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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="display: block; text-align: right;"&gt;[[toc]]
[[xenharmonie/Marvel|Deutsch]]
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=Marvel=
The head of the marvel family is marvel, which tempers out [[225_224|225/224]], the [[septimal kleisma]] or [[marvel comma]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].


Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[Kleismic family|catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[Pythagorean family|compton temperament]], for which [[240edo]] may be used.
=Marvel=
The head of the marvel family is marvel, which tempers out [[225/224|225/224]], the [[septimal_kleisma|septimal kleisma]] or [[marvel_comma|marvel comma]]. Marvel has a [[Normal_lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic_Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo|197edo]].


See also [[Marvel temperaments]].
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[Kleismic_family|catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[Pythagorean_family|compton temperament]], for which [[240edo|240edo]] may be used.


==Vital statistics==  
See also [[Marvel_temperaments|Marvel temperaments]].
[[Comma]] c = 225/224
 
Related linear temperament: [[Kleismic family|catakleismic temperament]]
==Vital statistics==
[[Comma|Comma]] c = 225/224
 
Related linear temperament: [[Kleismic_family|catakleismic temperament]]


7-limit minimax: 3 and 5 1/4c flat, 7 just
7-limit minimax: 3 and 5 1/4c flat, 7 just
[|1 0 0 0&gt;, |5/4 1/2 -1/2 1/4&gt;, |5/4 -1/2 1/2 1/4&gt;, |0 0 0 1&gt;]
[|1 0 0 0&gt;, |5/4 1/2 -1/2 1/4&gt;, |5/4 -1/2 1/2 1/4&gt;, |0 0 0 1&gt;]
[[Eigenmonzo subgroup]]: 2.5/3.7
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.5/3.7


9-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just
9-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just
[|1 0 0 0&gt;, |5/6 2/3 -1/3 1/6&gt;, |5/3 -2/3 1/3 1/3&gt;, |0 0 0 1&gt;]
[|1 0 0 0&gt;, |5/6 2/3 -1/3 1/6&gt;, |5/3 -2/3 1/3 1/3&gt;, |0 0 0 1&gt;]
[[Eigenmonzo subgroup]]: 2.9/5.7
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.7


Lattice basis: secor length 1.256, 3/2 length 1.369
Lattice basis: secor length 1.256, 3/2 length 1.369
Angle(secor, 3/2) = 106.958 degrees
Angle(secor, 3/2) = 106.958 degrees
Map to lattice: [&lt;0 0 -1 -2|, &lt;0 1 -1 0|]
Map to lattice: [&lt;0 0 -1 -2|, &lt;0 1 -1 0|]


Map: [&lt;1 0 0 -5|, &lt;0 1 0 2|, &lt;0 0 1 2|]
Map: [&lt;1 0 0 -5|, &lt;0 1 0 2|, &lt;0 0 1 2|]
Generators: 2, 3, 5
Generators: 2, 3, 5
[[edo|EDOs]]: [[10edo|10]], [[12edo|12]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]],[[72edo|72]], [[197edo|197]], [[269edo|269c]]
 
[[EDO|EDOs]]: [[10edo|10]], [[12edo|12]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]],[[72edo|72]], [[197edo|197]], [[269edo|269c]]
 
Badness: 0.0000365
Badness: 0.0000365


[[Projection pair]]s: 7 225/32
[[Projection_pair|Projection pair]]s: 7 225/32
[[Spectrum of a temperament|Spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9


Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]]
[[Spectrum_of_a_temperament|Spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9


==[[Minkowski blocks]]==  
Scales: [[marvel9|marvel9]], [[marvel10|marvel10]], [[marvel11|marvel11]], [[marvel12|marvel12]], [[marvel19|marvel19]], [[marvel22|marvel22]], [[pump12_1|pump12_1]], [[pump12_2|pump12_2]], [[pump13|pump13]], [[pump14|pump14]], [[pump15|pump15]], [[pump16|pump16]], [[pump17|pump17]], [[pump18|pump18]]
 
==[[Minkowski_blocks|Minkowski blocks]]==
{2, 3, 5} subgroup
{2, 3, 5} subgroup


8: 16/15, 250/243
8: 16/15, 250/243
9: 135/128, 128/125
9: 135/128, 128/125
10: 25/24, 2048/2025
10: 25/24, 2048/2025
11: 135/128, 2048/1875
11: 135/128, 2048/1875
12: 2048/2025, 128/125
12: 2048/2025, 128/125
15: 128/125, 32768/30375
15: 128/125, 32768/30375
17: 25/24, 2278125/2097152
17: 25/24, 2278125/2097152
19: 16875/16384, 81/80
19: 16875/16384, 81/80
21: 128/125, 273375/262144
21: 128/125, 273375/262144
22: 2048/2025, 3125/3072
22: 2048/2025, 3125/3072
29: 16875/16384, 32805/32768
29: 16875/16384, 32805/32768
31: 81/80, 34171875/33554432
31: 81/80, 34171875/33554432
41: 34171875/33554432, 3125/3072
41: 34171875/33554432, 3125/3072


==Music==  
==Music==
[[http://chrisvaisvil.com/?p=314|Semimarvelous Blue Drawf]] by [[Chris Vaisvil]]
[http://chrisvaisvil.com/?p=314 Semimarvelous Blue Drawf] by [[Chris_Vaisvil|Chris Vaisvil]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/marvel10_2.mp3|notJoelTaylorsTreeSpirit-Marvel10-2]] by [[Billy Stiltner]]
 
[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/marvel10_2.mp3 notJoelTaylorsTreeSpirit-Marvel10-2] by [[Billy_Stiltner|Billy Stiltner]]


==11-limit (Unimarv)==  
==11-limit (Unimarv)==
[[Comma|Commas]]: 225/224, 385/384
[[Comma|Commas]]: 225/224, 385/384
Related linear temperament: [[Kleismic family|catakleismic temperament]]


[[Minimax tuning]]:
Related linear temperament: [[Kleismic_family|catakleismic temperament]]
 
[[Minimax_tuning|Minimax tuning]]:
 
[|1 0 0 0 0&gt;, |4/3 8/9 -1/3 0 -1/9&gt;, |8/3 -2/9 1/3 0 -2/9&gt;,
[|1 0 0 0 0&gt;, |4/3 8/9 -1/3 0 -1/9&gt;, |8/3 -2/9 1/3 0 -2/9&gt;,
|3 4/3 0 0 -2/3&gt;, |8/3 -2/9 -2/3 0 7/9&gt;]
|3 4/3 0 0 -2/3&gt;, |8/3 -2/9 -2/3 0 7/9&gt;]
[[Eigenmonzo subgroup]]: 2.9/5.11/9
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.11/9


Lattice basis: secor length 1.0364 5/4 length 1.0759
Lattice basis: secor length 1.0364 5/4 length 1.0759
Angle(secor, 5/4) = 104.028 degrees
Angle(secor, 5/4) = 104.028 degrees
Map to lattice: [&lt;0 -1 0 -2 1|, &lt;0 -1 1 0 -2|]
Map to lattice: [&lt;0 -1 0 -2 1|, &lt;0 -1 1 0 -2|]


Map: [&lt;1 0 0 -5 12|, &lt;0 1 0 2 -1|, &lt;0 0 1 2 -3|]
Map: [&lt;1 0 0 -5 12|, &lt;0 1 0 2 -1|, &lt;0 0 1 2 -3|]
[[Generator|Generators]]: 2, 3, 5
 
[[edo|Edos]]: [[10edo|10]], [[12edo|12e]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[53edo|53]], [[72edo|72]], [[166edo|166]], [[197edo|197e]], [[269edo|269ce]], [[341edo|341ce]]
[[generator|Generators]]: 2, 3, 5
 
[[EDO|Edos]]: [[10edo|10]], [[12edo|12e]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[53edo|53]], [[72edo|72]], [[166edo|166]], [[197edo|197e]], [[269edo|269ce]], [[341edo|341ce]]
 
Badness: 0.000255
Badness: 0.000255


[[Projection pair]]s: 7 225/32 11 4096/375
[[Projection_pair|Projection pair]]s: 7 225/32 11 4096/375
[[Spectrum of a temperament|Spectrum]]: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11
 
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]
[[Spectrum_of_a_temperament|Spectrum]]: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11
 
Scales: [[marvel22_11|marvel22_11]], [[unimarv19|unimarv19]], [[unimarv22|unimarv22]]


