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Sensamagic clan: Difference between revisions

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→Sensi: for the same reason as the change made to the Sensipent family page: removing for now because 1) it's definitely not a "play on words", though possibly it may be a contraction of those two words; 2) this could be covered better on the Temperament names page; 3) this fact is contentious and under discussion here: https://en.xen.wiki/w/Talk:Temperament_names
Update keys and copy data from sensipent family
Line 8: Line 8:
[[Comma list]]: 245/243
[[Comma list]]: 245/243


[[Sval]] [[mapping]]: [{{val| 1 1 2 }}, {{val| 0 -2 1 }}]
{{mapping|legend=2| 1 1 2 | 0 -2 1 }}


Sval mapping generators: ~3, ~9/7
: sval mapping generators: ~3, ~9/7


[[Optimal tuning]] ([[POTE]]): ~3 = 1\1edt, ~9/7 = 440.4881
[[Optimal tuning]] ([[POTE]]): ~3 = 1\1edt, ~9/7 = 440.4881
Line 52: Line 52:
[[Comma list]]: 126/125, 245/243
[[Comma list]]: 126/125, 245/243


[[Mapping]]: [{{val| 1 -1 -1 -2 }}, {{val| 0 7 9 13 }}]
{{Mapping|legend=1| 1 6 8 11 | 0 -7 -9 -13 }}


Mapping generators: ~2, ~9/7
: mapping generators: ~2, ~14/9


{{Multival|legend=1| 7 9 13 -2 1 5 }}
{{Multival|legend=1| 7 9 13 -2 1 5 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 443.383
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 443.383
[[Minimax tuning]]:
* [[7-odd-limit]]: ~9/7 = {{monzo| 2/13 0 0 1/13 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7
* [[9-odd-limit]]: ~9/7 = {{monzo| 1/5 2/5 -1/5 0 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5
[[Tuning ranges of regular temperaments|Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~9/7 = [442.105, 450.000] (7\19 to 3\8)
* 9-odd-limit diamond monotone: ~9/7 = [442.105, 444.444] (7\19 to 10\27)
* 7-odd-limit [[diamond tradeoff]]: ~9/7 = [442.179, 445.628]
* 9-odd-limit diamond tradeoff: ~9/7 = [435.084, 445.628]
* 7-odd-limit diamond monotone and tradeoff: ~9/7 = [442.179, 445.628]
* 9-odd-limit diamond monotone and tradeoff: ~9/7 = [442.105, 444.444]
[[Algebraic generator]]: The real root of ''x''<sup>5</sup> + ''x''<sup>4</sup> - 4''x''<sup>2</sup> + ''x'' - 1, at 443.3783 cents.


{{Optimal ET sequence|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}
Line 64: Line 80:
[[Badness]]: 0.025622
[[Badness]]: 0.025622


==== Sensation ====
==== 2.3.5.7.13 subgroup (sensation) ====
Subgroup: 2.3.5.7.13
Subgroup: 2.3.5.7.13


Comma list: 91/90, 126/125, 169/168
Comma list: 91/90, 126/125, 169/168


Sval mapping: [{{val| 1 -1 -1 -2 0 }}, {{val| 0 7 9 13 10 }}]
Sval mapping: {{mapping| 1 6 8 11 10 | 0 -7 -9 -13 -10 }}


Gencom mapping: [{{val| 1 -1 -1 -2 0 0 }}, {{val| 0 7 9 13 0 10 }}]
Gencom mapping: {{mapping| 1 6 8 11 0 10 | 0 -7 -9 -13 0 -10 }}


Gencom: [2 9/7; 91/90 126/125 169/168]
Gencom: [2 14/9; 91/90 126/125 169/168]


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.322
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.322
Line 84: Line 100:
Comma list: 126/125, 245/243, 385/384
Comma list: 126/125, 245/243, 385/384


Mapping: [{{val| 1 -1 -1 -2 9 }}, {{val| 0 7 9 13 -15 }}]
Mapping: {{mapping| 1 6 8 11 -6 | 0 -7 -9 -13 15 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.294
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.294
Line 97: Line 113:
Comma list: 91/90, 126/125, 169/168, 385/384
Comma list: 91/90, 126/125, 169/168, 385/384


Mapping: [{{val| 1 -1 -1 -2 9 0 }}, {{val| 0 7 9 13 -15 10 }}]
Mapping: {{mapping| 1 6 8 11 -6 10 | 0 -7 -9 -13 15 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.321
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.321
Line 110: Line 126:
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255


