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Marvel family: Difference between revisions

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Badness: 0.9997 × 10<sup>-3</sup>
Badness: 0.9997 × 10<sup>-3</sup>
</div></div>
= Mirage =
Period: 1\1
Optimal ([[POTE]]) generators: ~15/14 = 116.6327, ~13/8 = 837.7040
EDO generators: [[31edo|(3, 22)\31]], [[41edo|(4, 29)\41]], [[72edo|(7, 50)\22]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 385/384
Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 6 -7 -2 15 0 }}, {{val| 0 0 0 0 0 1 }}]
{{Val list|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
Badness: 0.738 × 10<sup>-3</sup>


</div></div>
</div></div>
Line 515: Line 489:
</div></div>
</div></div>


= Spectacle =
= Apollo =


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~11/9 = 350.0570, ~5/4 = 383.9323
Optimal ([[POTE]]) generators: ~3/2 = 703.4846, ~5/4 = 381.6033
 
EDO generators: [[12edo|(7, 4)\12]], [[19edo|(11, 6)\19]], [[22edo|(13, 7)\22]]


EDO generators: [[31edo|(9, 10)\31]], [[34edo|(10, 11)\34]], [[41edo|(12, 13)\41]]
Scales (Scala files):


Scales (Scala files): [[spectacle31]]
Associated temperament: [[Magic family #magic|magic]]


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Line 531: Line 507:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 225/224, 243/242
[[Comma list]]: 100/99, 225/224


[[Associated temperament]]: [[Marvel temperaments #Marvo|marvo]]
[[Mapping]]: [{{val| 1 0 0 -5 2 }}, {{val| 0 1 0 2 -2 }}, {{val| 0 0 1 2 2 }}]


Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 0 4 5 }}, {{val| 0 0 1 2 0 }}]
Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7/5.11/9


Mapping generators: ~2, ~11/9, ~5
{{Val list|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}


[[Minimax tuning]]:
[[Projection pair]]s: 7 225/32 11 100/9
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1/5 0 0 0 2/5 }}, {{monzo| 2/5 -2 1 0 4/5 }}, {{monzo| -19/5 -4 2 0 12/5 }}, {{monzo| 0 0 0 0 1 }}]
: [[Eigenmonzo subgroup]]: 2.9/5.11
 
{{Val list|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
 
Badness: 0.499 × 10<sup>-3</sup>
 
Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9


</div></div>
</div></div>
Line 556: Line 523:
Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~11/9 = 349.9247, ~5/4 = 384.3505
Optimal ([[POTE]]) generators: ~3/2 = 703.9984, ~5/4 = 381.5352


EDO generators: [[31edo|(9, 10)\31]], [[34edo|(10, 11)\34]], [[72edo|(21, 23)\72]]
EDO generators: [[12edo|(7, 4)\12]], [[22edo|(13, 7)\22]], [[29edo|(17, 9)\29]]


Scales (Scala files):  
Scales (Scala files):  
Line 568: Line 535:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 243/242, 351/350
Comma list: 100/99, 225/224, 275/273
 
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 1 0 -3 2 -5 }}, {{val| 0 2 0 4 5 -2 }}, {{val| 0 0 1 2 0 4 }}]
Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9


{{Val list|legend=1| 31, 72, 103, 175f, (240) }}
{{Val list|legend=1| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}


Badness: 1.009 × 10<sup>-3</sup>
Projection pairs: 7 225/32 11 100/9 13 3200/243


</div></div>
</div></div>


= Apollo =
= Potassium =


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 703.4846, ~5/4 = 381.6033
Optimal ([[POTE]]) generators: ~3/2 = 696.1714, ~5/4 = 385.0500


EDO generators: [[12edo|(7, 4)\12]], [[19edo|(11, 6)\19]], [[22edo|(13, 7)\22]]
EDO generators: [[7edo|(4, 2)\7]], [[9edo|(5, 3)\9]], [[12edo|(7, 4)\12]]


Scales (Scala files):  
Scales (Scala files):  
Associated temperament: [[Magic family #magic|magic]]


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Line 596: Line 563:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 100/99, 225/224
Comma list: 45/44, 56/55
 
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 2 }}]
Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.9/7.11


Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7/5.11/9
{{Val list|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}


{{Val list|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}
Badness: 0.464 × 10<sup>-3</sup>


[[Projection pair]]s: 7 225/32 11 100/9
Projection pairs: 7 225/32 11 45/4


</div></div>
</div></div>
Line 612: Line 581:
Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 703.9984, ~5/4 = 381.5352
Optimal ([[POTE]]) generators: ~3/2 = 696.0103, ~5/4 = 384.6785


