99/98, 120/119, 126/125, 144/143


Mapping: [{{val| 1 0 -4 -13 -25 29 12 }}, {{val| 0 1 4 10 18 -16 -5 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2996
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2996
Line 293: Line 293:
Comma list: 81/80, 96/95, 99/98, 120/119, 126/125, 144/143
Comma list: 81/80, 96/95, 99/98, 120/119, 126/125, 144/143


Mapping: [{{val| 1 0 -4 -13 -25 29 12 9 }}, {{val| 0 1 4 10 18 -16 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.3271
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.3271
Line 306: Line 306:
Comma list: 78/77, 81/80, 99/98, 126/125
Comma list: 78/77, 81/80, 99/98, 126/125


Mapping: [{{val| 1 0 -4 -13 -25 -39 }}, {{val| 0 1 4 10 18 27 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5155
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5155
Line 323: Line 323:
Comma list: 78/77, 81/80, 99/98, 126/125, 273/272
Comma list: 78/77, 81/80, 99/98, 126/125, 273/272


Mapping: [{{val| 1 0 -4 -13 -25 -39 -56 }}, {{val| 0 1 4 10 18 27 38 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 | 0 1 4 10 18 27 38 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5076
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5076
Line 336: Line 336:
Comma list: 78/77, 81/80, 99/98, 126/125, 153/152, 273/272
Comma list: 78/77, 81/80, 99/98, 126/125, 153/152, 273/272


Mapping: [{{val| 1 0 -4 -13 -25 -39 -56 -59 }}, {{val| 0 1 4 10 18 27 38 40 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 -59 | 0 1 4 10 18 27 38 40 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.4848
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.4848
Line 349: Line 349:
Comma list: 51/50, 78/77, 81/80, 85/84, 99/98
Comma list: 51/50, 78/77, 81/80, 85/84, 99/98


Mapping: [{{val| 1 0 -4 -13 -25 -39 -7 }}, {{val| 0 1 4 10 18 27 7 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 | 0 1 4 10 18 27 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.6098
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.6098
Line 362: Line 362:
Comma list: 51/50, 57/56, 78/77, 81/80, 85/84, 99/98
Comma list: 51/50, 57/56, 78/77, 81/80, 85/84, 99/98


Mapping: [{{val| 1 0 -4 -13 -25 -39 -7 -10 }}, {{val| 0 1 4 10 18 27 7 9 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 -10 | 0 1 4 10 18 27 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.7012
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.7012
Line 375: Line 375:
Comma list: 78/77, 81/80, 99/98, 120/119, 126/125
Comma list: 78/77, 81/80, 99/98, 120/119, 126/125


Mapping: [{{val| 1 0 -4 -13 -25 -39 12 }}, {{val| 0 1 4 10 18 27 -5 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5384
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5384
Line 388: Line 388:
Comma list: 78/77, 81/80, 96/95, 99/98, 120/119, 126/125
Comma list: 78/77, 81/80, 96/95, 99/98, 120/119, 126/125


Mapping: [{{val| 1 0 -4 -13 -25 -39 12 9 }}, {{val| 0 1 4 10 18 27 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5550
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5550
Line 401: Line 401:
Comma list: 81/80, 99/98, 126/125, 169/168
Comma list: 81/80, 99/98, 126/125, 169/168


Mapping: [{{val| 1 0 -4 -13 -25 -5 }}, {{val| 0 2 8 20 36 11 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -5 | 0 2 8 20 36 11 }}


: mapping generators: ~2, ~26/15
: mapping generators: ~2, ~26/15
Line 416: Line 416:
Comma list: 81/80, 99/98, 126/125, 169/168, 221/220
Comma list: 81/80, 99/98, 126/125, 169/168, 221/220


Mapping: [{{val| 1 0 -4 -13 -25 -5 -22 }}, {{val| 0 2 8 20 36 11 33 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}


Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6173
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6173
Line 429: Line 429:
Comma list: 81/80, 99/98, 126/125, 153/152, 169/168, 221/220
Comma list: 81/80, 99/98, 126/125, 153/152, 169/168, 221/220


Mapping: [{{val| 1 0 -4 -13 -25 -5 -22 -25 }}, {{val| 0 2 8 20 36 11 33 37 }}]
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}


Optimal tuning (CTE): ~2 = 1\1, ~19/11 = 948.6088
Optimal tuning (CTE): ~2 = 1\1, ~19/11 = 948.6088
Line 442: Line 442:
Comma list: 81/80, 99/98, 126/125, 847/845
Comma list: 81/80, 99/98, 126/125, 847/845


Mapping: [{{val| 2 0 -8 -26 -50 -59 }}, {{val| 0 1 4 10 18 21 }}]
Mapping: {{mapping| 2 0 -8 -26 -50 -59 | 0 1 4 10 18 21 }}


: mapping generators: ~55/39, ~3
: mapping generators: ~55/39, ~3
Line 457: Line 457:
Comma list: 81/80, 99/98, 126/125, 221/220, 289/288
Comma list: 81/80, 99/98, 126/125, 221/220, 289/288


Mapping: [{{val| 2 0 -8 -26 -50 -59 5 }}, {{val| 0 1 4 10 18 21 1 }}]
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1740
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1740
Line 470: Line 470:
Comma list: 81/80, 99/98, 126/125, 153/152, 209/208, 221/220
Comma list: 81/80, 99/98, 126/125, 153/152, 209/208, 221/220


Mapping: [{{val| 2 0 -8 -26 -50 -59 5 -1 }}, {{val| 0 1 4 10 18 21 1 3 }}]
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1871
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1871
Line 485: Line 485:
Comma list: 81/80, 126/125, 385/384
Comma list: 81/80, 126/125, 385/384


Mapping: [{{val| 1 0 -4 -13 24 }}, {{val| 0 1 4 10 -13 }}]
Mapping: {{mapping| 1 0 -4 -13 24 | 0 1 4 10 -13 }}


: mapping generator: ~2, ~3
: mapping generator: ~2, ~3
Line 498: Line 498:
Tuning ranges:  
Tuning ranges:  
* 11-odd-limit diamond monotone: ~3/2 = [694.737, 696.774] (11\19 to 18\31)
* 11-odd-limit diamond monotone: ~3/2 = [694.737, 696.774] (11\19 to 18\31)
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]


Line 516: Line 516:
Comma list: 81/80, 105/104, 126/125, 144/143
Comma list: 81/80, 105/104, 126/125, 144/143


Mapping: [{{val| 1 0 -4 -13 24 -20 }}, {{val| 0 1 4 10 -13 15 }}]
Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3563
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3563
Line 538: Line 538:
Comma list: 81/80, 105/104, 126/125, 144/143, 273/272
Comma list: 81/80, 105/104, 126/125, 144/143, 273/272


Mapping: [{{val| 1 0 -4 -13 24 -20 -37 }}, {{val| 0 1 4 10 -13 15 26 }}]
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3508
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3508
Line 551: Line 551:
Comma list: 81/80, 105/104, 126/125, 144/143, 153/152, 273/272
Comma list: 81/80, 105/104, 126/125, 144/143, 153/152, 273/272


Mapping: [{{val| 1 0 -4 -13 24 -20 -37 -40 }}, {{val| 0 1 4 10 -13 15 26 28 }}]
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3471
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3471
Line 564: Line 564:
Comma list: 81/80, 105/104, 120/119, 126/125, 144/143
Comma list: 81/80, 105/104, 120/119, 126/125, 144/143


Mapping: [{{val| 1 0 -4 -13 24 -20 12 }}, {{val| 0 1 4 10 -13 15 -5 }}]
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4388
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4388
Line 577: Line 577:
Comma list: 77/76, 81/80, 96/95, 105/104, 120/119, 126/125
Comma list: 77/76, 81/80, 96/95, 105/104, 120/119, 126/125