Mapping: [{{val| 1 -1 -1 -2 9 0 10 }}, {{val| 0 7 9 13 -15 10 -16 }}]
Mapping: {{mapping| 1 6 8 11 -6 10 -6 | 0 -7 -9 -13 15 -10 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.365
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.365
Line 117: Line 133:


Badness: 0.022908
Badness: 0.022908
=== Sensis ===
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: [{{val| 1 -1 -1 -2 2 }}, {{val| 0 7 9 13 4 }}]
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.962
{{Optimal ET sequence|legend=1| 8d, 19, 27e, 73ee }}
Badness: 0.028680
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: [{{val| 1 -1 -1 -2 2 0 }}, {{val| 0 7 9 13 4 10 }}]
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.945
{{Optimal ET sequence|legend=1| 19, 27e, 46e, 73ee }}
Badness: 0.020017


=== Sensus ===
=== Sensus ===
Line 149: Line 139:
Comma list: 126/125, 176/175, 245/243
Comma list: 126/125, 176/175, 245/243


Mapping: [{{val| 1 -1 -1 -2 -8 }}, {{val| 0 7 9 13 31 }}]
Mapping: {{mapping| 1 6 8 11 23 | 0 -7 -9 -13 -31 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.626
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.626
Line 162: Line 152:
Comma list: 91/90, 126/125, 169/168, 352/351
Comma list: 91/90, 126/125, 169/168, 352/351


Mapping: [{{val| 1 -1 -1 -2 -8 0 }}, {{val| 0 7 9 13 31 10 }}]
Mapping: {{mapping| 1 6 8 11 23 10 | 0 -7 -9 -13 -31 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.559
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.559
Line 175: Line 165:
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168


Mapping: [{{val| 1 -1 -1 -2 -8 0 -7 }}, {{val| 0 7 9 13 31 10 30 }}]
Mapping: {{mapping| 1 6 8 11 23 10 23 | 0 -7 -9 -13 -31 -10 -30 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.551
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.551
Line 182: Line 172:


Badness: 0.016238
Badness: 0.016238
=== Sensis ===
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: {{mapping| 1 6 8 11 6 | 0 -7 -9 -13 -4 }}
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.962
{{Optimal ET sequence|legend=1| 8d, 19, 27e, 73ee }}
Badness: 0.028680
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 6 8 11 6 10 | 0 -7 -9 -13 -4 -10 }}
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.945
{{Optimal ET sequence|legend=1| 19, 27e, 46e, 73ee }}
Badness: 0.020017


=== Sensa ===
=== Sensa ===
Line 188: Line 204:
Comma list: 55/54, 77/75, 99/98
Comma list: 55/54, 77/75, 99/98


Mapping: [{{val| 1 -1 -1 -2 -1 }}, {{val| 0 7 9 13 12 }}]
Mapping: {{mapping| 1 6 8 11 11 | 0 -7 -9 -13 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.518
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.518
Line 201: Line 217:
Comma list: 55/54, 66/65, 77/75, 143/140
Comma list: 55/54, 66/65, 77/75, 143/140


Mapping: [{{val| 1 -1 -1 -2 -1 0 }}, {{val| 0 7 9 13 12 11 }}]
Mapping: {{mapping| 1 6 8 11 11 11 | 0 -7 -9 -13 -12 -11 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.506
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.506
Line 209: Line 225:
Badness: 0.023258
Badness: 0.023258


=== Hemisensi ===
=== Bisensi ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 126/125, 243/242, 245/242
Comma list: 121/120, 126/125, 245/243
 
Mapping: {{mapping| 2 5 7 9 9 | 0 -7 -9 -13 -8 }}


Mapping: [{{val| 1 -1 -1 -2 -3 }}, {{val| 0 14 18 26 35 }}]
: mapping generators: ~99/70, ~11/10


Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.605
Optimal tuning (POTE): ~99/70 = 1\2, ~11/10 = 156.692


{{Optimal ET sequence|legend=1| 27e, 38d, 65, 157de, 222cde }}
{{Optimal ET sequence|legend=1| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}


Badness: 0.048714
Badness: 0.041723


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 91/90, 126/125, 169/168, 243/242
Comma list: 91/90, 121/120, 126/125, 169/168
 
Mapping: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}
 
Optimal tuning (POTE): ~55/39 = 1\2, ~11/10 = 156.725
 
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
 
Badness: 0.026339
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 91/90, 121/120, 126/125, 154/153, 169/168