===Hobbit bases===  
===Hobbit bases===
{2, 3, 5} subgroup
{2, 3, 5} subgroup


12: 128/125, 2048/2025
12: 128/125, 2048/2025
15: 128/125, 32768/30375
15: 128/125, 32768/30375
19: 16875/16384, 81/80
19: 16875/16384, 81/80
22: 2048/2025, 2109375/2097152
22: 2048/2025, 2109375/2097152
31: 2109375/2097152, 81/80
31: 2109375/2097152, 81/80
41: 3125/3072, 34171875/33554432
41: 3125/3072, 34171875/33554432


==13-limit==  
==13-limit==
Commas: 225/224, 385/384, 351/350
Commas: 225/224, 385/384, 351/350


13-limit eigenmonzo subgroup: 2.11/9.13/9
13-limit eigenmonzo subgroup: 2.11/9.13/9
15-limit eigenmonzo subgroup: 2.15/11.15/13
15-limit eigenmonzo subgroup: 2.15/11.15/13


Map: [&lt;1 0 0 -5 12 -4|, &lt;0 1 0 2 -1 -1|, &lt;0 0 1 2 -3 4|]
Map: [&lt;1 0 0 -5 12 -4|, &lt;0 1 0 2 -1 -1|, &lt;0 0 1 2 -3 4|]
EDOs: 19, 22, 31, 50, 53, 72, 103, [[175edo|175f]], [[300edo|300cef]], [[403bcef]]
 
EDOs: 19, 22, 31, 50, 53, 72, 103, [[175edo|175f]], [[300edo|300cef]], [[403bcef|403bcef]]
 
Badness: 0.000690
Badness: 0.000690


[[Spectrum of a temperament|Spectrum]]: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11
[[Spectrum_of_a_temperament|Spectrum]]: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11


=Hecate=  
=Hecate=
Commas: 225/224, 385/384, 325/324
Commas: 225/224, 385/384, 325/324


13-limit eigenmonzo subgroup: 2.7.13/5
13-limit eigenmonzo subgroup: 2.7.13/5
15-limit eigenmonzo subgroup: 2.7.15/13
15-limit eigenmonzo subgroup: 2.7.15/13


Map: [&lt;1 0 0 -5 12 2|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -2|]
Map: [&lt;1 0 0 -5 12 2|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -2|]
EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef
EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef
Badness: 0.000721
Badness: 0.000721


Projection pairs: 7 225/32 11 4096/375 13 324/25
Projection pairs: 7 225/32 11 4096/375 13 324/25
[[Spectrum of a temperament|Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11


==17-limit==  
[[Spectrum_of_a_temperament|Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11
 
==17-limit==
Commas: 225/224, 385/384, 325/324, 595/594
Commas: 225/224, 385/384, 325/324, 595/594


Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 -6|]
Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 -6|]
EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg
EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg
Badness: 0.000869
Badness: 0.000869


==Enodia==  
==Enodia==
Commas: 225/224, 385/384, 325/324, 375/374
Commas: 225/224, 385/384, 325/324, 375/374


Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 6|]
Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 6|]
EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg
EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg
Badness: .000917
Badness: .000917


=Marvelcat=  
=Marvelcat=
Commas: 169/168, 225/224, 385/384
Commas: 169/168, 225/224, 385/384


Map: [&lt;1 0 0 -5 12 -|, &lt;0 2 0 4 -2 3|, &lt;0 0 1 2 -3 1|]
Map: [&lt;1 0 0 -5 12 -|, &lt;0 2 0 4 -2 3|, &lt;0 0 1 2 -3 1|]
EDOs: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef
EDOs: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef
Badness: 0.0009997
Badness: 0.0009997


=Marvell=  
=Marvell=
Commas: 225/224, 385/384, 1573/1568
Commas: 225/224, 385/384, 1573/1568


13-limit eigenmonzo subgroup: 2.9/5.11/9
13-limit eigenmonzo subgroup: 2.9/5.11/9
15-limit eigenmonzo subgroup: 2.7.15/13
15-limit eigenmonzo subgroup: 2.7.15/13


Map: [&lt;1 0 0 -5 12 -29|, &lt;0 1 0 2 -1 6|, &lt;0 0 1 2 -3 10|]
Map: [&lt;1 0 0 -5 12 -29|, &lt;0 1 0 2 -1 6|, &lt;0 0 1 2 -3 10|]
EDOs: 9, 31, [[63edo|63]], 72, [[103edo|103]], [[166edo|166]], [[238edo|238cf]], [[269edo|269ce]], 507bcef, 610bcef
EDOs: 9, 31, [[63edo|63]], 72, [[103edo|103]], [[166edo|166]], [[238edo|238cf]], [[269edo|269ce]], 507bcef, 610bcef
Badness: 0.000862
Badness: 0.000862


=Isis=  
=Isis=
Commas: 225/224, 385/384, 275/273
Commas: 225/224, 385/384, 275/273


Map: [&lt;1 0 0 -5 12 17|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -3|]
Map: [&lt;1 0 0 -5 12 17|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -3|]
EDOs: 10, 22, 31, 41, 53, 94
EDOs: 10, 22, 31, 41, 53, 94
Badness: 0.000866
Badness: 0.000866


Projection pairs: 7 225/32 11 4096/375 13 131072/10125
Projection pairs: 7 225/32 11 4096/375 13 131072/10125


=Deecee=  
=Deecee=
Commas: 225/224, 385/384, 364/363
Commas: 225/224, 385/384, 364/363


13-limit eigenmonzo subgroup: 2.9/5.13/9
13-limit eigenmonzo subgroup: 2.9/5.13/9
15-limit eigenmonzo subgroup: 2.3.13/5
15-limit eigenmonzo subgroup: 2.3.13/5


Map: [&lt;1 0 0 -5 12 27|, &lt;0 1 0 2 -1 -3|, &lt;0 0 1 2 -3 -8|]
Map: [&lt;1 0 0 -5 12 27|, &lt;0 1 0 2 -1 -3|, &lt;0 0 1 2 -3 -8|]
EDOs: 9, 22, 41, 63, 72, [[185edo|185cf]], [[257edo|257cf]]
EDOs: 9, 22, 41, 63, 72, [[185edo|185cf]], [[257edo|257cf]]
Badness: 0.000920
Badness: 0.000920


Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875
Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875


=Mirage=  
=Mirage=
Commas: 225/224, 243/242, 385/384
Commas: 225/224, 243/242, 385/384


Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 0|, &lt;0 0 0 0 0 1|]
Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 0|, &lt;0 0 0 0 0 1|]
EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef
EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef
Badness: 0.000738
Badness: 0.000738


=Minerva=  
=Minerva=
[[Comma|Commas]]: 99/98, 176/175
[[Comma|Commas]]: 99/98, 176/175
Related linear temperament: [[Semicomma family|orwell]]


[[Eigenmonzo subgroup]]: 2.7/5.11/9
Related linear temperament: [[Semicomma_family|orwell]]
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.7/5.11/9


Lattice basis: 16/15 length 0.8997 5/4 length 1.0457
Lattice basis: 16/15 length 0.8997 5/4 length 1.0457
Angle(16/15, 5/4) = 98.6044 degrees
Angle(16/15, 5/4) = 98.6044 degrees
Map to lattice: [&lt;0 -1 0 -2 -2|, &lt;0 -1 1 0 2|]
Map to lattice: [&lt;0 -1 0 -2 -2|, &lt;0 -1 1 0 2|]


Map: [&lt;1 0 0 -5 -9|, &lt;0 1 0 2 2|, &lt;0 0 1 2 4|]
Map: [&lt;1 0 0 -5 -9|, &lt;0 1 0 2 2|, &lt;0 0 1 2 4|]
[[Generator|Generators]]: 2, 3, 5
 
[[edo|EDOs]]: [[9edo|9]], [[12edo|12]], [[21edo|21]], [[22edo|22]], [[31edo|31]], [[43edo|43]], [[53edo|53]], [[74edo|74]], [[75edo|75]], [[96edo|96]], [[127edo|127]]
[[generator|Generators]]: 2, 3, 5
 
[[EDO|EDOs]]: [[9edo|9]], [[12edo|12]], [[21edo|21]], [[22edo|22]], [[31edo|31]], [[43edo|43]], [[53edo|53]], [[74edo|74]], [[75edo|75]], [[96edo|96]], [[127edo|127]]
 
Badness: 0.000381
Badness: 0.000381


[[Projection pair]]s: 7 225/32 11 5625/512
[[Projection_pair|Projection pair]]s: 7 225/32 11 5625/512


