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Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[compton temperament]], for which [[240edo]] may be used. See [[marvel temperaments]] for some other rank-2 temperaments.  
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[compton temperament]], for which [[240edo]] may be used. See [[marvel temperaments]] for some other rank-2 temperaments.  


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224
[[Comma list]]: 225/224
Line 30: Line 30:
: Angle (secor, 3/2) = 106.958 degrees
: Angle (secor, 3/2) = 106.958 degrees


[[POTE generator]]s: ~3/2 = 700.4075, ~5/4 = 383.6376
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.4075, ~5/4 = 383.6376


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 69: Line 69:
}}
}}


=== Eleven-limit extensions ===
=== Overview to extensions ===
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 11-limit family member we are looking at.  
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 11-limit family member we are looking at.  
* 4125/4096 gives unidecimal marvel,  
* 4125/4096 gives unidecimal marvel,  
* 91125/90112 gives prodigy,  
* 91125/90112 gives prodigy,  
* 5632/5625 gives minerva, and
* 5632/5625 gives minerva,  
* 243/242 gives spectacle.
* 243/242 gives spectacle,
 
as well as others considered below. Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]).  


== Undecimal marvel (unimarv) ==
== Undecimal marvel (unimarv) ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 385/384
[[Comma list]]: 225/224, 385/384
Line 89: Line 91:
: Angle (secor, 5/4) = 104.028 degrees
: Angle (secor, 5/4) = 104.028 degrees


[[POTE generator]]s: ~3/2 = 700.3887, ~5/4 = 383.5403
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.3887, ~5/4 = 383.5403


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 125: Line 127:
Mapping: [{{val| 1 0 0 -5 12 -4 }}, {{val| 0 1 0 2 -1 -1 }}, {{val| 0 0 1 2 -3 4 }}]
Mapping: [{{val| 1 0 0 -5 12 -4 }}, {{val| 0 1 0 2 -1 -1 }}, {{val| 0 0 1 2 -3 4 }}]


POTE generators: ~3/2 = 699.7367, ~5/4 = 384.0613
Optimal tuning (POTE): ~3/2 = 699.7367, ~5/4 = 384.0613


Minimax tuning:  
Minimax tuning:  
Line 131: Line 133:
* 15-odd-limit eigenmonzo subgroup: 2.15/11.15/13
* 15-odd-limit eigenmonzo subgroup: 2.15/11.15/13


Vals: {{Val list| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}
Optimal GPV sequence: {{Val list| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}


Badness: 0.690 × 10<sup>-3</sup>
Badness: 0.690 × 10<sup>-3</sup>
Line 144: Line 146:
Mapping: [{{val| 1 0 0 -5 12 2 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -2 }}]
Mapping: [{{val| 1 0 0 -5 12 2 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -2 }}]


POTE generators: ~3/2 = 700.9779, ~5/4 = 383.1622
Optimal tuning (POTE): ~3/2 = 700.9779, ~5/4 = 383.1622


Minimax tuning:  
Minimax tuning:  
Line 150: Line 152:
* 15-odd-limit eigenmonzo subgroup: 2.7.15/13
* 15-odd-limit eigenmonzo subgroup: 2.7.15/13


Vals: {{Val list| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}
Optimal GPV sequence: {{Val list| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}


Badness: 0.721 × 10<sup>-3</sup>
Badness: 0.721 × 10<sup>-3</sup>
Line 165: Line 167:
Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 -6 }}]
Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 -6 }}]


POTE generators: ~3/2 = 700.9619, ~5/4 = 383.0310
Optimal tuning (POTE): ~3/2 = 700.9619, ~5/4 = 383.0310


Vals: {{Val list| 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg }}
Optimal GPV sequence: {{Val list| 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg }}


Badness: 0.869 × 10<sup>-3</sup>
Badness: 0.869 × 10<sup>-3</sup>
Line 178: Line 180:
Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 6 }}]
Mapping: [{{val| 1 0 0 -5 12 2 18 }}, {{val| 0 1 0 2 -1 4 0 }}, {{val| 0 0 1 2 -3 -2 6 }}]


POTE generators: ~3/2 = 700.9658, ~5/4 = 383.3063
Optimal tuning (POTE): ~3/2 = 700.9658, ~5/4 = 383.3063


