Xenharmonic Wiki

Schismatic family: Difference between revisions

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Edo and comma list reviewed
m Place POTE gen together with other tuning info
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[[Comma list]]: 32805/32768
[[Comma list]]: 32805/32768
[[POTE generator]]: ~3/2 = 701.736


[[Mapping]]: [{{val| 1 0 15 }}, {{val| 0 1 -8 }}]
[[Mapping]]: [{{val| 1 0 15 }}, {{val| 0 1 -8 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
[[POTE generator]]: ~3/2 = 701.736


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 50: Line 50:


[[Comma list]]: 225/224, 3125/3087
[[Comma list]]: 225/224, 3125/3087
[[POTE generator]]: ~3/2 = 702.085


[[Mapping]]: [{{val| 1 0 15 25 }}, {{val| 0 1 -8 -14 }}]
[[Mapping]]: [{{val| 1 0 15 25 }}, {{val| 0 1 -8 -14 }}]
Line 58: Line 56:


{{Multival|legend=1| 1 -8 -14 -15 -25 -10 }}
{{Multival|legend=1| 1 -8 -14 -15 -25 -10 }}
[[POTE generator]]: ~3/2 = 702.085


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 81: Line 81:


Comma list: 225/224, 385/384, 2200/2187
Comma list: 225/224, 385/384, 2200/2187
POTE generator: ~3/2 = 702.157


Mapping: [{{val| 1 0 15 25 -33 }}, {{val| 0 1 -8 -14 23 }}]
Mapping: [{{val| 1 0 15 25 -33 }}, {{val| 0 1 -8 -14 23 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 702.157


Minimax tuning:
Minimax tuning:
* [[11-odd-limit]]
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 0 }}, {{monzo| 5/2 -1 0 1/2 0 }}, {{monzo| 25/8 -7/4 0 7/8 0 }}, {{monzo| 47/16 23/8 0 -23/16 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 0 }}, {{monzo| 5/2 -1 0 1/2 0 }}, {{monzo| 25/8 -7/4 0 7/8 0 }}, {{monzo| 47/16 23/8 0 -23/16 0 }}]
: Eigenmonzos: 2, 9/7
: Eigenmonzos: 2, 9/7
Line 102: Line 102:


Comma list: 225/224, 275/273, 325/324, 385/384
Comma list: 225/224, 275/273, 325/324, 385/384
POTE generator: ~3/2 = 702.113


Mapping: [{{val| 1 0 15 25 -33 -28 }}, {{val| 0 1 -8 -14 23 20 }}]
Mapping: [{{val| 1 0 15 25 -33 -28 }}, {{val| 0 1 -8 -14 23 20 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 702.113


{{Val list|legend=1| 41, 53, 94, 429cdef, 523cdef }}
{{Val list|legend=1| 41, 53, 94, 429cdef, 523cdef }}
Line 118: Line 118:


Comma list: 100/99, 225/224, 245/242
Comma list: 100/99, 225/224, 245/242
[[POTE generator]]: ~3/2 = 702.321


Mapping: [{{val| 1 0 15 25 32 }}, {{val| 0 1 -8 -14 -18 }}]
Mapping: [{{val| 1 0 15 25 32 }}, {{val| 0 1 -8 -14 -18 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 702.321


{{Val list|legend=1| 12, 29, 41, 217ce, 258ce }}
{{Val list|legend=1| 12, 29, 41, 217ce, 258ce }}
Line 134: Line 134:


Comma list: 100/99, 105/104, 196/195, 245/242
Comma list: 100/99, 105/104, 196/195, 245/242
POTE generator: ~3/2 = 702.559


Mapping: [{{val| 1 0 15 25 32 37 }}, {{val| 0 1 -8 -14 -18 -21 }}]
Mapping: [{{val| 1 0 15 25 32 37 }}, {{val| 0 1 -8 -14 -18 -21 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 702.559