Scales: [[minerva12]], [[minerva22x]]
Scales: [[minerva12|minerva12]], [[minerva22x|minerva22x]]


==Athene==  
==Athene==
Commas: 99/98, 176/175, 275/273
Commas: 99/98, 176/175, 275/273


13-limit eigenmonzo subgroup: 2.11/9.13/7
13-limit eigenmonzo subgroup: 2.11/9.13/7
15-limit eigenmonzo subgroup: 2.11/9.13/7
15-limit eigenmonzo subgroup: 2.11/9.13/7


Map: [&lt;1 0 0 -5 -9 -4|, &lt;0 1 0 2 2 -1|, &lt;0 0 1 2 4 4|]
Map: [&lt;1 0 0 -5 -9 -4|, &lt;0 1 0 2 2 -1|, &lt;0 0 1 2 4 4|]
EDOs: 22, 31, 53, 84e, 118d, 149df, 171de, 202def
EDOs: 22, 31, 53, 84e, 118d, 149df, 171de, 202def
Badness: 0.000818
Badness: 0.000818


[[Projection pair]]s: 7 225/32 11 5625/512 13 625/48
[[Projection_pair|Projection pair]]s: 7 225/32 11 5625/512 13 625/48


==Other eleven limit marvel children==  
==Other eleven limit marvel children==
The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.
The second comma of the [[Normal_lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.


=Spectacle=  
=Spectacle=
[[Comma|Commas]]: 225/224, 243/242
[[Comma|Commas]]: 225/224, 243/242
Related linear temperament: [[Marvel temperaments|marvo]]


[[Minimax tuning]]:
Related linear temperament: [[Marvel_temperaments|marvo]]
 
[[Minimax_tuning|Minimax tuning]]:
 
[|1 0 0 0 0&gt;, |1/5 0 0 0 2/5&gt;, |2/5 -2 1 0 4/5&gt;, |-19/5 -4 2 0 12/5&gt;, |0 0 0 0 1&gt;]
[|1 0 0 0 0&gt;, |1/5 0 0 0 2/5&gt;, |2/5 -2 1 0 4/5&gt;, |-19/5 -4 2 0 12/5&gt;, |0 0 0 0 1&gt;]
[[Eigenmonzo subgroup]]: 2.9/5.11
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.11


Map: [&lt;1 1 0 -3 2|, &lt;0 2 0 4 5|, &lt;0 0 1 2 0|]
Map: [&lt;1 1 0 -3 2|, &lt;0 2 0 4 5|, &lt;0 0 1 2 0|]
[[Generator|Generators]]: 2, 11/9, 5
 
[[edo|EDOs]]: [[10edo|10]], [[31edo|31]], [[41edo|41]], [[72edo|72]], [[240edo|240]], [[259edo|259b]], [[269edo|269ce]], [[310edo|310c]], [[331edo|331bc]], [[353edo|353c]], [[497edo|497bc]], [[569edo|569bc]]
[[generator|Generators]]: 2, 11/9, 5
 
[[EDO|EDOs]]: [[10edo|10]], [[31edo|31]], [[41edo|41]], [[72edo|72]], [[240edo|240]], [[259edo|259b]], [[269edo|269ce]], [[310edo|310c]], [[331edo|331bc]], [[353edo|353c]], [[497edo|497bc]], [[569edo|569bc]]
 
Badness: 0.000499
Badness: 0.000499


Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9
Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9


Scales: [[spectacle31]]
Scales: [[spectacle31|spectacle31]]


==13-limit==  
==13-limit==
Commas: 225/224, 243/242, 351/350
Commas: 225/224, 243/242, 351/350


Map: [&lt;1 1 0 -3 2 -5|, &lt;0 2 0 4 5 -2|, &lt;0 0 1 2 0 4|]
Map: [&lt;1 1 0 -3 2 -5|, &lt;0 2 0 4 5 -2|, &lt;0 0 1 2 0 4|]
EDOs: 31, 72, 103, 175f, 209, 240
EDOs: 31, 72, 103, 175f, 209, 240
Badness: 0.001009
Badness: 0.001009


=Apollo=  
=Apollo=
[[Comma|Commas]]: 100/99, 225/224
[[Comma|Commas]]: 100/99, 225/224
Related linear temperament: [[Magic family|Magic]]
 
Related linear temperament: [[Magic_family|Magic]]


Eigenmonzo subgroup: 2.7/5.11/9
Eigenmonzo subgroup: 2.7/5.11/9


Map: [&lt;1 0 0 -5 2|, &lt;0 1 0 2 -2|, &lt;0 0 1 2 2|]
Map: [&lt;1 0 0 -5 2|, &lt;0 1 0 2 -2|, &lt;0 0 1 2 2|]
EDOs: 12, 19, 22, 41, [[104edo]], [[157edo|157ce]], [[198edo|198ce]], [[220edo|220ce]], [[261edo|261ce]]
 
EDOs: 12, 19, 22, 41, [[104edo|104edo]], [[157edo|157ce]], [[198edo|198ce]], [[220edo|220ce]], [[261edo|261ce]]


Projection pairs: 7 225/32 11 100/9
Projection pairs: 7 225/32 11 100/9


==13-limit==  
==13-limit==
[[Comma|Commas]]: 100/99, 225/224, 245/243
[[Comma|Commas]]: 100/99, 225/224, 245/243


Line 254: Line 329:


Map: [&lt;1 0 0 -5 2 7|, &lt;0 1 0 2 -2 -5|, &lt;0 0 1 2 2 2|]
Map: [&lt;1 0 0 -5 2 7|, &lt;0 1 0 2 -2 -5|, &lt;0 0 1 2 2 2|]
EDOs: 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef
EDOs: 22, 29, 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=
Commas: 45/44, 56/55
Commas: 45/44, 56/55


Line 264: Line 340:


Map: [&lt;1 0 0 -5 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 2 1|]
Map: [&lt;1 0 0 -5 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 2 1|]
EDOs: 9, 10, 12, 19, 31e, 50e
EDOs: 9, 10, 12, 19, 31e, 50e
Badness: 0.000464
Badness: 0.000464


Projection pairs: 7 225/32 11 45/4
Projection pairs: 7 225/32 11 45/4


==13-limit==  
==13-limit==
Commas: 45/44, 56/55, 78/77
Commas: 45/44, 56/55, 78/77


13-limit eigenmonzo subgroup: 2.9/7.13/9
13-limit eigenmonzo subgroup: 2.9/7.13/9
15-limit eigenmonzo subgroup: 2.9/7.13/9
15-limit eigenmonzo subgroup: 2.9/7.13/9


Map: [&lt;1 0 0 -5 -2 -8|, &lt;0 1 0 2 2 3|, &lt;0 0 1 2 1 3|]
Map: [&lt;1 0 0 -5 -2 -8|, &lt;0 1 0 2 2 3|, &lt;0 0 1 2 1 3|]
EDOs: 9, 10, 19, 31e, 50e
EDOs: 9, 10, 19, 31e, 50e
Badness: 0.000733
Badness: 0.000733


Projection pairs: 7 225/32 11 45/4 13 3375/256
Projection pairs: 7 225/32 11 45/4 13 3375/256


=Fantastic=  
=Fantastic=
Commas: 225/224, 4375/4356
Commas: 225/224, 4375/4356


Map: [&lt;2 0 0 -10 -7|, &lt;0 1 0 2 0|, &lt;0 0 1 2 3|]
Map: [&lt;2 0 0 -10 -7|, &lt;0 1 0 2 0|, &lt;0 0 1 2 3|]
EDOs: 12, 22, 50, 72, 166, 238c, 310c
EDOs: 12, 22, 50, 72, 166, 238c, 310c
Badness: 0.000743
Badness: 0.000743


=Catakleismoid=  
=Catakleismoid=
Commas: 225/224, 4375/4374
Commas: 225/224, 4375/4374


Map: [&lt;1 0 1 -3 0|, &lt;0 6 5 22 0|, &lt;0 0 0 0 1|]
Map: [&lt;1 0 1 -3 0|, &lt;0 6 5 22 0|, &lt;0 0 0 0 1|]
EDOs: 19, 53, 72, 197e, 269ce
EDOs: 19, 53, 72, 197e, 269ce
Badness: 0.001275
Badness: 0.001275


==13-limit==  
==13-limit==
Commas: 169/168, 225/224, 325/324
Commas: 169/168, 225/224, 325/324