Mapping: [{{val| 1 -1 -1 -2 -3 0 }}, {{val| 0 14 18 26 35 30 }}]
Mapping: {{mapping| 2 5 7 9 9 10 10 | 0 -7 -9 -13 -8 -10 -7 }}


Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.556
Optimal tuning (POTE): ~17/12 = 1\2, ~11/10 = 156.7158


{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}


Badness: 0.033016
Badness: 0.0188


=== Bisensi ===
=== Hemisensi ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 121/120, 126/125, 245/243
Comma list: 126/125, 243/242, 245/242
 
Mapping: {{mapping| 1 13 17 24 32 | 0 -14 -18 -26 -35 }}


Mapping: [{{val| 2 5 7 9 9 }}, {{val| 0 -7 -9 -13 -8 }}]
: mapping generators: ~2, ~44/25


Optimal tuning (POTE): ~99/70 = 1\2, ~11/10 = 156.692
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.605


{{Optimal ET sequence|legend=1| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}
{{Optimal ET sequence|legend=1| 27e, 38d, 65, 157de, 222cde }}


Badness: 0.041723
Badness: 0.048714


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 91/90, 121/120, 126/125, 169/168
Comma list: 91/90, 126/125, 169/168, 243/242


Mapping: [{{val| 2 5 7 9 9 10 }}, {{val| 0 -7 -9 -13 -8 -10 }}]
Mapping: {{mapping| 1 13 17 24 32 30 | 0 -14 -18 -26 -35 -30 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~11/10 = 156.725
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.556


{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}


Badness: 0.026339
Badness: 0.033016


== Cohemiripple ==
== Cohemiripple ==
Line 268: Line 301:
[[Comma list]]: 245/243, 1323/1250
[[Comma list]]: 245/243, 1323/1250


[[Mapping]]: [{{val| 1 -3 -5 -5 }}, {{val| 0 10 16 17 }}]
{{Mapping|legend=1| 1 7 11 12 | 0 -10 -16 -17 }}


{{Multival|legend=1| 10 16 17 2 -1 -5 }}
{{Multival|legend=1| 10 16 17 2 -1 -5 }}
Line 283: Line 316:
Comma list: 77/75, 243/242, 245/242
Comma list: 77/75, 243/242, 245/242


Mapping: [{{val| 1 -3 -5 -5 -8 }}, {{val| 0 10 16 17 25 }}]
Mapping: {{mapping| 1 7 11 12 17 | 0 -10 -16 -17 -25 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.945
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.945
Line 296: Line 329:
Comma list: 66/65, 77/75, 147/143, 243/242
Comma list: 66/65, 77/75, 147/143, 243/242


Mapping: [{{val| 1 -3 -5 -5 -8 -5 }}, {{val| 0 -10 -16 -17 -25 -19 }}]
Mapping: {{mapping| 1 7 11 12 17 14 | 0 -10 -16 -17 -25 -19 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.958
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.958
Line 314: Line 347:
[[Comma list]]: 245/243, 3125/3087
[[Comma list]]: 245/243, 3125/3087


[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 13 19 23 }}]
{{Mapping|legend=1| 1 0 0 0 | 0 13 19 23 }}


{{Multival|legend=1| 13 19 23 0 0 0 }}
{{Multival|legend=1| 13 19 23 0 0 0 }}


Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 146.474
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/25 = 146.474


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7-odd-limit: ~27/25 = {{monzo| 0 0 1/19 }}
* [[7-odd-limit]]: ~27/25 = {{monzo| 0 0 1/19 }}
: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5
* 9-odd-limit: ~27/25 = {{monzo| 0 1/13 }}
* [[9-odd-limit]]: ~27/25 = {{monzo| 0 1/13 }}
: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.3


{{Optimal ET sequence|legend=1| 41, 131, 172, 213c }}
{{Optimal ET sequence|legend=1| 41, 131, 172, 213c }}
Line 335: Line 368:
Comma list: 100/99, 245/243, 1344/1331
Comma list: 100/99, 245/243, 1344/1331


Mapping: [{{val| 1 0 0 0 2 }}, {{val| 0 13 19 23 12 }}]
Mapping: {{mapping| 1 0 0 0 2 | 0 13 19 23 12 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 146.545
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 146.545
Line 352: Line 385:
Comma list: 100/99, 144/143, 196/195, 275/273
Comma list: 100/99, 144/143, 196/195, 275/273


Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 13 19 23 12 14 }}]
Mapping: {{mapping| 1 0 0 0 2 2 | 0 13 19 23 12 14 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 146.603
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 146.603
Line 358: Line 391:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }}
* 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }}
: Eigenmonzo basis (unchanged-interval basis): 2.5
: Eigenmonzo (unchanged-interval) basis: 2.5


{{Optimal ET sequence|legend=1| 41, 90ef, 131ef, 221bdeff }}
{{Optimal ET sequence|legend=1| 41, 90ef, 131ef, 221bdeff }}
Line 376: Line 409:
Comma list: 245/243, 1331/1323, 3125/3087
Comma list: 245/243, 1331/1323, 3125/3087


Mapping: [{{val| 1 0 0 0 0 }}, {{val| 0 39 57 69 85 }}]
Mapping: {{mapping| 1 0 0 0 0 | 0 39 57 69 85 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.828
Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.828
Line 389: Line 422:
Comma list: 245/243, 275/273, 847/845, 1331/1323
Comma list: 245/243, 275/273, 847/845, 1331/1323


Mapping: [{{val| 1 0 0 0 0 0 }}, {{val| 0 39 57 69 85 91 }}]
Mapping: {{mapping| 1 0 0 0 0 0 | 0 39 57 69 85 91 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.822
Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.822
Line 404: Line 437:
[[Comma list]]: 245/243, 32805/32768
[[Comma list]]: 245/243, 32805/32768


[[Mapping]]: [{{val| 1 1 7 -1 }}, {{val| 0 2 -16 13 }}]
{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}


{{Multival|legend=1| 2 -16 13 -30 15 75 }}
{{Multival|legend=1| 2 -16 13 -30 15 75 }}
Line 419: Line 452:
Comma list: 243/242, 245/242, 385/384
Comma list: 243/242, 245/242, 385/384


Mapping: [{{val| 1 1 7 -1 2 }}, {{val| 0 2 -16 13 5 }}]
Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.014
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.014
Line 432: Line 465:
Comma list: 105/104, 144/143, 243/242, 245/242
Comma list: 105/104, 144/143, 243/242, 245/242


Mapping: [{{val| 1 1 7 -1 2 4 }}, {{val| 0 2 -16 13 5 -1 }}]
Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.025
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.025
Line 449: Line 482:
[[Comma list]]: 245/243, 525/512
[[Comma list]]: 245/243, 525/512


[[Mapping]]: [{{val| 1 3 -1 8 }}, {{val| 0 -3 7 -11 }}]
{{Mapping|legend=1| 1 3 -1 8 | 0 -3 7 -11 }}


{{Multival|legend=1| 3 -7 11 -18 9 45 }}
{{Multival|legend=1| 3 -7 11 -18 9 45 }}
Line 466: Line 499:
[[Comma list]]: 245/243, 78125/76832
[[Comma list]]: 245/243, 78125/76832


[[Mapping]]: [{{val| 1 -5 -5 -10 }}, {{val| 0 18 20 35 }}]
{{Mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }}


{{Multival|legend=1| 18 20 35 -10 5 25 }}
{{Multival|legend=1| 18 20 35 -10 5 25 }}
Line 481: Line 514:
Comma list: 100/99, 245/243, 78125/76832
Comma list: 100/99, 245/243, 78125/76832


Mapping: [{{val| 1 -5 -5 -10 2 }}, {{val| 0 18 20 35 4 }}]
Mapping: {{mapping| 1 -5 -5 -10 2 | 0 18 20 35 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.152
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.152
Line 494: Line 527:
Comma list: 100/99, 144/143, 196/195, 1375/1352
Comma list: 100/99, 144/143, 196/195, 1375/1352


Mapping: [{{val| 1 -5 -5 -10 2 -8 }}, {{val| 0 18 20 35 4 32 }}]
Mapping: {{mapping| 1 -5 -5 -10 2 -8 | 0 18 20 35 4 32 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.119
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.119
Line 509: Line 542:
[[Comma list]]: 245/243, 395136/390625
[[Comma list]]: 245/243, 395136/390625


[[Mapping]]: [{{val| 19 0 14 -7 }}, {{val| 0 1 1 2 }}]
{{Mapping|legend=1| 19 0 14 -7 | 0 1 1 2 }}