Vals: {{Val list| 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg }}
Optimal GPV sequence: {{Val list| 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg }}


Badness: 0.917 × 10<sup>-3</sup>
Badness: 0.917 × 10<sup>-3</sup>
Line 191: Line 193:
Mapping: [{{val| 1 0 0 -5 12 -29 }}, {{val| 0 1 0 2 -1 6 }}, {{val| 0 0 1 2 -3 10 }}]
Mapping: [{{val| 1 0 0 -5 12 -29 }}, {{val| 0 1 0 2 -1 6 }}, {{val| 0 0 1 2 -3 10 }}]


POTE generators: ~3/2 = 700.3937, ~5/4 = 383.5725
Optimal tuning (POTE): ~3/2 = 700.3937, ~5/4 = 383.5725


Minimax tuning:  
Minimax tuning:  
Line 197: Line 199:
* 15-odd-limit eigenmonzo subgroup: 2.7.15/13
* 15-odd-limit eigenmonzo subgroup: 2.7.15/13


Vals: {{Val list| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}
Optimal GPV sequence: {{Val list| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}


Badness: 0.862 × 10<sup>-3</sup>
Badness: 0.862 × 10<sup>-3</sup>
Line 208: Line 210:
Mapping: [{{val| 1 0 0 -5 12 17 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -3 }}]
Mapping: [{{val| 1 0 0 -5 12 17 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -3 }}]


POTE generators: ~3/2 = 701.9156, ~5/4 = 383.2445
Optimal tuning (POTE): ~3/2 = 701.9156, ~5/4 = 383.2445


Vals: {{Val list| 10, 19f, 22, 31, 41, 53, 94 }}
Optimal GPV sequence: {{Val list| 10, 19f, 22, 31, 41, 53, 94 }}


Badness: 0.866 × 10<sup>-3</sup>
Badness: 0.866 × 10<sup>-3</sup>
Line 223: Line 225:
Mapping: [{{val| 1 0 0 -5 12 27 }}, {{val| 0 1 0 2 -1 -3 }}, {{val| 0 0 1 2 -3 -8 }}]
Mapping: [{{val| 1 0 0 -5 12 27 }}, {{val| 0 1 0 2 -1 -3 }}, {{val| 0 0 1 2 -3 -8 }}]


POTE generators: ~3/2 = 700.4560, ~5/4 = 382.8177
Optimal tuning (POTE): ~3/2 = 700.4560, ~5/4 = 382.8177


Minimax tuning:  
Minimax tuning:  
Line 229: Line 231:
* 15-odd-limit eigenmonzo subgroup: 2.3.13/5
* 15-odd-limit eigenmonzo subgroup: 2.3.13/5


Vals: {{Val list| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}
Optimal GPV sequence: {{Val list| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}


Badness: 0.920 × 10<sup>-3</sup>
Badness: 0.920 × 10<sup>-3</sup>
Line 242: Line 244:
Mapping: [{{val| 1 0 0 -5 12 -8 }}, {{val| 0 1 0 2 -1 3 }}, {{val| 0 0 1 2 -3 3 }}]
Mapping: [{{val| 1 0 0 -5 12 -8 }}, {{val| 0 1 0 2 -1 3 }}, {{val| 0 0 1 2 -3 3 }}]


POTE generators: ~3/2 = 699.2335, ~5/4 = 382.9775
Optimal tuning (POTE): ~3/2 = 699.2335, ~5/4 = 382.9775


Minimax tuning:  
Minimax tuning:  
Line 248: Line 250:
* 15-odd-limit eigenmonzo subgroup: 2.5/3.13/11
* 15-odd-limit eigenmonzo subgroup: 2.5/3.13/11


Vals: {{Val list| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}
Optimal GPV sequence: {{Val list| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}


Badness: 0.745 × 10<sup>-3</sup>
Badness: 0.745 × 10<sup>-3</sup>
Line 263: Line 265:
Mapping generators: ~2, ~26/15, ~5
Mapping generators: ~2, ~26/15, ~5