Map: [&lt;1 0 1 -3 0 0|, &lt;0 6 5 22 0 14|, &lt;0 0 0 0 1 0|]
Map: [&lt;1 0 1 -3 0 0|, &lt;0 6 5 22 0 14|, &lt;0 0 0 0 1 0|]
EDOs: 19, 53, 72, 125f, 197ef, 269cef
EDOs: 19, 53, 72, 125f, 197ef, 269cef
Badness: 0.000916
Badness: 0.000916


=Hestia=  
=Hestia=
Commas: 225/224, 125000/124509
Commas: 225/224, 125000/124509


Map: [&lt;1 0 0 -5 9|, &lt;0 2 0 4 -7|, &lt;0 0 1 2 0|]
Map: [&lt;1 0 0 -5 9|, &lt;0 2 0 4 -7|, &lt;0 0 1 2 0|]
EDOs: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce
EDOs: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce
Badness: 0.00154
Badness: 0.00154


==13-limit==  
==13-limit==
Commas: 169/168, 225/224, 1001/1000
Commas: 169/168, 225/224, 1001/1000


Map: [&lt;1 0 0 -5 9 -1|, &lt;0 2 0 4 -7 3|, &lt;0 0 1 2 0 1|]
Map: [&lt;1 0 0 -5 9 -1|, &lt;0 2 0 4 -7 3|, &lt;0 0 1 2 0 1|]
EDOs: 19, 29, 43, 53, 72, 125f, 197ef, 269cef
EDOs: 19, 29, 43, 53, 72, 125f, 197ef, 269cef
Badness: 0.001062
Badness: 0.001062


=Malcolm=  
=Malcolm=
Commas: 225/224, 2200/2187
Commas: 225/224, 2200/2187


Map: [&lt;1 0 0 -5 -3|, &lt;0 1 0 2 7|, &lt;0 0 1 2 -2|]
Map: [&lt;1 0 0 -5 -3|, &lt;0 1 0 2 7|, &lt;0 0 1 2 -2|]
EDOs: 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce
EDOs: 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce
Badness: 0.001250
Badness: 0.001250


==13-limit==  
==13-limit==
commas: 225/224, 275/273, 325/324
commas: 225/224, 275/273, 325/324


Map: [&lt;1 0 0 -5 -3 2|, &lt;0 1 0 2 7 4|, &lt;0 0 1 2 -2 -2|]
Map: [&lt;1 0 0 -5 -3 2|, &lt;0 1 0 2 7 4|, &lt;0 0 1 2 -2 -2|]
EDOs: 41, 53, 94, 429cdef, 523cdef
EDOs: 41, 53, 94, 429cdef, 523cdef
Badness: 0.001075
Badness: 0.001075


=Tripod=  
=Tripod=
Commas: 105/104, 144/143, 196/195
Commas: 105/104, 144/143, 196/195


13-limit eigenmonzo subgroup: 2.9/7.13/11
13-limit eigenmonzo subgroup: 2.9/7.13/11
15-limit eigenmonzo subgroup: 2.5/3.13/11
15-limit eigenmonzo subgroup: 2.5/3.13/11


Map: [&lt;1 0 0 -5 12 -8|, &lt;0 1 0 2 -1 3|, &lt;0 0 1 2 -3 3|]
Map: [&lt;1 0 0 -5 12 -8|, &lt;0 1 0 2 -1 3|, &lt;0 0 1 2 -3 3|]
EDOs: 9, 10, 19, 31, 41, 72f, [[81edo|81]], [[91edo|91]], [[122edo|122f]], [[163edo|163df]]
EDOs: 9, 10, 19, 31, 41, 72f, [[81edo|81]], [[91edo|91]], [[122edo|122f]], [[163edo|163df]]
Badness: 0.000745
Badness: 0.000745


Projection pairs: 7 225/32 11 4096/375 13 3375/256
Projection pairs: 7 225/32 11 4096/375 13 3375/256


=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 [[Gamelismic clan|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 [[Gamelismic_clan|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|Commas]]: 225/224, 441/440
[[Comma|Commas]]: 225/224, 441/440
Related linear temperament: [[Gamelismic clan|miracle]]


[[Minimax tuning]]:
Related linear temperament: [[Gamelismic_clan|miracle]]
 
[[Minimax_tuning|Minimax tuning]]:
 
[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;,
[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;,
|13/6 -1 1/2 0 1/6&gt;,
|13/6 -1 1/2 0 1/6&gt;,
|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]
|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]
[[Eigenmonzo subgroup]]: 2.9/5.11
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.11


Lattice basis: secor length 0.9111, 3/2 length 0.9477
Lattice basis: secor length 0.9111, 3/2 length 0.9477
Angle(secor, 3/2) = 65.933
Angle(secor, 3/2) = 65.933
Map to lattice: [&lt;0 0 -1 -2 -3|, &lt;0 1 -1 0 3|]
Map to lattice: [&lt;0 0 -1 -2 -3|, &lt;0 1 -1 0 3|]


Map: [&lt;1 0 0 -5 -13|, &lt;0 1 0 2 6|, &lt;0 0 1 2 3|]
Map: [&lt;1 0 0 -5 -13|, &lt;0 1 0 2 6|, &lt;0 0 1 2 3|]
[[Generator|Generators]]: 2, 3, 5
 
[[edo|EDOs]]: [[10edo|10]], [[12edo|12]], [[29edo|29]], [[31edo|31]], [[41edo|41]], [[72edo|72]], [[247edo|247c]], [[319edo|319bcde]], [[391edo|391bcde]], [[463edo|463bcde]]
[[generator|Generators]]: 2, 3, 5
 
[[EDO|EDOs]]: [[10edo|10]], [[12edo|12]], [[29edo|29]], [[31edo|31]], [[41edo|41]], [[72edo|72]], [[247edo|247c]], [[319edo|319bcde]], [[391edo|391bcde]], [[463edo|463bcde]]
 
Badness: 0.000344
Badness: 0.000344


[[Projection pair]]s: 7 225/32 11 91125/8192
[[Projection_pair|Projection pair]]s: 7 225/32 11 91125/8192


Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
Scales: [[prodigy11|prodigy11]], [[prodigy12|prodigy12]], [[prodigy29|prodigy29]]


==Hobbit bases==  
==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


==13-limit==  
==13-limit==
Commas: 105/104, 196/195, 352/351
Commas: 105/104, 196/195, 352/351


Map: [&lt;1 0 0 -5 -13 -8|, &lt;0 1 0 2 6 3|, &lt;0 0 1 2 3 3|]
Map: [&lt;1 0 0 -5 -13 -8|, &lt;0 1 0 2 6 3|, &lt;0 0 1 2 3 3|]
EDOs: 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef
EDOs: 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef
Badness: 0.000736
Badness: 0.000736


==Prodigious==  
==Prodigious==
Commas: 225/224, 441/440, 364/363
Commas: 225/224, 441/440, 364/363


Map: [&lt;1 0 0 -5 -13 -23|, &lt;0 1 0 2 6 11|, &lt;0 0 1 2 3 4|]
Map: [&lt;1 0 0 -5 -13 -23|, &lt;0 1 0 2 6 11|, &lt;0 0 1 2 3 4|]
EDOs: 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf
EDOs: 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf
Badness: 0.000900
Badness: 0.000900


==Prodigal==  
==Prodigal==
Commas: 225/224, 441/440, 351/350
Commas: 225/224, 441/440, 351/350