Mapping: [{{val| 1 0 -4 -13 24 -20 12 9 }}, {{val| 0 1 4 10 -13 15 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4838
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4838
Line 590: Line 590:
Comma list: 65/64, 78/77, 81/80, 91/90
Comma list: 65/64, 78/77, 81/80, 91/90


Mapping: [{{val| 1 0 -4 -13 24 10 }}, {{val| 0 1 4 10 -13 -4 }}]
Mapping: {{mapping| 1 0 -4 -13 24 10 | 0 1 4 10 -13 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2827
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2827
Line 607: Line 607:
Comma list: 52/51, 65/64, 78/77, 81/80, 91/90
Comma list: 52/51, 65/64, 78/77, 81/80, 91/90


Mapping: [{{val| 1 0 -4 -13 24 10 12 }}, {{val| 0 1 4 10 -13 -4 -5 }}]
Mapping: {{mapping| 1 0 -4 -13 24 10 12 | 0 1 4 10 -13 -4 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4069
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4069
Line 620: Line 620:
Comma list: 39/38, 52/51, 65/64, 77/76, 81/80, 91/90
Comma list: 39/38, 52/51, 65/64, 77/76, 81/80, 91/90


Mapping: [{{val| 1 0 -4 -13 24 10 12 9 }}, {{val| 0 1 4 10 -13 -4 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 -13 24 10 12 9 | 0 1 4 10 -13 -4 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4731
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4731
Line 633: Line 633:
Comma list: 51/50, 65/64, 78/77, 81/80, 85/84
Comma list: 51/50, 65/64, 78/77, 81/80, 85/84


Mapping: [{{val| 1 0 -4 -13 24 10 -7 }}, {{val| 0 1 4 10 -13 -4 7 }}]
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 | 0 1 4 10 -13 -4 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6614
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6614
Line 646: Line 646:
Comma list: 51/50, 57/56, 65/64, 76/75, 78/77, 81/80
Comma list: 51/50, 57/56, 65/64, 76/75, 78/77, 81/80


Mapping: [{{val| 1 0 -4 -13 24 10 -7 -10 }}, {{val| 0 1 4 10 -13 -4 7 9 }}]
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 -10 | 0 1 4 10 -13 -4 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0160
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0160
Line 659: Line 659:
Comma list: 45/44, 56/55, 81/80
Comma list: 45/44, 56/55, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 }}, {{val| 0 1 4 10 6 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1527
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1527
Line 677: Line 677:
Comma list: 45/44, 56/55, 78/77, 81/80
Comma list: 45/44, 56/55, 78/77, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 -20 }}, {{val| 0 1 4 10 6 15 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0983
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0983
Line 690: Line 690:
Comma list: 45/44, 56/55, 78/77, 81/80, 120/119
Comma list: 45/44, 56/55, 78/77, 81/80, 120/119


Mapping: [{{val| 1 0 -4 -13 -6 -20 12 }}, {{val| 0 1 4 10 6 15 -5 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2161
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2161
Line 703: Line 703:
Comma list: 45/44, 56/55, 78/77, 81/80, 96/95, 120/119
Comma list: 45/44, 56/55, 78/77, 81/80, 96/95, 120/119


Mapping: [{{val| 1 0 -4 -13 -6 -20 12 9 }}, {{val| 0 1 4 10 6 15 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2774
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2774
Line 716: Line 716:
Comma list: 34/33, 45/44, 51/50, 56/55, 78/77
Comma list: 34/33, 45/44, 51/50, 56/55, 78/77


Mapping: [{{val| 1 0 -4 -13 -6 -20 -7 }}, {{val| 0 1 4 10 6 15 7 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 | 0 1 4 10 6 15 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4501
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4501
Line 729: Line 729:
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 78/77
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 78/77