EDO generators: [[12edo|(7, 4)\12]], [[22edo|(13, 7)\22]], [[29edo|(17, 9)\29]]
EDO generators: [[9edo|(5, 3)\9]], [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]]


Scales (Scala files):  
Scales (Scala files):  
Line 624: Line 593:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 100/99, 225/224, 275/273
Comma list: 45/44, 56/55, 78/77
 
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 7 }}, {{val| 0 1 0 2 -2 -5 }}, {{val| 0 0 1 2 2 2 }}]
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup: 2.9/7.13/9
* 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9


Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9
{{Val list|legend=1| 9, 10, 12f, 19, 31e, 50e }}


{{Val list|legend=1| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
Badness: 0.733 × 10<sup>-3</sup>


Projection pairs: 7 225/32 11 100/9 13 3200/243
Projection pairs: 7 225/32 11 45/4 13 3375/256


</div></div>
</div></div>


= Artemis =
= Malcolm =


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 699.8719, ~11/10 = 158.3232
Optimal ([[POTE]]) generators: ~3/2 = 701.8913, ~5/4 = 382.4083


EDO generators: [[7edo|(4, 2)\7]], [[22edo|(13, 7)\22]], [[31edo|(18, 10)\31]]
EDO generators: [[19edo|(11, 6)\19]], [[41edo|(24, 13)\41]], [[53edo|(31, 17)\53]]


Scales (Scala files):  
Scales (Scala files):  
Line 652: Line 625:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 121/120, 225/224
Comma list: 225/224, 2200/2187


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


Mapping generators: ~2, ~3, ~11/10
{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}


{{Val list|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
Badness: 1.250 × 10<sup>-3</sup>


</div></div>
</div></div>
Line 666: Line 639:
Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 698.7090, ~11/10 = 158.7117
Optimal ([[POTE]]) generators: ~3/2 = 701.8913, ~5/4 = 382.4083


EDO generators: [[9edo|(5, 3)\9]], [[29edo|(17, 9)\29]], [[31edo|(18, 10)\31]]
EDO generators: [[19edo|(11, 6)\19]], [[41edo|(24, 13)\41]], [[53edo|(31, 17)\53]]


Scales (Scala files):  
Scales (Scala files):  
Line 678: Line 651:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 105/104, 121/120, 196/195
Comma list: 225/224, 275/273, 325/324
 
Mapping: [{{val| 1 0 0 -5 -3 2 }}, {{val| 0 1 0 2 7 4 }}, {{val| 0 0 1 2 -2 -2 }}]
 
{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
 
Badness: 1.075 × 10<sup>-3</sup>
 
</div></div>
 
= Prodigy =
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.
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 699.7981, ~5/4 = 383.5114
 
EDO generators: [[12edo|(7, 4)\12]], [[31edo|(18, 10)\31]], [[41edo|(24, 13)\41]]
 
Scales (Scala files): [[prodigy11]], [[prodigy12]], [[prodigy29]]
 
[[Associated temperament]]: [[Gamelismic clan #Miracle|miracle]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 225/224, 441/440
 
[[Mapping]]: [{{val| 1 0 0 -5 -13 }}, {{val| 0 1 0 2 6 }}, {{val| 0 0 1 2 3 }}]
 
Mapping generators: ~2, ~3, ~5
 
Map to lattice: [{{val| 0 0 -1 -2 -3 }}, {{val| 0 1 -1 0 3 }}]
 
Lattice basis:
: secor length = 0.9111, 3/2 length = 0.9477
: Angle (secor, 3/2) = 65.933
 
[[Minimax tuning]]:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [[Eigenmonzo subgroup]]: 2.9/5.11
 
{{Val list|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}
 
Badness: 0.344 × 10<sup>-3</sup>
 
[[Projection pair]]s: 7 225/32 11 91125/8192


Mapping: [{{val| 1 0 1 -3 2 -5 }}, {{val| 0 1 1 4 1 6 }}, {{val| 0 0 -2 -4 -1 -6 }}]
</div></div>


Mapping generators: ~2, ~3, ~11/10
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Hobbit bases</div>
<div class="mw-collapsible-content">


{{Val list|legend=1| 9, 20, 22f, 29, 31 }}
{2, 3, 5} subgroup
* 31: 81/80, 34171875/33554432
* 41: 34171875/33554432, 32805/32768