[[Optimal tuning]] ([[POTE]]): ~392/375 = 1\19, ~3/2 = 704.166
[[Optimal tuning]] ([[POTE]]): ~392/375 = 1\19, ~3/2 = 704.166
Line 522: Line 555:
Comma list: 245/243, 2560/2541, 3773/3750
Comma list: 245/243, 2560/2541, 3773/3750


Mapping: [{{val| 19 0 14 -7 96 }}, {{val| 0 1 1 2 -1 }}]
Mapping: {{mapping| 19 0 14 -7 96 | 0 1 1 2 -1 }}


Optimal tuning (POTE): ~33/32 = 1\19, ~3/2 = 705.667
Optimal tuning (POTE): ~33/32 = 1\19, ~3/2 = 705.667
Line 535: Line 568:
Comma list: 196/195, 245/243, 832/825, 1001/1000
Comma list: 196/195, 245/243, 832/825, 1001/1000


Mapping: [{{val| 19 0 14 -7 96 10 }}, {{val| 0 1 1 2 -1 2 }}]
Mapping: {{mapping| 19 0 14 -7 96 10 | 0 1 1 2 -1 2 }}


Optimal tuning (POTE): ~33/32 = 1\19, ~3/2 = 705.801
Optimal tuning (POTE): ~33/32 = 1\19, ~3/2 = 705.801
Line 552: Line 585:
[[Comma list]]: 245/243, 28672/28125
[[Comma list]]: 245/243, 28672/28125


[[Mapping]]: [{{val| 1 -2 2 -6 }}, {{val| 0 11 1 27 }}]
{{Mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }}


{{Multival|legend=1| 11 1 27 -24 12 60 }}
{{Multival|legend=1| 11 1 27 -24 12 60 }}
Line 567: Line 600:
Comma list: 176/175, 245/243, 1331/1323
Comma list: 176/175, 245/243, 1331/1323


Mapping: [{{val| 1 -2 2 -6 -6 }}, {{val| 0 11 1 27 29 }}]
Mapping: {{mapping| 1 -2 2 -6 -6 | 0 11 1 27 29 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.503
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.503
Line 580: Line 613:
Comma list: 91/90, 176/175, 245/243, 1331/1323
Comma list: 91/90, 176/175, 245/243, 1331/1323


Mapping: [{{val| 1 -2 2 -6 -6 5 }}, {{val| 0 11 1 27 29 -4 }}]
Mapping: {{mapping| 1 -2 2 -6 -6 5 | 0 11 1 27 29 -4 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.366
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.366
Line 595: Line 628:
[[Comma list]]: 245/243, 2097152/2066715
[[Comma list]]: 245/243, 2097152/2066715


[[Mapping]]: [{{val| 1 0 42 -21 }}, {{val| 0 1 -25 15 }}]
{{Mapping|legend=1| 1 0 42 -21 | 0 1 -25 15 }}


Mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.536
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.536
Line 610: Line 643:
Comma list: 245/243, 385/384, 1331/1323
Comma list: 245/243, 385/384, 1331/1323


Mapping: [{{val| 1 0 42 -21 -14 }}, {{val| 0 1 -25 15 11 }}]
Mapping: {{mapping| 1 0 42 -21 -14 | 0 1 -25 15 11 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.554
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.554
Line 623: Line 656:
Comma list: 169/168, 245/243, 352/351, 364/363
Comma list: 169/168, 245/243, 352/351, 364/363


Mapping: [{{val| 1 0 42 -21 -14 -9 }}, {{val| 0 1 -25 15 11 8 }}]
Mapping: {{mapping| 1 0 42 -21 -14 -9 | 0 1 -25 15 11 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.571
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.571
Line 636: Line 669:
Comma list: 154/153, 169/168, 245/243, 256/255, 273/272
Comma list: 154/153, 169/168, 245/243, 256/255, 273/272


Mapping: [{{val| 1 0 42 -21 -14 -9 -34 }}, {{val| 0 1 -25 15 11 8 24 }}]
Mapping: {{mapping| 1 0 42 -21 -14 -9 -34 | 0 1 -25 15 11 8 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.540
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.540
Line 649: Line 682:
Comma list: 136/135, 169/168, 221/220, 245/243, 364/363
Comma list: 136/135, 169/168, 221/220, 245/243, 364/363


Mapping: [{{val| 1 0 42 -21 -14 -9 39 }}, {{val| 0 1 -25 15 11 8 -22 }}]
Mapping: {{mapping| 1 0 42 -21 -14 -9 39 | 0 1 -25 15 11 8 -22 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.537
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.537
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