Mapping: [{{val| 1 0 -4 -13 -6 -20 -7 -10 }}, {{val| 0 1 4 10 6 15 7 9 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 -10 | 0 1 4 10 6 15 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.121
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.121
Line 742: Line 742:
Comma list: 45/44, 56/55, 65/64, 81/80
Comma list: 45/44, 56/55, 65/64, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 10 }}, {{val| 0 1 4 10 6 -4 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7897
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7897
Line 755: Line 755:
Comma list: 45/44, 52/51, 56/55, 65/64, 81/80
Comma list: 45/44, 52/51, 56/55, 65/64, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 10 12 }}, {{val| 0 1 4 10 6 -4 -5 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0114
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0114
Line 768: Line 768:
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 }}, {{val| 0 1 4 10 6 -4 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1196
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1196
Line 781: Line 781:
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 69/68, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 65/64, 69/68, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 | 0 1 4 10 6 -4 -5 -3 -6 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0585
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0585
Line 794: Line 794:
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 | 0 1 4 10 6 -4 -5 -3 -6 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.9824
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.9824
Line 807: Line 807:
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80, 93/92
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 81/80, 93/92


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7980
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7980
Line 820: Line 820:
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6746
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6746
Line 833: Line 833:
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92, 124/123
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 93/92, 124/123


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7239
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7239
Line 846: Line 846:
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 124/123
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 124/123


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7160
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7160
Line 859: Line 859:
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 95/94, 124/123
Comma list: 39/38, 45/44, 52/51, 56/55, 58/57, 65/64, 69/68, 75/74, 81/80, 86/85, 93/92, 95/94, 124/123


Mapping: [{{val| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 4 }}, {{val| 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 1 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 4 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6849
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6849
Line 872: Line 872:
Comma list: 34/33, 45/44, 51/50, 56/55, 65/64
Comma list: 34/33, 45/44, 51/50, 56/55, 65/64


Mapping: [{{val| 1 0 -4 -13 -6 10 -7 }}, {{val| 0 1 4 10 6 -4 7 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 | 0 1 4 10 6 -4 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4125
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4125
Line 885: Line 885:
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 65/64
Comma list: 34/33, 45/44, 51/50, 56/55, 57/55, 65/64


Mapping: [{{val| 1 0 -4 -13 -6 10 -7 -10 }}, {{val| 0 1 4 10 6 -4 7 9 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 -10 | 0 1 4 10 6 -4 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9500
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9500
Line 898: Line 898:
Comma list: 27/26, 40/39, 45/44, 56/55
Comma list: 27/26, 40/39, 45/44, 56/55


Mapping: [{{val| 1 0 -4 -13 -6 -1 }}, {{val| 0 1 4 10 6 3 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -1 | 0 1 4 10 6 3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6202
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6202
Line 911: Line 911:
Comma list: 27/26, 34/33, 40/39, 45/44, 56/55
Comma list: 27/26, 34/33, 40/39, 45/44, 56/55


Mapping: [{{val| 1 0 -4 -13 -6 -1 -7 }}, {{val| 0 1 4 10 6 3 7 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 | 0 1 4 10 6 3 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2789
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2789
Line 924: Line 924:
Comma list: 27/26, 34/33, 40/39, 45/44, 56/55, 57/55
Comma list: 27/26, 34/33, 40/39, 45/44, 56/55, 57/55


Mapping: [{{val| 1 0 -4 -13 -6 -1 -7 -10 }}, {{val| 0 1 4 10 6 3 7 9 }}]
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 -10 | 0 1 4 10 6 3 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8486
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8486
Line 937: Line 937:
Comma list: 33/32, 55/54, 77/75
Comma list: 33/32, 55/54, 77/75


Mapping: [{{val| 1 0 -4 -13 5 }}, {{val| 0 1 4 10 -1 }}]
Mapping: {{mapping| 1 0 -4 -13 5 | 0 1 4 10 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7022
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7022
Line 950: Line 950:
Comma list: 33/32, 55/54, 65/64, 77/75
Comma list: 33/32, 55/54, 65/64, 77/75