Map: [&lt;1 0 0 -5 -13 -4|, &lt;0 1 0 2 6 -1|, &lt;0 0 1 2 3 4|]
Map: [&lt;1 0 0 -5 -13 -4|, &lt;0 1 0 2 6 -1|, &lt;0 0 1 2 3 4|]
EDOs: 31, 72, 103, 175f
EDOs: 31, 72, 103, 175f
Badness: 0.000889</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000889
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Marvel family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;!-- ws:start:WikiTextTocRule:74:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Marvel"&gt;Marvel&lt;/a&gt;&lt;/div&gt;
[[Category:family]]
&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvel-Vital statistics"&gt;Vital statistics&lt;/a&gt;&lt;/div&gt;
[[Category:marvel]]
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvel-Minkowski blocks"&gt;Minkowski blocks&lt;/a&gt;&lt;/div&gt;
[[Category:planar]]
&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvel-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
[[Category:theory]]
&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvel-11-limit (Unimarv)"&gt;11-limit (Unimarv)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Marvel-11-limit (Unimarv)-Hobbit bases"&gt;Hobbit bases&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvel-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hecate"&gt;Hecate&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hecate-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hecate-Enodia"&gt;Enodia&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Marvelcat"&gt;Marvelcat&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Marvell"&gt;Marvell&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Isis"&gt;Isis&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Deecee"&gt;Deecee&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mirage"&gt;Mirage&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Minerva"&gt;Minerva&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Minerva-Athene"&gt;Athene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Minerva-Other eleven limit marvel children"&gt;Other eleven limit marvel children&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Spectacle"&gt;Spectacle&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Spectacle-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Apollo"&gt;Apollo&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Apollo-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Potassium"&gt;Potassium&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Potassium-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Fantastic"&gt;Fantastic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Catakleismoid"&gt;Catakleismoid&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Catakleismoid-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hestia"&gt;Hestia&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hestia-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Malcolm"&gt;Malcolm&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Malcolm-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Tripod"&gt;Tripod&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Prodigy"&gt;Prodigy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Prodigy-Hobbit bases"&gt;Hobbit bases&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Prodigy-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Prodigy-Prodigious"&gt;Prodigious&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Prodigy-Prodigal"&gt;Prodigal&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Marvel"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Marvel&lt;/h1&gt;
The head of the marvel family is marvel, which tempers out &lt;a class="wiki_link" href="/225_224"&gt;225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt; or &lt;a class="wiki_link" href="/marvel%20comma"&gt;marvel comma&lt;/a&gt;. Marvel has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal list basis&lt;/a&gt; of [2, 3, 5]; hence a &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by &lt;a class="wiki_link" href="/197edo"&gt;197edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt;. Another temperament which does little damage to tuning accuracy is &lt;a class="wiki_link" href="/Pythagorean%20family"&gt;compton temperament&lt;/a&gt;, for which &lt;a class="wiki_link" href="/240edo"&gt;240edo&lt;/a&gt; may be used.&lt;br /&gt;
&lt;br /&gt;
See also &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Marvel temperaments&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Marvel-Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Vital statistics&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt; c = 225/224&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
7-limit minimax: 3 and 5 1/4c flat, 7 just&lt;br /&gt;
[|1 0 0 0&amp;gt;, |5/4 1/2 -1/2 1/4&amp;gt;, |5/4 -1/2 1/2 1/4&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.5/3.7&lt;br /&gt;
&lt;br /&gt;
9-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just&lt;br /&gt;
[|1 0 0 0&amp;gt;, |5/6 2/3 -1/3 1/6&amp;gt;, |5/3 -2/3 1/3 1/3&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.9/5.7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: secor length 1.256, 3/2 length 1.369&lt;br /&gt;
Angle(secor, 3/2) = 106.958 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 0 -1 -2|, &amp;lt;0 1 -1 0|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5|, &amp;lt;0 1 0 2|, &amp;lt;0 0 1 2|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;,&lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269c&lt;/a&gt;&lt;br /&gt;
Badness: 0.0000365&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/marvel9"&gt;marvel9&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel10"&gt;marvel10&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel11"&gt;marvel11&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel12"&gt;marvel12&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel19"&gt;marvel19&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel22"&gt;marvel22&lt;/a&gt;, &lt;a class="wiki_link" href="/pump12_1"&gt;pump12_1&lt;/a&gt;, &lt;a class="wiki_link" href="/pump12_2"&gt;pump12_2&lt;/a&gt;, &lt;a class="wiki_link" href="/pump13"&gt;pump13&lt;/a&gt;, &lt;a class="wiki_link" href="/pump14"&gt;pump14&lt;/a&gt;, &lt;a class="wiki_link" href="/pump15"&gt;pump15&lt;/a&gt;, &lt;a class="wiki_link" href="/pump16"&gt;pump16&lt;/a&gt;, &lt;a class="wiki_link" href="/pump17"&gt;pump17&lt;/a&gt;, &lt;a class="wiki_link" href="/pump18"&gt;pump18&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Marvel-Minkowski blocks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;a class="wiki_link" href="/Minkowski%20blocks"&gt;Minkowski blocks&lt;/a&gt;&lt;/h2&gt;
{2, 3, 5} subgroup&lt;br /&gt;
&lt;br /&gt;
8: 16/15, 250/243&lt;br /&gt;
9: 135/128, 128/125&lt;br /&gt;
10: 25/24, 2048/2025&lt;br /&gt;
11: 135/128, 2048/1875&lt;br /&gt;
12: 2048/2025, 128/125&lt;br /&gt;
15: 128/125, 32768/30375&lt;br /&gt;
17: 25/24, 2278125/2097152&lt;br /&gt;
19: 16875/16384, 81/80&lt;br /&gt;
21: 128/125, 273375/262144&lt;br /&gt;
22: 2048/2025, 3125/3072&lt;br /&gt;
29: 16875/16384, 32805/32768&lt;br /&gt;
31: 81/80, 34171875/33554432&lt;br /&gt;
41: 34171875/33554432, 3125/3072&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Marvel-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Music&lt;/h2&gt;
&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=314" rel="nofollow"&gt;Semimarvelous Blue Drawf&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/marvel10_2.mp3" rel="nofollow"&gt;notJoelTaylorsTreeSpirit-Marvel10-2&lt;/a&gt; by &lt;a class="wiki_link" href="/Billy%20Stiltner"&gt;Billy Stiltner&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Marvel-11-limit (Unimarv)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit (Unimarv)&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 385/384&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |4/3 8/9 -1/3 0 -1/9&amp;gt;, |8/3 -2/9 1/3 0 -2/9&amp;gt;,&lt;br /&gt;
|3 4/3 0 0 -2/3&amp;gt;, |8/3 -2/9 -2/3 0 7/9&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.9/5.11/9&lt;br /&gt;
&lt;br /&gt;
Lattice basis: secor length 1.0364 5/4 length 1.0759&lt;br /&gt;
Angle(secor, 5/4) = 104.028 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 -1 0 -2 1|, &amp;lt;0 -1 1 0 -2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12|, &amp;lt;0 1 0 2 -1|, &amp;lt;0 0 1 2 -3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12e&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197e&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269ce&lt;/a&gt;, &lt;a class="wiki_link" href="/341edo"&gt;341ce&lt;/a&gt;&lt;br /&gt;
Badness: 0.000255&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 4096/375&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/marvel22_11"&gt;marvel22_11&lt;/a&gt;, &lt;a class="wiki_link" href="/unimarv19"&gt;unimarv19&lt;/a&gt;, &lt;a class="wiki_link" href="/unimarv22"&gt;unimarv22&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Marvel-11-limit (Unimarv)-Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Hobbit bases&lt;/h3&gt;
{2, 3, 5} subgroup&lt;br /&gt;
&lt;br /&gt;
12: 128/125, 2048/2025&lt;br /&gt;
15: 128/125, 32768/30375&lt;br /&gt;
19: 16875/16384, 81/80&lt;br /&gt;
22: 2048/2025, 2109375/2097152&lt;br /&gt;
31: 2109375/2097152, 81/80&lt;br /&gt;
41: 3125/3072, 34171875/33554432&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Marvel-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 351/350&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.11/9.13/9&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.15/11.15/13&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 -4|, &amp;lt;0 1 0 2 -1 -1|, &amp;lt;0 0 1 2 -3 4|]&lt;br /&gt;
EDOs: 19, 22, 31, 50, 53, 72, 103, &lt;a class="wiki_link" href="/175edo"&gt;175f&lt;/a&gt;, &lt;a class="wiki_link" href="/300edo"&gt;300cef&lt;/a&gt;, &lt;a class="wiki_link" href="/403bcef"&gt;403bcef&lt;/a&gt;&lt;br /&gt;
Badness: 0.000690&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Hecate"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hecate&lt;/h1&gt;
Commas: 225/224, 385/384, 325/324&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.7.13/5&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.7.15/13&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 2|, &amp;lt;0 1 0 2 -1 4|, &amp;lt;0 0 1 2 -3 -2|]&lt;br /&gt;
EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef&lt;br /&gt;
Badness: 0.000721&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 324/25&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Hecate-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;17-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 325/324, 595/594&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 2 18|, &amp;lt;0 1 0 2 -1 4 0|, &amp;lt;0 0 1 2 -3 -2 -6|]&lt;br /&gt;
EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg&lt;br /&gt;
Badness: 0.000869&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Hecate-Enodia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Enodia&lt;/h2&gt;
Commas: 225/224, 385/384, 325/324, 375/374&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 2 18|, &amp;lt;0 1 0 2 -1 4 0|, &amp;lt;0 0 1 2 -3 -2 6|]&lt;br /&gt;
EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg&lt;br /&gt;
Badness: .000917&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Marvelcat"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Marvelcat&lt;/h1&gt;
Commas: 169/168, 225/224, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 -|, &amp;lt;0 2 0 4 -2 3|, &amp;lt;0 0 1 2 -3 1|]&lt;br /&gt;
EDOs: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef&lt;br /&gt;
Badness: 0.0009997&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Marvell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Marvell&lt;/h1&gt;
Commas: 225/224, 385/384, 1573/1568&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.9/5.11/9&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.7.15/13&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 -29|, &amp;lt;0 1 0 2 -1 6|, &amp;lt;0 0 1 2 -3 10|]&lt;br /&gt;
EDOs: 9, 31, &lt;a class="wiki_link" href="/63edo"&gt;63&lt;/a&gt;, 72, &lt;a class="wiki_link" href="/103edo"&gt;103&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238cf&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269ce&lt;/a&gt;, 507bcef, 610bcef&lt;br /&gt;
Badness: 0.000862&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Isis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Isis&lt;/h1&gt;
Commas: 225/224, 385/384, 275/273&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 17|, &amp;lt;0 1 0 2 -1 4|, &amp;lt;0 0 1 2 -3 -3|]&lt;br /&gt;
EDOs: 10, 22, 31, 41, 53, 94&lt;br /&gt;