POTE generators: ~15/13 = 249.7138, ~5/4 = 383.5816
Optimal tuning (POTE): ~15/13 = 249.7138, ~5/4 = 383.5816


Vals: {{Val list| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}
Optimal GPV sequence: {{Val list| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}


Badness: 0.9997 × 10<sup>-3</sup>
Badness: 0.9997 × 10<sup>-3</sup>


== Minerva ==
== Minerva ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 99/98, 176/175
[[Comma list]]: 99/98, 176/175
Line 282: Line 284:
: Angle (16/15, 5/4) = 98.6044 degrees
: Angle (16/15, 5/4) = 98.6044 degrees


[[POTE generator]]s: ~3/2 = 700.2593, ~5/4 = 386.5581
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.2593, ~5/4 = 386.5581


[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo subgroup]]: 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo subgroup]]: 2.7/5.11/9
Line 303: Line 305:
Mapping: [{{val| 1 0 0 -5 -9 -4 }}, {{val| 0 1 0 2 2 -1 }}, {{val| 0 0 1 2 4 4 }}]
Mapping: [{{val| 1 0 0 -5 -9 -4 }}, {{val| 0 1 0 2 2 -1 }}, {{val| 0 0 1 2 4 4 }}]


POTE generators: ~3/2 = 701.2342, ~5/4 = 385.9594
Optimal tuning (POTE): ~3/2 = 701.2342, ~5/4 = 385.9594


Minimax tuning:  
Minimax tuning:  
Line 309: Line 311:
* 15-odd-limit eigenmonzo subgroup: 2.11/9.13/7
* 15-odd-limit eigenmonzo subgroup: 2.11/9.13/7


Vals: {{Val list| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}
Optimal GPV sequence: {{Val list| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}


Badness: 0.818 × 10<sup>-3</sup>
Badness: 0.818 × 10<sup>-3</sup>
Line 316: Line 318:


== Apollo ==
== Apollo ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 100/99, 225/224
[[Comma list]]: 100/99, 225/224
Line 322: Line 324:
[[Mapping]]: [{{val| 1 0 0 -5 2 }}, {{val| 0 1 0 2 -2 }}, {{val| 0 0 1 2 2 }}]
[[Mapping]]: [{{val| 1 0 0 -5 2 }}, {{val| 0 1 0 2 -2 }}, {{val| 0 0 1 2 2 }}]


[[POTE generator]]s: ~3/2 = 703.4846, ~5/4 = 381.6033
[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.4846, ~5/4 = 381.6033


[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo subgroup]]: 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo subgroup]]: 2.7/5.11/9
Line 339: Line 341:
Mapping: [{{val| 1 0 0 -5 2 7 }}, {{val| 0 1 0 2 -2 -5 }}, {{val| 0 0 1 2 2 2 }}]
Mapping: [{{val| 1 0 0 -5 2 7 }}, {{val| 0 1 0 2 -2 -5 }}, {{val| 0 0 1 2 2 2 }}]


POTE generators: ~3/2 = 703.9984, ~5/4 = 381.5352
Optimal tuning (POTE): ~3/2 = 703.9984, ~5/4 = 381.5352


Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9
Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9


Vals: {{Val list| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
Optimal GPV sequence: {{Val list| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}


Projection pairs: 7 225/32 11 100/9 13 3200/243
Projection pairs: 7 225/32 11 100/9 13 3200/243


== Potassium ==
== Potassium ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 45/44, 56/55
[[Comma list]]: 45/44, 56/55
Line 354: Line 356:
[[Mapping]]: [{{val| 1 0 0 -5 -2 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 2 1 }}]
[[Mapping]]: [{{val| 1 0 0 -5 -2 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 2 1 }}]


[[POTE generator]]s: ~3/2 = 696.1714, ~5/4 = 385.0500
[[Optimal tuning]] ([[POTE]]): ~3/2 = 696.1714, ~5/4 = 385.0500


[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo subgroup]]: 2.9/7.11
[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo subgroup]]: 2.9/7.11
Line 371: Line 373:
Mapping: [{{val| 1 0 0 -5 -2 -8 }}, {{val| 0 1 0 2 2 3 }}, {{val| 0 0 1 2 1 3 }}]
Mapping: [{{val| 1 0 0 -5 -2 -8 }}, {{val| 0 1 0 2 2 3 }}, {{val| 0 0 1 2 1 3 }}]