Mapping: [{{val| 1 0 -4 -13 5 10 }}, {{val| 0 1 4 10 -1 -4 }}]
Mapping: {{mapping| 1 0 -4 -13 5 10 | 0 1 4 10 -1 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2408
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2408
Line 963: Line 963:
Comma list: 81/80, 121/120, 126/125
Comma list: 81/80, 121/120, 126/125


Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 8 20 5 }}]
Mapping: {{mapping| 1 1 0 -3 2 | 0 2 8 20 5 }}


: mapping generators: ~2, ~11/9
: mapping generators: ~2, ~11/9
Line 978: Line 978:
Comma list: 66/65, 81/80, 121/120, 126/125
Comma list: 66/65, 81/80, 121/120, 126/125


Mapping: [{{val| 1 1 0 -3 2 4 }}, {{val| 0 2 8 20 5 -1 }}]
Mapping: {{mapping| 1 1 0 -3 2 4 | 0 2 8 20 5 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5444
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5444
Line 993: Line 993:
Comma list: 81/80, 126/125, 245/242
Comma list: 81/80, 126/125, 245/242


Mapping: [{{val| 2 0 -8 -26 -31 }}, {{val| 0 1 4 10 12 }}]
Mapping: {{mapping| 2 0 -8 -26 -31 | 0 1 4 10 12 }}


: mapping generators: ~63/44, ~3
: mapping generators: ~63/44, ~3
Line 1,008: Line 1,008:
Comma list: 81/80, 105/104, 126/125, 245/242
Comma list: 81/80, 105/104, 126/125, 245/242


Mapping: [{{val| 2 0 -8 -26 -31 -40 }}, {{val| 0 1 4 10 12 15 }}]
Mapping: {{mapping| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}


Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 696.3410
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 696.3410
Line 1,021: Line 1,021:
Comma list: 81/80, 105/104, 126/125, 189/187, 221/220
Comma list: 81/80, 105/104, 126/125, 189/187, 221/220


Mapping: [{{val| 2 0 -8 -26 -31 -40 5 }}, {{val| 0 1 4 10 12 15 1 }}]
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3526
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3526
Line 1,034: Line 1,034:
Comma list: 81/80, 105/104, 126/125, 153/152, 189/187, 221/220
Comma list: 81/80, 105/104, 126/125, 153/152, 189/187, 221/220


Mapping: [{{val| 2 0 -8 -26 -31 -40 5 -1 }}, {{val| 0 1 4 10 12 15 1 3 }}]
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3837
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3837
Line 1,047: Line 1,047:
Comma list: 81/80, 126/125, 1344/1331
Comma list: 81/80, 126/125, 1344/1331


Mapping: [{{val| 1 2 4 7 5 }}, {{val| 0 -3 -12 -30 -11 }}]
Mapping: {{mapping| 1 2 4 7 5 | 0 -3 -12 -30 -11 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7074
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7074
Line 1,060: Line 1,060:
Comma list: 81/80, 126/125, 144/143, 364/363
Comma list: 81/80, 126/125, 144/143, 364/363


Mapping: [{{val| 1 2 4 7 5 3 }}, {{val| 0 -3 -12 -30 -11 5 }}]
Mapping: {{mapping| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7121
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7121
Line 1,073: Line 1,073:
Comma list: 81/80, 126/125, 144/143, 189/187, 221/220
Comma list: 81/80, 126/125, 144/143, 189/187, 221/220


Mapping: [{{val| 1 2 4 7 5 3 8 }}, {{val| 0 -3 -12 -30 -11 5 -28 }}]
Mapping: {{mapping| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7047
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7047
Line 1,082: Line 1,082:


== Flattone ==
== Flattone ==
In flattone, 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4]] is a diminished seventh interval (C-Bbb). Other intervals are [[7/6]], a diminished third (C-Ebb), and [[7/5]], a doubly diminshed fifth (C-Gbb). In general, most septimal subminor intervals are diminished and most septimal supermajor intervals are augmented, which makes it quite easy to learn flattone notation. Good tunings for flattone are [[26edo|26EDO]], [[45edo|45EDO]] and [[64edo|64EDO]].
In flattone, 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4]] is a diminished seventh interval (C-Bbb). Other intervals are [[7/6]], a diminished third (C-Ebb), and [[7/5]], a doubly diminshed fifth (C-Gbb). In general, most septimal subminor intervals are diminished and most septimal supermajor intervals are augmented, which makes it quite easy to learn flattone notation. Good tunings for flattone are [[26edo]], [[45edo]] and [[64edo]].