{{Val list|legend=1| 12f, 29, 41, 152cdf, 193cdf, 234cdf }}
{{Val list|legend=1| 12f, 29, 41, 152cdf, 193cdf, 234cdf }}
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Comma list: 99/98, 176/175, 3125/3087
Comma list: 99/98, 176/175, 3125/3087
POTE generator: ~3/2 = 701.725


Mapping: [{{val| 1 0 15 25 51 }}, {{val| 0 1 -8 -14 -30 }}]
Mapping: [{{val| 1 0 15 25 51 }}, {{val| 0 1 -8 -14 -30 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 701.725


{{Val list|legend=1| 53, 118d, 171de }}
{{Val list|legend=1| 53, 118d, 171de }}
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Comma list: 99/98, 176/175, 275/273, 847/845
Comma list: 99/98, 176/175, 275/273, 847/845
POTE generator: ~3/2 = 701.747


Mapping: [{{val| 1 0 15 25 51 56 }}, {{val| 0 1 -8 -14 -30 -33 }}]
Mapping: [{{val| 1 0 15 25 51 56 }}, {{val| 0 1 -8 -14 -30 -33 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 701.747


{{Val list|legend=1| 53, 118d, 171de }}
{{Val list|legend=1| 53, 118d, 171de }}
Line 182: Line 182:


Comma list: 121/120, 225/224, 3125/3087
Comma list: 121/120, 225/224, 3125/3087
POTE generator: ~63/55 = 248.918


Mapping: [{{val| 1 0 15 25 9 }}, {{val| 0 2 -16 -28 -7 }}]
Mapping: [{{val| 1 0 15 25 9 }}, {{val| 0 2 -16 -28 -7 }}]


Mapping generators: ~2, ~110/63
Mapping generators: ~2, ~110/63
POTE generator: ~63/55 = 248.918


{{Val list|legend=1| 29, 53, 82e, 135e, 188ce }}
{{Val list|legend=1| 29, 53, 82e, 135e, 188ce }}
Line 198: Line 198:


Comma list: 121/120, 169/168, 225/224, 275/273
Comma list: 121/120, 169/168, 225/224, 275/273
POTE generator: ~15/13 = 248.918


Mapping: [{{val| 1 0 15 25 9 14 }}, {{val| 0 2 -16 -28 -7 -13 }}]
Mapping: [{{val| 1 0 15 25 9 14 }}, {{val| 0 2 -16 -28 -7 -13 }}]


Mapping generators: ~2, ~26/15
Mapping generators: ~2, ~26/15
POTE generator: ~15/13 = 248.918


{{Val list|legend=1| 29, 53, 82e, 135ef, 188cef }}
{{Val list|legend=1| 29, 53, 82e, 135ef, 188cef }}
Line 214: Line 214:


Comma list: 225/224, 1331/1323, 3125/3087
Comma list: 225/224, 1331/1323, 3125/3087
POTE generator: ~11/10 = 165.974


Mapping: [{{val| 1 2 -1 -3 0 }}, {{val| 0 -3 24 42 25 }}]
Mapping: [{{val| 1 2 -1 -3 0 }}, {{val| 0 -3 24 42 25 }}]


Mapping generators: ~2, ~11/10
Mapping generators: ~2, ~11/10
POTE generator: ~11/10 = 165.974


{{Val list|legend=1| 29, 65d, 94, 441cde, 535cde, 629cde }}
{{Val list|legend=1| 29, 65d, 94, 441cde, 535cde, 629cde }}
Line 230: Line 230:


Comma list: 225/224, 275/273, 847/845, 1331/1323
Comma list: 225/224, 275/273, 847/845, 1331/1323
POTE generator: ~11/10 = 165.963


Mapping: [{{val| 1 2 -1 -3 0 -1 }}, {{val| 0 -3 24 42 25 34 }}]
Mapping: [{{val| 1 2 -1 -3 0 -1 }}, {{val| 0 -3 24 42 25 34 }}]


Mapping generators: ~2, ~11/10
Mapping generators: ~2, ~11/10
POTE generator: ~11/10 = 165.963


{{Val list|legend=1| 29, 65d, 94 }}
{{Val list|legend=1| 29, 65d, 94 }}
Line 247: Line 247:


[[Comma list]]: 64/63, 360/343
[[Comma list]]: 64/63, 360/343
[[POTE generator]]: ~3/2 = 701.556


[[Mapping]]: [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2 }}]
[[Mapping]]: [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
[[POTE generator]]: ~3/2 = 701.556


{{Multival|legend=1| 1 -8 -2 -15 -6 18 }}
{{Multival|legend=1| 1 -8 -2 -15 -6 18 }}
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Comma list: 45/44, 64/63, 99/98
Comma list: 45/44, 64/63, 99/98
POTE generator ~3/2 = 702.136


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


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
POTE generator ~3/2 = 702.136


{{Val list|legend=1| 12, 29de, 41de }}
{{Val list|legend=1| 12, 29de, 41de }}
Line 281: Line 281:


[[Comma list]]: 4375/4374, 32805/32768
[[Comma list]]: 4375/4374, 32805/32768
[[POTE generator]]: ~3/2 = 701.757


[[Mapping]]: [{{val| 1 0 15 -59 }}, {{val| 0 1 -8 39 }}]
[[Mapping]]: [{{val| 1 0 15 -59 }}, {{val| 0 1 -8 39 }}]
Line 289: Line 287:


{{Multival|legend=1| 1 -8 39 -15 59 113 }}
{{Multival|legend=1| 1 -8 39 -15 59 113 }}
[[POTE generator]]: ~3/2 = 701.757


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 74/47 0 -1/47 1/47 }}, {{monzo| 113/47 0 8/47 -8/47 }}, {{monzo| 113/47 0 -39/47 39/47 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 74/47 0 -1/47 1/47 }}, {{monzo| 113/47 0 8/47 -8/47 }}, {{monzo| 113/47 0 -39/47 39/47 }}]
: Eigenmonzos: 2, 7/5
: Eigenmonzos: 2, 7/5
* [[9-odd-limit]]:
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/5 -1/10 0 }}, {{monzo| 3 -8/5 4/5 0 }}, {{monzo| -1/2 39/5 -39/10 0 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/5 -1/10 0 }}, {{monzo| 3 -8/5 4/5 0 }}, {{monzo| -1/2 39/5 -39/10 0 }}]
: Eigenmonzos: 2, 10/9
: Eigenmonzos: 2, 10/9
Line 307: Line 307:


[[Comma list]]: 126/125, 32805/32768
[[Comma list]]: 126/125, 32805/32768
[[POTE generator]]: ~3/2 = 701.239


[[Mapping]]: [{{val| 1 0 15 -44 }}, {{val| 0 1 -8 -26 }}]
[[Mapping]]: [{{val| 1 0 15 -44 }}, {{val| 0 1 -8 -26 }}]
Line 315: Line 313:


{{Multival|legend=1| 1 -8 -26 -15 -44 -38 }}
{{Multival|legend=1| 1 -8 -26 -15 -44 -38 }}
[[POTE generator]]: ~3/2 = 701.239


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 329: Line 329:


[[Comma list]]: 3136/3125, 32805/32768
[[Comma list]]: 3136/3125, 32805/32768
[[POTE generator]]: ~3/2 = 701.592


[[Mapping]]: [{{val| 2 0 30 69 }}, {{val| 0 1 -8 -20 }}]
[[Mapping]]: [{{val| 2 0 30 69 }}, {{val| 0 1 -8 -20 }}]
Line 337: Line 335:


{{Multival|legend=1| 2 -16 -40 -30 -69 -48 }}
{{Multival|legend=1| 2 -16 -40 -30 -69 -48 }}
[[POTE generator]]: ~3/2 = 701.592


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 351: Line 351:


Comma list: 441/440, 3136/3125, 8019/8000
Comma list: 441/440, 3136/3125, 8019/8000
POTE generator: ~3/2 = 701.612


Mapping: [{{val| 2 0 30 69 102 }}, {{val| 0 1 -8 -20 -30 }}]
Mapping: [{{val| 2 0 30 69 102 }}, {{val| 0 1 -8 -20 -30 }}]