</div></div>
</div></div>


== Diana ==
== 13-limit ==


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 700.9789, ~11/10 = 159.0048
Optimal ([[POTE]]) generators: ~3/2 = 700.4006, ~5/4 = 381.4025


EDO generators: [[22edo|(13, 7)\22]], [[29edo|(17, 9)\29]], [[31edo|(18, 10)\31]]
EDO generators: [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]], [[19edo|(11, 6)\19]]


Scales (Scala files):  
Scales (Scala files):  
Line 704: Line 731:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 121/120, 225/224, 275/273
Comma list: 105/104, 196/195, 352/351


Mapping: [{{val| 1 0 1 -3 2 7 }}, {{val| 0 1 1 4 1 -2 }}, {{val| 0 0 -2 -4 -1 -1 }}]
Mapping: [{{val| 1 0 0 -5 -13 -8 }}, {{val| 0 1 0 2 6 3 }}, {{val| 0 0 1 2 3 3 }}]


Mapping generators: ~2, ~3, ~11/10
{{Val list|legend=1| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}


{{Val list|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
Badness: 0.736 × 10<sup>-3</sup>


</div></div>
</div></div>


= Potassium =
== Prodigious ==


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 696.1714, ~5/4 = 385.0500
Optimal ([[POTE]]) generators: ~3/2 = 700.3407, ~5/4 = 383.2592


EDO generators: [[7edo|(4, 2)\7]], [[9edo|(5, 3)\9]], [[12edo|(7, 4)\12]]
EDO generators: [[12edo|(7, 4)\12]], [[41edo|(24, 13)\41]], [[72edo|(42, 23)\72]]


Scales (Scala files):  
Scales (Scala files):  
Line 728: Line 755:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 45/44, 56/55
Comma list: 225/224, 364/363, 441/440


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 -13 -23 }}, {{val| 0 1 0 2 6 11 }}, {{val| 0 0 1 2 3 4 }}]


Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.9/7.11
{{Val list|legend=1| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}


{{Val list|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}
Badness: 0.900 × 10<sup>-3</sup>
 
Badness: 0.464 × 10<sup>-3</sup>
 
Projection pairs: 7 225/32 11 45/4


</div></div>
</div></div>


== 13-limit ==
== Prodigal ==


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 696.0103, ~5/4 = 384.6785
Optimal ([[POTE]]) generators: ~3/2 = 699.4864, ~5/4 = 384.0998


EDO generators: [[9edo|(5, 3)\9]], [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]]
EDO generators: [[19edo|(11, 6)\19]], [[31edo|(18, 10)\31]], [[72edo|(42, 23)\72]]


Scales (Scala files):  
Scales (Scala files):  
Line 760: Line 783:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 45/44, 56/55, 78/77
Comma list: 225/224, 351/350, 441/440


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 -13 -4 }}, {{val| 0 1 0 2 6 -1 }}, {{val| 0 0 1 2 3 4 }}]


Minimax tuning:
{{Val list|legend=1| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
* 13-odd-limit eigenmonzo subgroup: 2.9/7.13/9
* 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9


{{Val list|legend=1| 9, 10, 12f, 19, 31e, 50e }}
Badness: 0.889 × 10<sup>-3</sup>
 
Badness: 0.733 × 10<sup>-3</sup>
 
Projection pairs: 7 225/32 11 45/4 13 3375/256


</div></div>
</div></div>
Line 804: Line 821:
</div></div>
</div></div>


= Catakleismoid =
= Spectacle =


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~6/5 = 316.7318, ~11/8 = 549.2528
Optimal ([[POTE]]) generators: ~11/9 = 350.0570, ~5/4 = 383.9323
 
EDO generators: [[31edo|(9, 10)\31]], [[34edo|(10, 11)\34]], [[41edo|(12, 13)\41]]


EDO generators: [[19edo|(5, 8)\19]], [[53edo|(14, 24)\53]], [[72edo|(19, 33)\72]]
Scales (Scala files): [[spectacle31]]


Scales (Scala files):  
[[Associated temperament]]: [[Marvel temperaments #Marvo|marvo]]


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Line 820: Line 839:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 4375/4374
[[Comma list]]: 225/224, 243/242
 
Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 0 4 5 }}, {{val| 0 0 1 2 0 }}]
 
Mapping generators: ~2, ~11/9, ~5
 
[[Minimax tuning]]:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1/5 0 0 0 2/5 }}, {{monzo| 2/5 -2 1 0 4/5 }}, {{monzo| -19/5 -4 2 0 12/5 }}, {{monzo| 0 0 0 0 1 }}]
: [[Eigenmonzo subgroup]]: 2.9/5.11