POTE generators: ~3/2 = 696.0103, ~5/4 = 384.6785
Optimal tuning (POTE): ~3/2 = 696.0103, ~5/4 = 384.6785


Minimax tuning:  
Minimax tuning:  
Line 377: Line 379:
* 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9
* 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9


Vals: {{Val list| 9, 10, 12f, 19, 31e, 50e }}
Optimal GPV sequence: {{Val list| 9, 10, 12f, 19, 31e, 50e }}


Badness: 0.733 × 10<sup>-3</sup>
Badness: 0.733 × 10<sup>-3</sup>
Line 384: Line 386:


== Malcolm ==
== Malcolm ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 2200/2187
[[Comma list]]: 225/224, 2200/2187
Line 390: Line 392:
[[Mapping]]: [{{val| 1 0 0 -5 -3 }}, {{val| 0 1 0 2 7 }}, {{val| 0 0 1 2 -2 }}]
[[Mapping]]: [{{val| 1 0 0 -5 -3 }}, {{val| 0 1 0 2 7 }}, {{val| 0 0 1 2 -2 }}]


[[POTE generator]]s: ~3/2 = 701.8913, ~5/4 = 382.4083
[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.8913, ~5/4 = 382.4083


{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
Line 403: Line 405:
Mapping: [{{val| 1 0 0 -5 -3 2 }}, {{val| 0 1 0 2 7 4 }}, {{val| 0 0 1 2 -2 -2 }}]
Mapping: [{{val| 1 0 0 -5 -3 2 }}, {{val| 0 1 0 2 7 4 }}, {{val| 0 0 1 2 -2 -2 }}]


POTE generators: ~3/2 = 701.8913, ~5/4 = 382.4083
Optimal tuning (POTE): ~3/2 = 701.8913, ~5/4 = 382.4083


Vals: {{Val list| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
Optimal GPV sequence: {{Val list| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}


Badness: 1.075 × 10<sup>-3</sup>
Badness: 1.075 × 10<sup>-3</sup>
Line 412: Line 414:
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.


Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 441/440
[[Comma list]]: 225/224, 441/440
Line 424: Line 426:
: Angle (secor, 3/2) = 65.933
: Angle (secor, 3/2) = 65.933


[[POTE generator]]s: ~3/2 = 699.7981, ~5/4 = 383.5114
[[Optimal tuning]] ([[POTE]]): ~3/2 = 699.7981, ~5/4 = 383.5114


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 454: Line 456:
Mapping: [{{val| 1 0 0 -5 -13 -8 }}, {{val| 0 1 0 2 6 3 }}, {{val| 0 0 1 2 3 3 }}]
Mapping: [{{val| 1 0 0 -5 -13 -8 }}, {{val| 0 1 0 2 6 3 }}, {{val| 0 0 1 2 3 3 }}]


POTE generators: ~3/2 = 700.4006, ~5/4 = 381.4025
Optimal tuning (POTE): ~3/2 = 700.4006, ~5/4 = 381.4025


Vals: {{Val list| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}
Optimal GPV sequence: {{Val list| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}


Badness: 0.736 × 10<sup>-3</sup>
Badness: 0.736 × 10<sup>-3</sup>
Line 467: Line 469:
Mapping: [{{val| 1 0 0 -5 -13 -23 }}, {{val| 0 1 0 2 6 11 }}, {{val| 0 0 1 2 3 4 }}]
Mapping: [{{val| 1 0 0 -5 -13 -23 }}, {{val| 0 1 0 2 6 11 }}, {{val| 0 0 1 2 3 4 }}]


POTE generators: ~3/2 = 700.3407, ~5/4 = 383.2592
Optimal tuning (POTE): ~3/2 = 700.3407, ~5/4 = 383.2592


Vals: {{Val list| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}
Optimal GPV sequence: {{Val list| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}


