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Marvel family: Difference between revisions

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Databox for potassium to hestia
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= Malcolm =
= Malcolm =
Comma list: 225/224, 2200/2187
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 701.8913, ~5/4 = 382.4083
 
EDO generators: [[19edo|(11, 6)\19]], [[41edo|(24, 13)\41]], [[53edo|(31, 17)\53]]
 
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
Subgroup: 2.3.5.7.11
Comma list: 225/224, 2200/2187


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 }}]


{{Val list|legend=1| 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce }}
{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}


Badness: 1.250 × 10<sup>-3</sup>
Badness: 1.250 × 10<sup>-3</sup>
</div></div>


== 13-limit ==
== 13-limit ==
Comma list: 225/224, 275/273, 325/324
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 701.8913, ~5/4 = 382.4083
 
EDO generators: [[19edo|(11, 6)\19]], [[41edo|(24, 13)\41]], [[53edo|(31, 17)\53]]
 
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
Subgroup: 2.3.5.7.11.13
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 }}]
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| 41, 53, 94, 429cdef, 523cdef }}
{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}


Badness: 1.075 × 10<sup>-3</sup>
Badness: 1.075 × 10<sup>-3</sup>
</div></div>


= Prodigy =
= 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.
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.


[[Comma list]]: 225/224, 441/440
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
Subgroup: 2.3.5.7.11


[[Associated temperament]]: [[Gamelismic clan #Miracle|miracle]]
[[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]]: [{{val| 1 0 0 -5 -13 }}, {{val| 0 1 0 2 6 }}, {{val| 0 0 1 2 3 }}]


Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~5
Line 954: Line 996:
: [[Eigenmonzo subgroup]]: 2.9/5.11
: [[Eigenmonzo subgroup]]: 2.9/5.11


{{Val list|legend=1| 10, 12, 29, 31, 41, 72, 247c, 319bcde, 391bcde, 463bcde }}
{{Val list|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}


Badness: 0.344 × 10<sup>-3</sup>
Badness: 0.344 × 10<sup>-3</sup>
Line 960: Line 1,002:
[[Projection pair]]s: 7 225/32 11 91125/8192
[[Projection pair]]s: 7 225/32 11 91125/8192


Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
</div></div>
 
<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">


; Hobbit bases
{2, 3, 5} subgroup
{2, 3, 5} subgroup
* 31: 81/80, 34171875/33554432
* 31: 81/80, 34171875/33554432
* 41: 34171875/33554432, 32805/32768
* 41: 34171875/33554432, 32805/32768
</div></div>


== 13-limit ==
== 13-limit ==
Comma list: 105/104, 196/195, 352/351
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 700.4006, ~5/4 = 381.4025
 
EDO generators: [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]], [[19edo|(11, 6)\19]]
 
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
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 352/351


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 }}]


{{Val list|legend=1| 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef }}
{{Val list|legend=1| 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>
</div></div>


== Prodigious ==
== Prodigious ==
Comma list: 225/224, 441/440, 364/363
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 700.3407, ~5/4 = 383.2592
 
EDO generators: [[12edo|(7, 4)\12]], [[41edo|(24, 13)\41]], [[72edo|(42, 23)\72]]
 
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
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 364/363, 441/440


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 }}]


{{Val list|legend=1| 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf }}
{{Val list|legend=1| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}


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


== Prodigal ==
== Prodigal ==
Comma list: 225/224, 441/440, 351/350
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 699.4864, ~5/4 = 384.0998
 
EDO generators: [[19edo|(11, 6)\19]], [[31edo|(18, 10)\31]], [[72edo|(42, 23)\72]]
 
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
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 441/440


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 }}]


{{Val list|legend=1| 31, 72, 103, 175f }}
{{Val list|legend=1| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}


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


[[Category:Theory]]
[[Category:Theory]]
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