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 1,088: Line 1,088:
[[Comma list]]: 81/80, 525/512
[[Comma list]]: 81/80, 525/512


[[Mapping]]: [{{val| 1 0 -4 17 }}, {{val| 0 1 4 -9 }}]
{{Mapping|legend=1| 1 0 -4 17 | 0 1 4 -9 }}


{{Multival|legend=1| 1 4 -9 4 -17 -32 }}
{{Multival|legend=1| 1 4 -9 4 -17 -32 }}
Line 1,122: Line 1,122:
Comma list: 45/44, 81/80, 385/384
Comma list: 45/44, 81/80, 385/384


Mapping: [{{val| 1 0 -4 17 -6 }}, {{val| 0 1 4 -9 6 }}]
Mapping: {{mapping| 1 0 -4 17 -6 | 0 1 4 -9 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 693.126
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 693.126
Line 1,142: Line 1,142:
Comma list: 45/44, 65/64, 78/77, 81/80
Comma list: 45/44, 65/64, 78/77, 81/80


Mapping: [{{val| 1 0 -4 17 -6 10 }}, {{val| 0 1 4 -9 6 -4 }}]
Mapping: {{mapping| 1 0 -4 17 -6 10 | 0 1 4 -9 6 -4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 693.058
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 693.058
Line 1,162: Line 1,162:
Comma list: 81/80, 121/120, 525/512
Comma list: 81/80, 121/120, 525/512


Mapping: [{{val| 1 1 0 8 2 }}, {{val| 0 2 8 -18 5 }}]
Mapping: {{mapping| 1 1 0 8 2 | 0 2 8 -18 5 }}


: mapping generators: ~2, ~11/9
: mapping generators: ~2, ~11/9
Line 1,177: Line 1,177:
Comma list: 65/64, 81/80, 105/104, 121/120
Comma list: 65/64, 81/80, 105/104, 121/120


Mapping: [{{val| 1 1 0 8 2 6 }}, {{val| 0 2 8 -18 5 -8 }}]
Mapping: {{mapping| 1 1 0 8 2 6 | 0 2 8 -18 5 -8 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 346.910
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 346.910
Line 1,192: Line 1,192:
[[Comma list]]: 36/35, 64/63
[[Comma list]]: 36/35, 64/63


[[Mapping]]: [{{val| 1 0 -4 6 }}, {{val| 0 1 4 -2 }}]
{{Mapping|legend=1| 1 0 -4 6 | 0 1 4 -2 }}


{{Multival|legend=1| 1 4 -2 4 -6 -16 }}
{{Multival|legend=1| 1 4 -2 4 -6 -16 }}
Line 1,213: Line 1,213:
Comma list: 36/35, 56/55, 64/63
Comma list: 36/35, 56/55, 64/63


Mapping: [{{val| 1 0 -4 6 13 }}, {{val| 0 1 4 -2 -6 }}]
Mapping: {{mapping| 1 0 -4 6 13 | 0 1 4 -2 -6 }}


Tuning ranges:  
Tuning ranges:  
Line 1,231: Line 1,231:
Comma list: 36/35, 56/55, 64/63, 66/65
Comma list: 36/35, 56/55, 64/63, 66/65


Mapping: [{{val| 1 0 -4 6 13 18 }}, {{val| 0 1 4 -2 -6 -9 }}]
Mapping: {{mapping| 1 0 -4 6 13 18 | 0 1 4 -2 -6 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.636
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.636
Line 1,249: Line 1,249:
Comma list: 26/25, 36/35, 56/55, 64/63
Comma list: 26/25, 36/35, 56/55, 64/63