Mapping generators: ~99/70, ~3
Mapping generators: ~99/70, ~3
POTE generator: ~3/2 = 701.612


{{Val list|legend=1| 118, 130, 248 }}
{{Val list|legend=1| 118, 130, 248 }}
Line 367: Line 367:


Comma list: 441/440, 729/728, 1001/1000, 3136/3125
Comma list: 441/440, 729/728, 1001/1000, 3136/3125
POTE generator: ~3/2 = 701.590


Mapping generators: ~99/70, ~3
Mapping generators: ~99/70, ~3


Mapping: [{{val| 2 0 30 69 102 -75 }}, {{val| 0 1 -8 -20 -30 26 }}]
Mapping: [{{val| 2 0 30 69 102 -75 }}, {{val| 0 1 -8 -20 -30 26 }}]
POTE generator: ~3/2 = 701.590


{{Val list|legend=1| 118, 130, 248, 378 }}
{{Val list|legend=1| 118, 130, 248, 378 }}
Line 383: Line 383:


[[Comma list]]: 32805/32768, 1500625/1492992
[[Comma list]]: 32805/32768, 1500625/1492992
[[POTE generator]]: ~36/35 = 50.920


[[Mapping]]: [{{val| 2 1 22 -15 }}, {{val| 0 2 -16 19 }}]
[[Mapping]]: [{{val| 2 1 22 -15 }}, {{val| 0 2 -16 19 }}]
Line 391: Line 389:


{{Multival|legend=1| 4 -32 38 -60 49 178 }}
{{Multival|legend=1| 4 -32 38 -60 49 178 }}
[[POTE generator]]: ~36/35 = 50.920


{{Val list|legend=1| 94, 118, 212, 330, 542d, 872cd }}
{{Val list|legend=1| 94, 118, 212, 330, 542d, 872cd }}
Line 401: Line 401:


Comma list: 385/384, 9801/9800, 14641/14580
Comma list: 385/384, 9801/9800, 14641/14580
POTE generator: ~36/35 = 50.918


Mapping: [{{val| 2 1 22 -15 8 }}, {{val| 0 2 -16 19 -1 }}]
Mapping: [{{val| 2 1 22 -15 8 }}, {{val| 0 2 -16 19 -1 }}]


Mapping generators: ~99/70, ~16/11
Mapping generators: ~99/70, ~16/11
POTE generator: ~36/35 = 50.918


{{Val list|legend=1| 94, 118, 212, 330e, 542de }}
{{Val list|legend=1| 94, 118, 212, 330e, 542de }}
Line 417: Line 417:


Comma list: 352/351, 385/384, 729/728, 1575/1573
Comma list: 352/351, 385/384, 729/728, 1575/1573
POTE generator: ~36/35 = 50.938


Mapping: [{{val| 2 1 22 -15 8 15 }}, {{val| 0 2 -16 19 -1 -7 }}]
Mapping: [{{val| 2 1 22 -15 8 15 }}, {{val| 0 2 -16 19 -1 -7 }}]


Mapping generators: ~99/70, ~16/11
Mapping generators: ~99/70, ~16/11
POTE generator: ~36/35 = 50.938


{{Val list|legend=1| 94, 118, 212f }}
{{Val list|legend=1| 94, 118, 212f }}
Line 434: Line 434:


[[Comma list]]: 1029/1024, 10976/10935
[[Comma list]]: 1029/1024, 10976/10935
[[POTE generator]]: ~8/7 = 233.930


[[Mapping]]: [{{val| 1 1 7 3 }}, {{val| 0 3 -24 -1 }}]
[[Mapping]]: [{{val| 1 1 7 3 }}, {{val| 0 3 -24 -1 }}]


Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7
[[POTE generator]]: ~8/7 = 233.930


{{Multival|legend=1| 3 -24 -1 -45 -10 65 }}
{{Multival|legend=1| 3 -24 -1 -45 -10 65 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
* 7- and [[9-odd-limit]]:
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}]
: [[Eigenmonzo]]s: 2, 5/4
: [[Eigenmonzo]]s: 2, 5/4
Line 457: Line 457:


Comma list: 385/384, 441/440, 10976/10935
Comma list: 385/384, 441/440, 10976/10935
[[POTE generator]]: ~8/7 = 233.931


Mapping: [{{val| 1 1 7 3 -2 }}, {{val| 0 3 -24 -1 28 }}]
Mapping: [{{val| 1 1 7 3 -2 }}, {{val| 0 3 -24 -1 28 }}]


Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7
POTE generator: ~8/7 = 233.931


Minimax tuning:
Minimax tuning:
* [[11-odd-limit]]:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]  
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]  
: [[Eigenmonzo]]s: 2, 5/4
: Eigenmonzos: 2, 5/4


{{Val list|legend=1| 36e, 41, 77, 118, 159, 277d }}
{{Val list|legend=1| 36e, 41, 77, 118, 159, 277d }}
Line 478: Line 478:


Comma list: 196/195, 352/351, 385/384, 729/728
Comma list: 196/195, 352/351, 385/384, 729/728
POTE generator: ~8/7 = 233.890


Mapping generators: ~2, ~8/7
Mapping generators: ~2, ~8/7


Mapping: [{{val| 1 1 7 3 -2 0 }}, {{val| 0 3 -24 -1 28 19 }}]
Mapping: [{{val| 1 1 7 3 -2 0 }}, {{val| 0 3 -24 -1 28 19 }}]
POTE generator: ~8/7 = 233.890


{{Val list|legend=1| 36e, 41, 77, 118 }}
{{Val list|legend=1| 36e, 41, 77, 118 }}
Line 494: Line 494:


[[Comma list]]: 32805/32768, 118098/117649
[[Comma list]]: 32805/32768, 118098/117649
[[POTE generator]]: ~9/7 = 433.901


[[Mapping]]: [{{val| 2 1 22 2 }}, {{val| 0 3 -24 5 }}]
[[Mapping]]: [{{val| 2 1 22 2 }}, {{val| 0 3 -24 5 }}]


Mapping generators: ~343/243, ~9/7
Mapping generators: ~343/243, ~9/7
[[POTE generator]]: ~9/7 = 433.901


{{Val list|legend=1| 36, 94, 130, 224, 354 }}
{{Val list|legend=1| 36, 94, 130, 224, 354 }}
Line 510: Line 510:


Comma list: 540/539, 4000/3993, 32805/32768
Comma list: 540/539, 4000/3993, 32805/32768
POTE generator: ~9/7 = 433.911


Mapping: [{{val| 2 1 22 2 25 }}, {{val| 0 3 -24 5 -25 }}]
Mapping: [{{val| 2 1 22 2 25 }}, {{val| 0 3 -24 5 -25 }}]


Mapping generators: ~99/70, ~9/7
Mapping generators: ~99/70, ~9/7
POTE generator: ~9/7 = 433.911


{{Val list|legend=1| 36, 94, 130, 224, 354, 578 }}
{{Val list|legend=1| 36, 94, 130, 224, 354, 578 }}
Line 526: Line 526:


Comma list: 540/539, 729/728, 4000/3993, 4225/4224
Comma list: 540/539, 729/728, 4000/3993, 4225/4224
POTE generator: ~9/7 = 433.911


Mapping: [{{val| 2 1 22 2 25 -2 }}, {{val| 0 3 -24 5 -25 13 }}]
Mapping: [{{val| 2 1 22 2 25 -2 }}, {{val| 0 3 -24 5 -25 13 }}]


Mapping generators: ~99/70, ~9/7
Mapping generators: ~99/70, ~9/7
POTE generator: ~9/7 = 433.911


{{Val list|legend=1| 36, 94, 130, 224, 354, 578 }}
{{Val list|legend=1| 36, 94, 130, 224, 354, 578 }}
Line 542: Line 542:


[[Comma list]]: 686/675, 32805/32768
[[Comma list]]: 686/675, 32805/32768
[[Mapping]]: [{{val| 1 2 -1 1 }}, {{val| 0 -3 24 13 }}]