Badness: 0.000866&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 131072/10125&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Deecee"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Deecee&lt;/h1&gt;
Commas: 225/224, 385/384, 364/363&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.9/5.13/9&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.3.13/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 27|, &amp;lt;0 1 0 2 -1 -3|, &amp;lt;0 0 1 2 -3 -8|]&lt;br /&gt;
EDOs: 9, 22, 41, 63, 72, &lt;a class="wiki_link" href="/185edo"&gt;185cf&lt;/a&gt;, &lt;a class="wiki_link" href="/257edo"&gt;257cf&lt;/a&gt;&lt;br /&gt;
Badness: 0.000920&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Mirage"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Mirage&lt;/h1&gt;
Commas: 225/224, 243/242, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 3 2 0|, &amp;lt;0 6 -7 -2 15 0|, &amp;lt;0 0 0 0 0 1|]&lt;br /&gt;
EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef&lt;br /&gt;
Badness: 0.000738&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Minerva"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Minerva&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 99/98, 176/175&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Semicomma%20family"&gt;orwell&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.7/5.11/9&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 16/15 length 0.8997 5/4 length 1.0457&lt;br /&gt;
Angle(16/15, 5/4) = 98.6044 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 -1 0 -2 -2|, &amp;lt;0 -1 1 0 2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -9|, &amp;lt;0 1 0 2 2|, &amp;lt;0 0 1 2 4|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/21edo"&gt;21&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/43edo"&gt;43&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/74edo"&gt;74&lt;/a&gt;, &lt;a class="wiki_link" href="/75edo"&gt;75&lt;/a&gt;, &lt;a class="wiki_link" href="/96edo"&gt;96&lt;/a&gt;, &lt;a class="wiki_link" href="/127edo"&gt;127&lt;/a&gt;&lt;br /&gt;
Badness: 0.000381&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 5625/512&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/minerva12"&gt;minerva12&lt;/a&gt;, &lt;a class="wiki_link" href="/minerva22x"&gt;minerva22x&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Minerva-Athene"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Athene&lt;/h2&gt;
Commas: 99/98, 176/175, 275/273&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.11/9.13/7&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.11/9.13/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -9 -4|, &amp;lt;0 1 0 2 2 -1|, &amp;lt;0 0 1 2 4 4|]&lt;br /&gt;
EDOs: 22, 31, 53, 84e, 118d, 149df, 171de, 202def&lt;br /&gt;
Badness: 0.000818&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 5625/512 13 625/48&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Minerva-Other eleven limit marvel children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Other eleven limit marvel children&lt;/h2&gt;
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Spectacle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Spectacle&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 243/242&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;marvo&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |1/5 0 0 0 2/5&amp;gt;, |2/5 -2 1 0 4/5&amp;gt;, |-19/5 -4 2 0 12/5&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.9/5.11&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 -3 2|, &amp;lt;0 2 0 4 5|, &amp;lt;0 0 1 2 0|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 11/9, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/240edo"&gt;240&lt;/a&gt;, &lt;a class="wiki_link" href="/259edo"&gt;259b&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269ce&lt;/a&gt;, &lt;a class="wiki_link" href="/310edo"&gt;310c&lt;/a&gt;, &lt;a class="wiki_link" href="/331edo"&gt;331bc&lt;/a&gt;, &lt;a class="wiki_link" href="/353edo"&gt;353c&lt;/a&gt;, &lt;a class="wiki_link" href="/497edo"&gt;497bc&lt;/a&gt;, &lt;a class="wiki_link" href="/569edo"&gt;569bc&lt;/a&gt;&lt;br /&gt;
Badness: 0.000499&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/spectacle31"&gt;spectacle31&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Spectacle-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;13-limit&lt;/h2&gt;
Commas: 225/224, 243/242, 351/350&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 -3 2 -5|, &amp;lt;0 2 0 4 5 -2|, &amp;lt;0 0 1 2 0 4|]&lt;br /&gt;
EDOs: 31, 72, 103, 175f, 209, 240&lt;br /&gt;
Badness: 0.001009&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Apollo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Apollo&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 100/99, 225/224&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
Eigenmonzo subgroup: 2.7/5.11/9&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 2|, &amp;lt;0 1 0 2 -2|, &amp;lt;0 0 1 2 2|]&lt;br /&gt;
EDOs: 12, 19, 22, 41, &lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt;, &lt;a class="wiki_link" href="/157edo"&gt;157ce&lt;/a&gt;, &lt;a class="wiki_link" href="/198edo"&gt;198ce&lt;/a&gt;, &lt;a class="wiki_link" href="/220edo"&gt;220ce&lt;/a&gt;, &lt;a class="wiki_link" href="/261edo"&gt;261ce&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 100/9&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Apollo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 100/99, 225/224, 245/243&lt;br /&gt;
&lt;br /&gt;
Eigenmonzo subgroup: 2.11/9.13/9&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 2 7|, &amp;lt;0 1 0 2 -2 -5|, &amp;lt;0 0 1 2 2 2|]&lt;br /&gt;
EDOs: 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 100/9 13 3200/243&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Potassium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Potassium&lt;/h1&gt;
Commas: 45/44, 56/55&lt;br /&gt;
&lt;br /&gt;
Eigenmonzo subgroup: 2.9/7.11&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -2|, &amp;lt;0 1 0 2 2|, &amp;lt;0 0 1 2 1|]&lt;br /&gt;
EDOs: 9, 10, 12, 19, 31e, 50e&lt;br /&gt;
Badness: 0.000464&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 45/4&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Potassium-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h2&gt;
Commas: 45/44, 56/55, 78/77&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.9/7.13/9&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.9/7.13/9&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -2 -8|, &amp;lt;0 1 0 2 2 3|, &amp;lt;0 0 1 2 1 3|]&lt;br /&gt;
EDOs: 9, 10, 19, 31e, 50e&lt;br /&gt;
Badness: 0.000733&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 45/4 13 3375/256&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Fantastic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Fantastic&lt;/h1&gt;
Commas: 225/224, 4375/4356&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 -10 -7|, &amp;lt;0 1 0 2 0|, &amp;lt;0 0 1 2 3|]&lt;br /&gt;
EDOs: 12, 22, 50, 72, 166, 238c, 310c&lt;br /&gt;
Badness: 0.000743&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Catakleismoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Catakleismoid&lt;/h1&gt;
Commas: 225/224, 4375/4374&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 -3 0|, &amp;lt;0 6 5 22 0|, &amp;lt;0 0 0 0 1|]&lt;br /&gt;
EDOs: 19, 53, 72, 197e, 269ce&lt;br /&gt;
Badness: 0.001275&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Catakleismoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 325/324&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 1 -3 0 0|, &amp;lt;0 6 5 22 0 14|, &amp;lt;0 0 0 0 1 0|]&lt;br /&gt;
EDOs: 19, 53, 72, 125f, 197ef, 269cef&lt;br /&gt;
Badness: 0.000916&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Hestia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Hestia&lt;/h1&gt;
Commas: 225/224, 125000/124509&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 9|, &amp;lt;0 2 0 4 -7|, &amp;lt;0 0 1 2 0|]&lt;br /&gt;
EDOs: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce&lt;br /&gt;
Badness: 0.00154&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Hestia-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 1001/1000&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 9 -1|, &amp;lt;0 2 0 4 -7 3|, &amp;lt;0 0 1 2 0 1|]&lt;br /&gt;
EDOs: 19, 29, 43, 53, 72, 125f, 197ef, 269cef&lt;br /&gt;
Badness: 0.001062&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Malcolm"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Malcolm&lt;/h1&gt;
Commas: 225/224, 2200/2187&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -3|, &amp;lt;0 1 0 2 7|, &amp;lt;0 0 1 2 -2|]&lt;br /&gt;
EDOs: 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce&lt;br /&gt;
Badness: 0.001250&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Malcolm-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;13-limit&lt;/h2&gt;
commas: 225/224, 275/273, 325/324&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -3 2|, &amp;lt;0 1 0 2 7 4|, &amp;lt;0 0 1 2 -2 -2|]&lt;br /&gt;
EDOs: 41, 53, 94, 429cdef, 523cdef&lt;br /&gt;
Badness: 0.001075&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="Tripod"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;Tripod&lt;/h1&gt;
Commas: 105/104, 144/143, 196/195&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.9/7.13/11&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.5/3.13/11&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 -8|, &amp;lt;0 1 0 2 -1 3|, &amp;lt;0 0 1 2 -3 3|]&lt;br /&gt;
EDOs: 9, 10, 19, 31, 41, 72f, &lt;a class="wiki_link" href="/81edo"&gt;81&lt;/a&gt;, &lt;a class="wiki_link" href="/91edo"&gt;91&lt;/a&gt;, &lt;a class="wiki_link" href="/122edo"&gt;122f&lt;/a&gt;, &lt;a class="wiki_link" href="/163edo"&gt;163df&lt;/a&gt;&lt;br /&gt;
Badness: 0.000745&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 3375/256&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Prodigy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Prodigy&lt;/h1&gt;
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 &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;miracle temperament&lt;/a&gt;. 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.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 441/440&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;miracle&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |13/12 1/2 -1/4 0 1/12&amp;gt;,&lt;br /&gt;
|13/6 -1 1/2 0 1/6&amp;gt;,&lt;br /&gt;
|3/2 -1 1/2 0 1/2&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.9/5.11&lt;br /&gt;
&lt;br /&gt;
Lattice basis: secor length 0.9111, 3/2 length 0.9477&lt;br /&gt;
Angle(secor, 3/2) = 65.933&lt;br /&gt;
Map to lattice: [&amp;lt;0 0 -1 -2 -3|, &amp;lt;0 1 -1 0 3|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -13|, &amp;lt;0 1 0 2 6|, &amp;lt;0 0 1 2 3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/247edo"&gt;247c&lt;/a&gt;, &lt;a class="wiki_link" href="/319edo"&gt;319bcde&lt;/a&gt;, &lt;a class="wiki_link" href="/391edo"&gt;391bcde&lt;/a&gt;, &lt;a class="wiki_link" href="/463edo"&gt;463bcde&lt;/a&gt;&lt;br /&gt;
Badness: 0.000344&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 91125/8192&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/prodigy11"&gt;prodigy11&lt;/a&gt;, &lt;a class="wiki_link" href="/prodigy12"&gt;prodigy12&lt;/a&gt;, &lt;a class="wiki_link" href="/prodigy29"&gt;prodigy29&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Prodigy-Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;Hobbit bases&lt;/h2&gt;
{2, 3, 5} subgroup&lt;br /&gt;
&lt;br /&gt;
31: 81/80, 34171875/33554432&lt;br /&gt;
41: 34171875/33554432, 32805/32768&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Prodigy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 196/195, 352/351&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -13 -8|, &amp;lt;0 1 0 2 6 3|, &amp;lt;0 0 1 2 3 3|]&lt;br /&gt;
EDOs: 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef&lt;br /&gt;
Badness: 0.000736&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Prodigy-Prodigious"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Prodigious&lt;/h2&gt;
Commas: 225/224, 441/440, 364/363&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -13 -23|, &amp;lt;0 1 0 2 6 11|, &amp;lt;0 0 1 2 3 4|]&lt;br /&gt;
EDOs: 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf&lt;br /&gt;
Badness: 0.000900&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Prodigy-Prodigal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;Prodigal&lt;/h2&gt;
Commas: 225/224, 441/440, 351/350&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 -13 -4|, &amp;lt;0 1 0 2 6 -1|, &amp;lt;0 0 1 2 3 4|]&lt;br /&gt;
EDOs: 31, 72, 103, 175f&lt;br /&gt;
Badness: 0.000889&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