Mapping: [{{val| 1 0 -4 6 13 -9 }}, {{val| 0 1 4 -2 -6 8 }}]
Mapping: {{mapping| 1 0 -4 6 13 -9 | 0 1 4 -2 -6 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.905
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.905
Line 1,262: Line 1,262:
Comma list: 36/35, 45/44, 64/63
Comma list: 36/35, 45/44, 64/63


Mapping: [{{val| 1 0 -4 6 -6 }}, {{val| 0 1 4 -2 6 }}]
Mapping: {{mapping| 1 0 -4 6 -6 | 0 1 4 -2 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.776
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.776
Line 1,275: Line 1,275:
Comma list: 36/35, 45/44, 52/49, 64/63
Comma list: 36/35, 45/44, 52/49, 64/63


Mapping: [{{val| 1 0 -4 6 -6 10 }}, {{val| 0 1 4 -2 6 -4 }}]
Mapping: {{mapping| 1 0 -4 6 -6 10 | 0 1 4 -2 6 -4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 695.762
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 695.762
Line 1,288: Line 1,288:
Comma list: 36/35, 45/44, 51/49, 52/49, 64/63
Comma list: 36/35, 45/44, 51/49, 52/49, 64/63


Mapping: [{{val| 1 0 -4 6 -6 10 12 }}, {{val| 0 1 4 -2 6 -4 -5 }}]
Mapping: {{mapping| 1 0 -4 6 -6 10 12 | 0 1 4 -2 6 -4 -5 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.115
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.115
Line 1,301: Line 1,301:
Comma list: 36/35, 39/38, 45/44, 51/49, 52/49, 57/56
Comma list: 36/35, 39/38, 45/44, 51/49, 52/49, 57/56


Mapping: [{{val| 1 0 -4 6 -6 10 12 9 }}, {{val| 0 1 4 -2 6 -4 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 6 -6 10 12 9 | 0 1 4 -2 6 -4 -5 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.217
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.217
Line 1,314: Line 1,314:
Comma list: 27/26, 36/35, 45/44, 64/63
Comma list: 27/26, 36/35, 45/44, 64/63


Mapping: [{{val| 1 0 -4 6 -6 -1 }}, {{val| 0 1 4 -2 6 3 }}]
Mapping: {{mapping| 1 0 -4 6 -6 -1 | 0 1 4 -2 6 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.544
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.544
Line 1,327: Line 1,327:
Comma list: 36/35, 64/63, 77/75
Comma list: 36/35, 64/63, 77/75


Mapping: [{{val| 1 0 -4 6 -14 }}, {{val| 0 1 4 -2 11 }}]
Mapping: {{mapping| 1 0 -4 6 -14 | 0 1 4 -2 11 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.004
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.004
Line 1,340: Line 1,340:
Comma list: 26/25, 36/35, 64/63, 66/65
Comma list: 26/25, 36/35, 64/63, 66/65


Mapping: [{{val| 1 0 -4 6 -14 -9 }}, {{val| 0 1 4 -2 11 8 }}]
Mapping: {{mapping| 1 0 -4 6 -14 -9 | 0 1 4 -2 11 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.496
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.496
Line 1,353: Line 1,353:
Comma list: 22/21, 33/32, 36/35
Comma list: 22/21, 33/32, 36/35


Mapping: [{{val| 1 0 -4 6 5 }}, {{val| 0 1 4 -2 -1 }}]
Mapping: {{mapping| 1 0 -4 6 5 | 0 1 4 -2 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.491
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.491
Line 1,366: Line 1,366:
Comma list: 22/21, 27/26, 33/32, 36/35
Comma list: 22/21, 27/26, 33/32, 36/35