Mapping: [{{val| 1 0 1 -3 0 }}, {{val| 0 6 5 22 0 }}, {{val| 0 0 0 0 1 }}]
{{Val list|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}


{{Val list|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
Badness: 0.499 × 10<sup>-3</sup>


Badness: 1.275 × 10<sup>-3</sup>
Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9


</div></div>
</div></div>
Line 834: Line 862:
Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~6/5 = 316.7410, ~11/8 = 548.6028
Optimal ([[POTE]]) generators: ~11/9 = 349.9247, ~5/4 = 384.3505


EDO generators: [[19edo|(5, 8)\19]], [[53edo|(14, 24)\53]], [[72edo|(19, 33)\72]]
EDO generators: [[31edo|(9, 10)\31]], [[34edo|(10, 11)\34]], [[72edo|(21, 23)\72]]


Scales (Scala files):  
Scales (Scala files):  
Line 846: Line 874:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 169/168, 225/224, 325/324
Comma list: 225/224, 243/242, 351/350


Mapping: [{{val| 1 0 1 -3 0 0 }}, {{val| 0 6 5 22 0 14 }}, {{val| 0 0 0 0 1 0 }}]
Mapping: [{{val| 1 1 0 -3 2 -5 }}, {{val| 0 2 0 4 5 -2 }}, {{val| 0 0 1 2 0 4 }}]


{{Val list|legend=1| 19, 34d, 53, 72, 125f, 197ef, 269cef }}
{{Val list|legend=1| 31, 72, 103, 175f, (240) }}


Badness: 0.916 × 10<sup>-3</sup>
Badness: 1.009 × 10<sup>-3</sup>


</div></div>
</div></div>
Line 912: Line 940:
</div></div>
</div></div>


= Malcolm =
= Artemis =


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 701.8913, ~5/4 = 382.4083
Optimal ([[POTE]]) generators: ~3/2 = 699.8719, ~11/10 = 158.3232


EDO generators: [[19edo|(11, 6)\19]], [[41edo|(24, 13)\41]], [[53edo|(31, 17)\53]]
EDO generators: [[7edo|(4, 2)\7]], [[22edo|(13, 7)\22]], [[31edo|(18, 10)\31]]


Scales (Scala files):  
Scales (Scala files):  
Line 928: Line 956:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 2200/2187
Comma list: 121/120, 225/224


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


{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
Mapping generators: ~2, ~3, ~11/10


Badness: 1.250 × 10<sup>-3</sup>
{{Val list|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}


</div></div>
</div></div>
Line 942: Line 970:
Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 701.8913, ~5/4 = 382.4083
Optimal ([[POTE]]) generators: ~3/2 = 698.7090, ~11/10 = 158.7117


EDO generators: [[19edo|(11, 6)\19]], [[41edo|(24, 13)\41]], [[53edo|(31, 17)\53]]
EDO generators: [[9edo|(5, 3)\9]], [[29edo|(17, 9)\29]], [[31edo|(18, 10)\31]]


Scales (Scala files):  
Scales (Scala files):  
Line 954: Line 982:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 275/273, 325/324
Comma list: 105/104, 121/120, 196/195


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 1 -3 2 -5 }}, {{val| 0 1 1 4 1 6 }}, {{val| 0 0 -2 -4 -1 -6 }}]


{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
Mapping generators: ~2, ~3, ~11/10


Badness: 1.075 × 10<sup>-3</sup>
{{Val list|legend=1| 9, 20, 22f, 29, 31 }}


</div></div>
</div></div>


= Prodigy =
== Diana ==
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.


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 699.7981, ~5/4 = 383.5114
Optimal ([[POTE]]) generators: ~3/2 = 700.9789, ~11/10 = 159.0048


EDO generators: [[12edo|(7, 4)\12]], [[31edo|(18, 10)\31]], [[41edo|(24, 13)\41]]
EDO generators: [[22edo|(13, 7)\22]], [[29edo|(17, 9)\29]], [[31edo|(18, 10)\31]]


Scales (Scala files): [[prodigy11]], [[prodigy12]], [[prodigy29]]
Scales (Scala files):  
 
[[Associated temperament]]: [[Gamelismic clan #Miracle|miracle]]


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
Line 981: Line 1,006:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 225/224, 441/440
Comma list: 121/120, 225/224, 275/273


[[Mapping]]: [{{val| 1 0 0 -5 -13 }}, {{val| 0 1 0 2 6 }}, {{val| 0 0 1 2 3 }}]
Mapping: [{{val| 1 0 1 -3 2 7 }}, {{val| 0 1 1 4 1 -2 }}, {{val| 0 0 -2 -4 -1 -1 }}]


Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~11/10


Map to lattice: [{{val| 0 0 -1 -2 -3 }}, {{val| 0 1 -1 0 3 }}]
{{Val list|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
 
Lattice basis:
: secor length = 0.9111, 3/2 length = 0.9477
: Angle (secor, 3/2) = 65.933
 
[[Minimax tuning]]:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [[Eigenmonzo subgroup]]: 2.9/5.11
 
{{Val list|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}
 
Badness: 0.344 × 10<sup>-3</sup>
 
[[Projection pair]]s: 7 225/32 11 91125/8192


</div></div>
</div></div>


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
= Catakleismoid =
<div style="line-height:1.6;">Hobbit bases</div>
<div class="mw-collapsible-content">
 
{2, 3, 5} subgroup
* 31: 81/80, 34171875/33554432
* 41: 34171875/33554432, 32805/32768
 
</div></div>
 
== 13-limit ==


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 700.4006, ~5/4 = 381.4025
Optimal ([[POTE]]) generators: ~6/5 = 316.7318, ~11/8 = 549.2528


EDO generators: [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]], [[19edo|(11, 6)\19]]
EDO generators: [[19edo|(5, 8)\19]], [[53edo|(14, 24)\53]], [[72edo|(19, 33)\72]]


Scales (Scala files):  
Scales (Scala files):  
Line 1,032: Line 1,032:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 4375/4374


Comma list: 105/104, 196/195, 352/351
Mapping: [{{val| 1 0 1 -3 0 }}, {{val| 0 6 5 22 0 }}, {{val| 0 0 0 0 1 }}]


Mapping: [{{val| 1 0 0 -5 -13 -8 }}, {{val| 0 1 0 2 6 3 }}, {{val| 0 0 1 2 3 3 }}]
Mapping generators: ~2, ~6/5, ~11


{{Val list|legend=1| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}
{{Val list|legend=1| 19, 34d, 53, 72, 197e, 269ce }}


Badness: 0.736 × 10<sup>-3</sup>
Badness: 1.275 × 10<sup>-3</sup>


</div></div>
</div></div>


== Prodigious ==
== 13-limit ==


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 700.3407, ~5/4 = 383.2592
Optimal ([[POTE]]) generators: ~6/5 = 316.7410, ~11/8 = 548.6028


EDO generators: [[12edo|(7, 4)\12]], [[41edo|(24, 13)\41]], [[72edo|(42, 23)\72]]
EDO generators: [[19edo|(5, 8)\19]], [[53edo|(14, 24)\53]], [[72edo|(19, 33)\72]]


Scales (Scala files):  
Scales (Scala files):  
Line 1,060: Line 1,062:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 364/363, 441/440
Comma list: 169/168, 225/224, 325/324
 
Mapping: [{{val| 1 0 1 -3 0 0 }}, {{val| 0 6 5 22 0 14 }}, {{val| 0 0 0 0 1 0 }}]


Mapping: [{{val| 1 0 0 -5 -13 -23 }}, {{val| 0 1 0 2 6 11 }}, {{val| 0 0 1 2 3 4 }}]
Mapping generators: ~2, ~6/5, ~11


{{Val list|legend=1| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}
{{Val list|legend=1| 19, 34d, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.900 × 10<sup>-3</sup>
Badness: 0.916 × 10<sup>-3</sup>


</div></div>
</div></div>


== Prodigal ==
= Mirage =


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generators: ~3/2 = 699.4864, ~5/4 = 384.0998
Optimal ([[POTE]]) generators: ~15/14 = 116.6327, ~13/8 = 837.7040


EDO generators: [[19edo|(11, 6)\19]], [[31edo|(18, 10)\31]], [[72edo|(42, 23)\72]]
EDO generators: [[31edo|(3, 22)\31]], [[41edo|(4, 29)\41]], [[72edo|(7, 50)\22]]


Scales (Scala files):  
Scales (Scala files):  
Line 1,086: Line 1,090:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 351/350, 441/440
Comma list: 225/224, 243/242, 385/384


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 1 3 3 2 0 }}, {{val| 0 6 -7 -2 15 0 }}, {{val| 0 0 0 0 0 1 }}]


{{Val list|legend=1| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
{{Val list|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}


Badness: 0.889 × 10<sup>-3</sup>
Badness: 0.738 × 10<sup>-3</sup>


</div></div>
</div></div>
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