Badness: 0.900 × 10<sup>-3</sup>
Badness: 0.900 × 10<sup>-3</sup>
Line 480: Line 482:
Mapping: [{{val| 1 0 0 -5 -13 -4 }}, {{val| 0 1 0 2 6 -1 }}, {{val| 0 0 1 2 3 4 }}]
Mapping: [{{val| 1 0 0 -5 -13 -4 }}, {{val| 0 1 0 2 6 -1 }}, {{val| 0 0 1 2 3 4 }}]


POTE generators: ~3/2 = 699.4864, ~5/4 = 384.0998
Optimal tuning (POTE): ~3/2 = 699.4864, ~5/4 = 384.0998


Vals: {{Val list| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
Optimal GPV sequence: {{Val list| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}


Badness: 0.889 × 10<sup>-3</sup>
Badness: 0.889 × 10<sup>-3</sup>
Line 493: Line 495:
Mapping: [{{val| 1 0 0 -5 -13 21 }}, {{val| 0 1 0 2 6 -8 }}, {{val| 0 0 1 2 3 -2 }}]
Mapping: [{{val| 1 0 0 -5 -13 21 }}, {{val| 0 1 0 2 6 -8 }}, {{val| 0 0 1 2 3 -2 }}]


POTE generators: ~3/2 = 699.5536, ~5/4 = 383.5696
Optimal tuning (POTE): ~3/2 = 699.5536, ~5/4 = 383.5696


Vals: {{val list| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
Optimal GPV sequence: {{val list| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}


Badness: 0.953 × 10<sup>-3</sup>
Badness: 0.953 × 10<sup>-3</sup>
Line 506: Line 508:
Mapping: [{{val| 1 0 0 -5 -13 21 12 }}, {{val| 0 1 0 2 6 -8 -5 }}, {{val| 0 0 1 2 3 -2 0 }}]
Mapping: [{{val| 1 0 0 -5 -13 21 12 }}, {{val| 0 1 0 2 6 -8 -5 }}, {{val| 0 0 1 2 3 -2 0 }}]


POTE generators: ~3/2 = 699.6262, ~5/4 = 383.4458
Optimal tuning (POTE): ~3/2 = 699.6262, ~5/4 = 383.4458


Vals: {{val list| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
Optimal GPV sequence: {{val list| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}


Badness: 0.772 × 10<sup>-3</sup>
Badness: 0.772 × 10<sup>-3</sup>


== Fantastic ==
== Fantastic ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 4375/4356
[[Comma list]]: 225/224, 4375/4356
Line 521: Line 523:
Mapping generators: ~99/70, ~3, ~5
Mapping generators: ~99/70, ~3, ~5


[[POTE generator]]s: ~3/2 = 700.6242, ~5/4 = 383.2978
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.6242, ~5/4 = 383.2978


{{Val list|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
{{Val list|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
Line 528: Line 530:


== Spectacle ==
== Spectacle ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 243/242
[[Comma list]]: 225/224, 243/242
Line 536: Line 538:
Mapping generators: ~2, ~11/9, ~5
Mapping generators: ~2, ~11/9, ~5


[[POTE generator]]s: ~11/9 = 350.0570, ~5/4 = 383.9323
[[Optimal tuning]] ([[POTE]]): ~11/9 = 350.0570, ~5/4 = 383.9323


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 562: Line 564:
Mapping generators: ~2, ~11/9, ~5
Mapping generators: ~2, ~11/9, ~5


POTE generators: ~11/9 = 349.9247, ~5/4 = 384.3505
Optimal tuning (POTE): ~11/9 = 349.9247, ~5/4 = 384.3505


Vals: {{Val list| 31, 72, 103, 175f }} <nowiki>*</nowiki>
Optimal GPV sequence: {{Val list| 31, 72, 103, 175f }} <nowiki>*</nowiki>


<nowiki>*</nowiki> optimal patent val: [[240edo|240]]
<nowiki>*</nowiki> optimal patent val: [[240edo|240]]
Line 571: Line 573:


== Hestia ==
== Hestia ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 125000/124509
[[Comma list]]: 225/224, 125000/124509
Line 579: Line 581:
Mapping generators: ~2, ~400/231, ~5
Mapping generators: ~2, ~400/231, ~5


[[POTE generator]]s: ~231/200 = 249.8526, ~5/4 = 383.6467
[[Optimal tuning]] ([[POTE]]): ~231/200 = 249.8526, ~5/4 = 383.6467