[[POTE generator]]: ~160/147 = 166.140
[[POTE generator]]: ~160/147 = 166.140
[[Mapping]]: [{{val| 1 2 -1 1 }}, {{val| 0 -3 24 13 }}]


{{Val list|legend=1| 29, 36, 65 }}
{{Val list|legend=1| 29, 36, 65 }}
Line 556: Line 556:


Comma list: 245/242, 686/675, 896/891
Comma list: 245/242, 686/675, 896/891
Mapping: [{{val| 1 2 -1 1 0 }}, {{val| 0 -3 24 13 25 }}]


POTE generator: ~11/10 = 166.097
POTE generator: ~11/10 = 166.097
Mapping: [{{val| 1 2 -1 1 0 }}, {{val| 0 -3 24 13 25 }}]


{{Val list|legend=1| 29, 36, 65 }}
{{Val list|legend=1| 29, 36, 65 }}
Line 570: Line 570:


Comma list: 91/90, 169/168, 245/242, 896/891
Comma list: 91/90, 169/168, 245/242, 896/891
Mapping: [{{val| 1 2 -1 1 0 3 }}, {{val| 0 -3 24 13 25 5 }}]


POTE generator: ~11/10 = 166.054
POTE generator: ~11/10 = 166.054
Mapping: [{{val| 1 2 -1 1 0 3 }}, {{val| 0 -3 24 13 25 5 }}]


{{Val list|legend=1| 29, 36, 65f, 94df, 159df }}
{{Val list|legend=1| 29, 36, 65f, 94df, 159df }}
Line 584: Line 584:


[[Comma list]]: 32805/32768, 250047/250000
[[Comma list]]: 32805/32768, 250047/250000
[[POTE generator]]: ~3/2 = 701.742


[[Mapping]]: [{{val| 3 0 45 94 }}, {{val| 0 1 -8 -18 }}]
[[Mapping]]: [{{val| 3 0 45 94 }}, {{val| 0 1 -8 -18 }}]
Line 592: Line 590:


{{Multival|legend=1| 3 -24 -54 -45 -94 -58 }}
{{Multival|legend=1| 3 -24 -54 -45 -94 -58 }}
[[POTE generator]]: ~3/2 = 701.742


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 606: Line 606:


[[Comma list]]: 2401/2400, 32805/32768
[[Comma list]]: 2401/2400, 32805/32768
[[POTE generator]]: ~448/405 = 175.434


[[Mapping]]: [{{val| 1 1 7 5 }}, {{val| 0 4 -32 -15 }}]
[[Mapping]]: [{{val| 1 1 7 5 }}, {{val| 0 4 -32 -15 }}]
Line 614: Line 612:


{{Multival|legend=1| 4 -32 -15 -60 -35 55 }}
{{Multival|legend=1| 4 -32 -15 -60 -35 55 }}
[[POTE generator]]: ~448/405 = 175.434


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 628: Line 628:


Comma list: 243/242, 441/440, 16384/16335
Comma list: 243/242, 441/440, 16384/16335
POTE generator: ~256/231 = 175.406


Mapping: [{{val| 1 1 7 5 2 }}, {{val| 0 4 -32 -15 10 }}]
Mapping: [{{val| 1 1 7 5 2 }}, {{val| 0 4 -32 -15 10 }}]


Mapping generators: ~2, ~256/231
Mapping generators: ~2, ~256/231
POTE generator: ~256/231 = 175.406


{{Val list|legend=1| 41, 89, 130, 301e, 431e }}
{{Val list|legend=1| 41, 89, 130, 301e, 431e }}
Line 644: Line 644:


Comma list: 243/242, 364/363, 441/440, 3584/3575
Comma list: 243/242, 364/363, 441/440, 3584/3575
Mapping: [{{val| 1 1 7 5 2 -2 }}, {{val| 0 4 -32 -15 10 39 }}]


POTE generator: ~256/231 = 175.409
POTE generator: ~256/231 = 175.409
Mapping: [{{val| 1 1 7 5 2 -2 }}, {{val| 0 4 -32 -15 10 39 }}]