Mapping: [{{val| 1 0 -4 6 5 -1 }}, {{val| 0 1 4 -2 -1 3 }}]
Mapping: {{mapping| 1 0 -4 6 5 -1 | 0 1 4 -2 -1 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.743
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.743
Line 1,379: Line 1,379:
Comma list: 22/21, 27/26, 33/32, 36/35, 51/49
Comma list: 22/21, 27/26, 33/32, 36/35, 51/49


Mapping: [{{val| 1 0 -4 6 5 -1 12 }}, {{val| 0 1 4 -2 -1 3 -5 }}]
Mapping: {{mapping| 1 0 -4 6 5 -1 12 | 0 1 4 -2 -1 3 -5 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.978
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.978
Line 1,392: Line 1,392:
Comma list: 22/21, 27/26, 33/32, 36/35, 51/49, 57/56
Comma list: 22/21, 27/26, 33/32, 36/35, 51/49, 57/56


Mapping: [{{val| 1 0 -4 6 5 -1 12 9 }}, {{val| 0 1 4 -2 -1 3 -5 -3 }}]
Mapping: {{mapping| 1 0 -4 6 5 -1 12 9 | 0 1 4 -2 -1 3 -5 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 697.068
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 697.068
Line 1,410: Line 1,410:
Comma list: 36/35, 64/63, 121/120
Comma list: 36/35, 64/63, 121/120


Mapping: [{{val| 1 1 0 4 2 }}, {{val| 0 2 8 -4 5 }}]
Mapping: {{mapping| 1 1 0 4 2 | 0 2 8 -4 5 }}


: mapping generators: ~2, ~11/9
: mapping generators: ~2, ~11/9
Line 1,425: Line 1,425:
Comma list: 36/35, 64/63, 66/65, 121/120
Comma list: 36/35, 64/63, 66/65, 121/120


Mapping: [{{val| 1 1 0 4 2 4 }}, {{val| 0 2 8 -4 5 -1 }}]
Mapping: {{mapping| 1 1 0 4 2 4 | 0 2 8 -4 5 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.816
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.816
Line 1,440: Line 1,440:
[[Comma list]]: 21/20, 28/27
[[Comma list]]: 21/20, 28/27


[[Mapping]]: [{{val| 1 0 -4 -2 }}, {{val| 0 1 4 3 }}]
{{Mapping|legend=1| 1 0 -4 -2 | 0 1 4 3 }}


{{Multival|legend=1| 1 4 3 4 2 -4 }}
{{Multival|legend=1| 1 4 3 4 2 -4 }}
Line 1,455: Line 1,455:
Comma list: 21/20, 28/27, 33/32
Comma list: 21/20, 28/27, 33/32


Mapping: [{{val| 1 0 -4 -2 5 }}, {{val| 0 1 4 3 -1 }}]
Mapping: {{mapping| 1 0 -4 -2 5 | 0 1 4 3 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.615
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.615
Line 1,468: Line 1,468:
[[Comma list]]: 81/80, 672/625
[[Comma list]]: 81/80, 672/625


[[Mapping]]: [{{val| 1 0 -4 -21 }}, {{val| 0 1 4 15 }}]
{{Mapping|legend=1| 1 0 -4 -21 | 0 1 4 15 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.889
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.889
Line 1,481: Line 1,481:
Comma list: 56/55, 81/80, 132/125
Comma list: 56/55, 81/80, 132/125


Mapping: [{{val| 1 0 -4 -21 -14 }}, {{val| 0 1 4 15 11 }}]
Mapping: {{mapping| 1 0 -4 -21 -14 | 0 1 4 15 11 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.096
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.096
Line 1,494: Line 1,494:
Comma list: 26/25, 56/55, 66/65, 81/80
Comma list: 26/25, 56/55, 66/65, 81/80


Mapping: [{{val| 1 0 -4 -21 -14 -9 }}, {{val| 0 1 4 15 11 8 }}]
Mapping: {{mapping| 1 0 -4 -21 -14 -9 | 0 1 4 15 11 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.094
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.094
Retrieved from "https://en.xen.wiki/w/Meantone_family"