{{Val list|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
{{Val list|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
Line 594: Line 596:
Mapping generators: ~2, ~26/15, ~5
Mapping generators: ~2, ~26/15, ~5


POTE generators: ~15/13 = 249.7651, ~5/4 = 383.5558
Optimal tuning (POTE): ~15/13 = 249.7651, ~5/4 = 383.5558


Vals: {{Val list| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
Optimal GPV sequence: {{Val list| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}


Badness: 1.062 × 10<sup>-3</sup>
Badness: 1.062 × 10<sup>-3</sup>


== Artemis ==
== Artemis ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 121/120, 225/224
[[Comma list]]: 121/120, 225/224
Line 609: Line 611:
Mapping generators: ~2, ~3, ~11/10
Mapping generators: ~2, ~3, ~11/10


[[POTE generator]]s: ~3/2 = 699.8719, ~11/10 = 158.3232
[[Optimal tuning]] ([[POTE]]): ~3/2 = 699.8719, ~11/10 = 158.3232


{{Val list|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
{{Val list|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
Line 622: Line 624:
Mapping generators: ~2, ~3, ~11/10
Mapping generators: ~2, ~3, ~11/10


POTE generators: ~3/2 = 698.7090, ~11/10 = 158.7117
Optimal tuning (POTE): ~3/2 = 698.7090, ~11/10 = 158.7117


Vals: {{Val list| 9, 20, 22f, 29, 31 }}
Optimal GPV sequence: {{Val list| 9, 20, 22f, 29, 31 }}


=== Diana ===
=== Diana ===
Line 635: Line 637:
Mapping generators: ~2, ~3, ~11/10
Mapping generators: ~2, ~3, ~11/10


POTE generators: ~3/2 = 700.9789, ~11/10 = 159.0048
Optimal tuning (POTE): ~3/2 = 700.9789, ~11/10 = 159.0048


Vals: {{Val list| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
Optimal GPV sequence: {{Val list| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}


== Morfil ==
== Morfil ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 1331/1323
[[Comma list]]: 225/224, 1331/1323
Line 648: Line 650:
Mapping generators: ~2, ~3, ~84/55
Mapping generators: ~2, ~3, ~84/55


[[POTE generator]]s: ~3/2 = 700.8983, ~84/55 = 739.3812
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.8983, ~84/55 = 739.3812


{{Val list|legend=1| 29, 31, 60e, 91e, 94, 125 }}
{{Val list|legend=1| 29, 31, 60e, 91e, 94, 125 }}
Line 655: Line 657:


== Catakleismoid ==
== Catakleismoid ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 4375/4374
[[Comma list]]: 225/224, 4375/4374
Line 663: Line 665:
Mapping generators: ~2, ~6/5, ~11
Mapping generators: ~2, ~6/5, ~11


[[POTE generator]]s: ~6/5 = 316.7318, ~11/8 = 549.2528
[[Optimal tuning]] ([[POTE]]): ~6/5 = 316.7318, ~11/8 = 549.2528


{{Val list|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
{{Val list|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
Line 678: Line 680:
Mapping generators: ~2, ~6/5, ~11
Mapping generators: ~2, ~6/5, ~11


POTE generators: ~6/5 = 316.7410, ~11/8 = 548.6028
Optimal tuning (POTE): ~6/5 = 316.7410, ~11/8 = 548.6028


Vals: {{Val list| 19, 34d, 53, 72, 125f, 197ef, 269cef }}
Optimal GPV sequence: {{Val list| 19, 34d, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.916 × 10<sup>-3</sup>
Badness: 0.916 × 10<sup>-3</sup>
Line 693: Line 695:
Mapping generators: ~2, ~15/14, ~13
Mapping generators: ~2, ~15/14, ~13


POTE generators: ~15/14 = 116.6327, ~13/8 = 837.7040
Optimal tuning (POTE): ~15/14 = 116.6327, ~13/8 = 837.7040


Vals: {{Val list| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
Optimal GPV sequence: {{Val list| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}


Badness: 0.738 × 10<sup>-3</sup>
Badness: 0.738 × 10<sup>-3</sup>
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