{{Val list|legend=1| 41, 89, 130, 301e, 431e }}
{{Val list|legend=1| 41, 89, 130, 301e, 431e }}
Line 658: Line 658:


Comma list: 2401/2400, 9801/9800, 32805/32768
Comma list: 2401/2400, 9801/9800, 32805/32768
Mapping: [{{val| 2 2 14 10 23 }}, {{val| 0 4 -32 -15 -55 }}]


POTE generator: ~448/405 = 175.435
POTE generator: ~448/405 = 175.435
Mapping: [{{val| 2 2 14 10 23 }}, {{val| 0 4 -32 -15 -55 }}]


{{Val list|legend=1| 82e, 130, 212, 342, 1156, 1498, 1840d }}
{{Val list|legend=1| 82e, 130, 212, 342, 1156, 1498, 1840d }}
Line 672: Line 672:


[[Comma list]]: 32768/32805, 235298/234375
[[Comma list]]: 32768/32805, 235298/234375
[[POTE generator]]: ~21/20 = 83.053


[[Mapping]]: [{{val| 1 2 -1 -1 }}, {{val| 0 -6 48 55 }}]
[[Mapping]]: [{{val| 1 2 -1 -1 }}, {{val| 0 -6 48 55 }}]


Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20
[[POTE generator]]: ~21/20 = 83.053


{{Val list|legend=1| 29, 72cd, 101, 130, 289, 419 }}
{{Val list|legend=1| 29, 72cd, 101, 130, 289, 419 }}
Line 688: Line 688:


Comma list: 441/440, 4000/3993, 235298/234375
Comma list: 441/440, 4000/3993, 235298/234375
POTE generator: ~21/20 = 83.049


Mapping: [{{val| 1 2 -1 -1 0 }}, {{val| 0 -6 48 55 50| }}]
Mapping: [{{val| 1 2 -1 -1 0 }}, {{val| 0 -6 48 55 50| }}]


Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 83.049


{{Val list|legend=1| 29, 72cde, 101e, 130, 289 }}
{{Val list|legend=1| 29, 72cde, 101e, 130, 289 }}
Line 704: Line 704:


Comma list: 364/363, 441/440, 676/675, 10985/10976
Comma list: 364/363, 441/440, 676/675, 10985/10976
POTE generator: ~21/20 = 83.049


Mapping: [{{val| 1 2 -1 -1 0 1 }}, {{val| 0 -6 48 55 50 39 }}]
Mapping: [{{val| 1 2 -1 -1 0 1 }}, {{val| 0 -6 48 55 50 39 }}]


Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 83.049


{{Val list|legend=1| 29, 72cdef, 101e, 130, 289 }}
{{Val list|legend=1| 29, 72cdef, 101e, 130, 289 }}
Line 720: Line 720:


[[Comma list]]: 32805/32768, 420175/419904
[[Comma list]]: 32805/32768, 420175/419904
[[POTE generator]]: ~243/224 = 140.350


[[Mapping]]: [{{val| 1 1 7 0 }}, {{val| 0 5 -40 24 }}]
[[Mapping]]: [{{val| 1 1 7 0 }}, {{val| 0 5 -40 24 }}]
Line 728: Line 726:


{{Multival|legend=1| 5 -40 24 -75 24 168 }}
{{Multival|legend=1| 5 -40 24 -75 24 168 }}
[[POTE generator]]: ~243/224 = 140.350


{{Val list|legend=1| 17, 60c, 77, 94, 171 }}
{{Val list|legend=1| 17, 60c, 77, 94, 171 }}
Line 738: Line 738:


[[Comma list]]: 16875/16807, 32805/32768
[[Comma list]]: 16875/16807, 32805/32768
[[POTE generator]]: ~56/45 = 380.355


[[Mapping]]: [{{val| 1 0 15 12 }}, {{val| 0 5 -40 -29 }}]
[[Mapping]]: [{{val| 1 0 15 12 }}, {{val| 0 5 -40 -29 }}]
Line 746: Line 744:


{{Multival|legend=1| 5 -40 -29 -75 -60 45 }}
{{Multival|legend=1| 5 -40 -29 -75 -60 45 }}
[[POTE generator]]: ~56/45 = 380.355


{{Val list|legend=1| 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd }}
{{Val list|legend=1| 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd }}
Line 756: Line 756:


Comma list: 540/539, 1375/1372, 32805/32768
Comma list: 540/539, 1375/1372, 32805/32768
POTE generator: ~56/45 = 380.352


Mapping: [{{val| 1 0 15 12 -7 }}, {{val| 0 5 -40 -29 33 }}]
Mapping: [{{val| 1 0 15 12 -7 }}, {{val| 0 5 -40 -29 33 }}]


Mapping generators: ~2, ~56/45
Mapping generators: ~2, ~56/45
POTE generator: ~56/45 = 380.352


{{Val list|legend=1| 41, 142, 183, 224, 631d, 855d, 1079d }}
{{Val list|legend=1| 41, 142, 183, 224, 631d, 855d, 1079d }}
Line 772: Line 772:


Comma list: 540/539, 729/728, 1375/1372, 4096/4095
Comma list: 540/539, 729/728, 1375/1372, 4096/4095
POTE generator: ~56/45 = 380.351


Mapping: [{{val| 1 0 15 12 -7 -15 }}, {{val| 0 5 -40 -29 33 59 }}]
Mapping: [{{val| 1 0 15 12 -7 -15 }}, {{val| 0 5 -40 -29 33 59 }}]


Mapping generators: ~2, ~56/45
Mapping generators: ~2, ~56/45
POTE generator: ~56/45 = 380.351


{{Val list|legend=1| 41, 142, 183, 224, 631d, 855d }}
{{Val list|legend=1| 41, 142, 183, 224, 631d, 855d }}
Line 787: Line 787:
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 32805/32768, 2259436291848/2251875390625
[[Comma list]]: 32805/32768, 2259436291848/2251875390625
 
POTE generator: ~3/2 = 701.713


Mapping: [{{val| 8 0 120 -117 }}, {{val| 0 1 -8 11 }}]
[[Mapping]]: [{{val| 8 0 120 -117 }}, {{val| 0 1 -8 11 }}]


Mapping generators: ~42875/39366, ~3
Mapping generators: ~42875/39366, ~3


{{Multival|legend=1| 8 -64 88 -120 117 384 }}
{{Multival|legend=1| 8 -64 88 -120 117 384 }}
[[POTE generator]]: ~3/2 = 701.713


{{Val list|legend=1| 224, 472, 696, 1168 }}
{{Val list|legend=1| 224, 472, 696, 1168 }}


Badness: 0.1572
[[Badness]]: 0.1572


== 11-limit ==
== 11-limit ==
Line 806: Line 806:


Comma list: 9801/9800, 32805/32768, 46656/46585
Comma list: 9801/9800, 32805/32768, 46656/46585
POTE generator: ~3/2 = 701.713


Mapping: [{{val| 8 0 120 -117 15 }}, {{val| 0 1 -8 11 1 }}]
Mapping: [{{val| 8 0 120 -117 15 }}, {{val| 0 1 -8 11 1 }}]


Mapping generators: ~12/11, ~3
Mapping generators: ~12/11, ~3
POTE generator: ~3/2 = 701.713


{{Val list|legend=1| 224, 472, 696, 1168 }}
{{Val list|legend=1| 224, 472, 696, 1168 }}
Line 822: Line 822:


Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655
Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655
POTE generator: ~3/2 = 701.725


Mapping: [{{val| 8 0 120 -117 15 93 }}, {{val| 0 1 -8 11 1 -5 }}]
Mapping: [{{val| 8 0 120 -117 15 93 }}, {{val| 0 1 -8 11 1 -5 }}]


Mapping generators: ~12/11, ~3
Mapping generators: ~12/11, ~3
POTE generator: ~3/2 = 701.725


{{Val list|legend=1| 224, 472, 696 }}
{{Val list|legend=1| 224, 472, 696 }}
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