de:Marvel Deutsch

Marvel

The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by 197edo.

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 also Marvel temperaments.

Vital statistics

Comma c = 225/224

Related linear temperament: catakleismic temperament

7-limit minimax: 3 and 5 1/4c flat, 7 just

[|1 0 0 0>, |5/4 1/2 -1/2 1/4>, |5/4 -1/2 1/2 1/4>, |0 0 0 1>]

Eigenmonzo subgroup: 2.5/3.7

9-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just

[|1 0 0 0>, |5/6 2/3 -1/3 1/6>, |5/3 -2/3 1/3 1/3>, |0 0 0 1>]

Eigenmonzo subgroup: 2.9/5.7

Lattice basis: secor length 1.256, 3/2 length 1.369

Angle(secor, 3/2) = 106.958 degrees

Map to lattice: [<0 0 -1 -2|, <0 1 -1 0|]

Map: [<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|]

Generators: 2, 3, 5

EDOs: 10, 12, 19, 22, 31, 41,72, 197, 269c

Badness: 0.0000365

Projection pairs: 7 225/32

Spectrum: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9

Scales: marvel9, marvel10, marvel11, marvel12, marvel19, marvel22, pump12_1, pump12_2, pump13, pump14, pump15, pump16, pump17, pump18

Minkowski blocks

{2, 3, 5} subgroup

8: 16/15, 250/243

9: 135/128, 128/125

10: 25/24, 2048/2025

11: 135/128, 2048/1875

12: 2048/2025, 128/125

15: 128/125, 32768/30375

17: 25/24, 2278125/2097152

19: 16875/16384, 81/80

21: 128/125, 273375/262144

22: 2048/2025, 3125/3072

29: 16875/16384, 32805/32768

31: 81/80, 34171875/33554432

41: 34171875/33554432, 3125/3072

Music

Semimarvelous Blue Drawf by Chris Vaisvil

notJoelTaylorsTreeSpirit-Marvel10-2 by Billy Stiltner

11-limit (Unimarv)

Commas: 225/224, 385/384

Related linear temperament: catakleismic temperament

Minimax tuning:

[|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>, |3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>]

Eigenmonzo subgroup: 2.9/5.11/9

Lattice basis: secor length 1.0364 5/4 length 1.0759

Angle(secor, 5/4) = 104.028 degrees

Map to lattice: [<0 -1 0 -2 1|, <0 -1 1 0 -2|]

Map: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]

Generators: 2, 3, 5

Edos: 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 269ce, 341ce

Badness: 0.000255

Projection pairs: 7 225/32 11 4096/375

Spectrum: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11

Scales: marvel22_11, unimarv19, unimarv22

Hobbit bases

{2, 3, 5} subgroup

12: 128/125, 2048/2025

15: 128/125, 32768/30375

19: 16875/16384, 81/80

22: 2048/2025, 2109375/2097152

31: 2109375/2097152, 81/80

41: 3125/3072, 34171875/33554432

13-limit

Commas: 225/224, 385/384, 351/350

13-limit eigenmonzo subgroup: 2.11/9.13/9

15-limit eigenmonzo subgroup: 2.15/11.15/13

Map: [<1 0 0 -5 12 -4|, <0 1 0 2 -1 -1|, <0 0 1 2 -3 4|]

EDOs: 19, 22, 31, 50, 53, 72, 103, 175f, 300cef, 403bcef

Badness: 0.000690

Spectrum: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11

Hecate

Commas: 225/224, 385/384, 325/324

13-limit eigenmonzo subgroup: 2.7.13/5

15-limit eigenmonzo subgroup: 2.7.15/13

Map: [<1 0 0 -5 12 2|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -2|]

EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef

Badness: 0.000721

Projection pairs: 7 225/32 11 4096/375 13 324/25

Spectrum: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11

17-limit

Commas: 225/224, 385/384, 325/324, 595/594

Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 -6|]

EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg

Badness: 0.000869

Enodia

Commas: 225/224, 385/384, 325/324, 375/374

Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 6|]

EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg

Badness: .000917

Marvelcat

Commas: 169/168, 225/224, 385/384

Map: [<1 0 0 -5 12 -|, <0 2 0 4 -2 3|, <0 0 1 2 -3 1|]

EDOs: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef

Badness: 0.0009997

Marvell

Commas: 225/224, 385/384, 1573/1568

13-limit eigenmonzo subgroup: 2.9/5.11/9

15-limit eigenmonzo subgroup: 2.7.15/13

Map: [<1 0 0 -5 12 -29|, <0 1 0 2 -1 6|, <0 0 1 2 -3 10|]

EDOs: 9, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcef, 610bcef

Badness: 0.000862

Isis

Commas: 225/224, 385/384, 275/273

Map: [<1 0 0 -5 12 17|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -3|]

EDOs: 10, 22, 31, 41, 53, 94

Badness: 0.000866

Projection pairs: 7 225/32 11 4096/375 13 131072/10125

Deecee

Commas: 225/224, 385/384, 364/363

13-limit eigenmonzo subgroup: 2.9/5.13/9

15-limit eigenmonzo subgroup: 2.3.13/5

Map: [<1 0 0 -5 12 27|, <0 1 0 2 -1 -3|, <0 0 1 2 -3 -8|]

EDOs: 9, 22, 41, 63, 72, 185cf, 257cf

Badness: 0.000920

Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875

Mirage

Commas: 225/224, 243/242, 385/384

Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 0|, <0 0 0 0 0 1|]

EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef

Badness: 0.000738

Minerva

Commas: 99/98, 176/175

Related linear temperament: orwell

Eigenmonzo subgroup: 2.7/5.11/9

Lattice basis: 16/15 length 0.8997 5/4 length 1.0457

Angle(16/15, 5/4) = 98.6044 degrees

Map to lattice: [<0 -1 0 -2 -2|, <0 -1 1 0 2|]

Map: [<1 0 0 -5 -9|, <0 1 0 2 2|, <0 0 1 2 4|]

Generators: 2, 3, 5

EDOs: 9, 12, 21, 22, 31, 43, 53, 74, 75, 96, 127

Badness: 0.000381

Projection pairs: 7 225/32 11 5625/512

Scales: minerva12, minerva22x

Athene

Commas: 99/98, 176/175, 275/273

13-limit eigenmonzo subgroup: 2.11/9.13/7

15-limit eigenmonzo subgroup: 2.11/9.13/7

Map: [<1 0 0 -5 -9 -4|, <0 1 0 2 2 -1|, <0 0 1 2 4 4|]

EDOs: 22, 31, 53, 84e, 118d, 149df, 171de, 202def

Badness: 0.000818

Projection pairs: 7 225/32 11 5625/512 13 625/48

Other eleven limit marvel children

The second comma of the normal comma list defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.

Spectacle

Commas: 225/224, 243/242

Related linear temperament: marvo

Minimax tuning:

[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |2/5 -2 1 0 4/5>, |-19/5 -4 2 0 12/5>, |0 0 0 0 1>]

Eigenmonzo subgroup: 2.9/5.11

Map: [<1 1 0 -3 2|, <0 2 0 4 5|, <0 0 1 2 0|]

Generators: 2, 11/9, 5

EDOs: 10, 31, 41, 72, 240, 259b, 269ce, 310c, 331bc, 353c, 497bc, 569bc

Badness: 0.000499

Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9

Scales: spectacle31

13-limit

Commas: 225/224, 243/242, 351/350

Map: [<1 1 0 -3 2 -5|, <0 2 0 4 5 -2|, <0 0 1 2 0 4|]

EDOs: 31, 72, 103, 175f, 209, 240

Badness: 0.001009

Apollo

Commas: 100/99, 225/224

Related linear temperament: Magic

Eigenmonzo subgroup: 2.7/5.11/9

Map: [<1 0 0 -5 2|, <0 1 0 2 -2|, <0 0 1 2 2|]

EDOs: 12, 19, 22, 41, 104edo, 157ce, 198ce, 220ce, 261ce

Projection pairs: 7 225/32 11 100/9

13-limit

Commas: 100/99, 225/224, 245/243

Eigenmonzo subgroup: 2.11/9.13/9

Map: [<1 0 0 -5 2 7|, <0 1 0 2 -2 -5|, <0 0 1 2 2 2|]

EDOs: 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef

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

Potassium

Commas: 45/44, 56/55

Eigenmonzo subgroup: 2.9/7.11

Map: [<1 0 0 -5 -2|, <0 1 0 2 2|, <0 0 1 2 1|]

EDOs: 9, 10, 12, 19, 31e, 50e

Badness: 0.000464

Projection pairs: 7 225/32 11 45/4

13-limit

Commas: 45/44, 56/55, 78/77

13-limit eigenmonzo subgroup: 2.9/7.13/9

15-limit eigenmonzo subgroup: 2.9/7.13/9

Map: [<1 0 0 -5 -2 -8|, <0 1 0 2 2 3|, <0 0 1 2 1 3|]

EDOs: 9, 10, 19, 31e, 50e

Badness: 0.000733

Projection pairs: 7 225/32 11 45/4 13 3375/256

Fantastic

Commas: 225/224, 4375/4356

Map: [<2 0 0 -10 -7|, <0 1 0 2 0|, <0 0 1 2 3|]

EDOs: 12, 22, 50, 72, 166, 238c, 310c

Badness: 0.000743

Catakleismoid

Commas: 225/224, 4375/4374

Map: [<1 0 1 -3 0|, <0 6 5 22 0|, <0 0 0 0 1|]

EDOs: 19, 53, 72, 197e, 269ce

Badness: 0.001275

13-limit

Commas: 169/168, 225/224, 325/324

Map: [<1 0 1 -3 0 0|, <0 6 5 22 0 14|, <0 0 0 0 1 0|]

EDOs: 19, 53, 72, 125f, 197ef, 269cef

Badness: 0.000916

Hestia

Commas: 225/224, 125000/124509

Map: [<1 0 0 -5 9|, <0 2 0 4 -7|, <0 0 1 2 0|]

EDOs: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce

Badness: 0.00154

13-limit

Commas: 169/168, 225/224, 1001/1000

Map: [<1 0 0 -5 9 -1|, <0 2 0 4 -7 3|, <0 0 1 2 0 1|]

EDOs: 19, 29, 43, 53, 72, 125f, 197ef, 269cef

Badness: 0.001062

Malcolm

Commas: 225/224, 2200/2187

Map: [<1 0 0 -5 -3|, <0 1 0 2 7|, <0 0 1 2 -2|]

EDOs: 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce

Badness: 0.001250

13-limit

commas: 225/224, 275/273, 325/324

Map: [<1 0 0 -5 -3 2|, <0 1 0 2 7 4|, <0 0 1 2 -2 -2|]

EDOs: 41, 53, 94, 429cdef, 523cdef

Badness: 0.001075

Tripod

Commas: 105/104, 144/143, 196/195

13-limit eigenmonzo subgroup: 2.9/7.13/11

15-limit eigenmonzo subgroup: 2.5/3.13/11

Map: [<1 0 0 -5 12 -8|, <0 1 0 2 -1 3|, <0 0 1 2 -3 3|]

EDOs: 9, 10, 19, 31, 41, 72f, 81, 91, 122f, 163df

Badness: 0.000745

Projection pairs: 7 225/32 11 4096/375 13 3375/256

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.

Commas: 225/224, 441/440

Related linear temperament: miracle

Minimax tuning:

[|1 0 0 0 0>, |13/12 1/2 -1/4 0 1/12>, |13/6 -1 1/2 0 1/6>, |3/2 -1 1/2 0 1/2>, |0 0 0 0 1>]

Eigenmonzo subgroup: 2.9/5.11

Lattice basis: secor length 0.9111, 3/2 length 0.9477

Angle(secor, 3/2) = 65.933

Map to lattice: [<0 0 -1 -2 -3|, <0 1 -1 0 3|]

Map: [<1 0 0 -5 -13|, <0 1 0 2 6|, <0 0 1 2 3|]

Generators: 2, 3, 5

EDOs: 10, 12, 29, 31, 41, 72, 247c, 319bcde, 391bcde, 463bcde

Badness: 0.000344

Projection pairs: 7 225/32 11 91125/8192

Scales: prodigy11, prodigy12, prodigy29

Hobbit bases

{2, 3, 5} subgroup

31: 81/80, 34171875/33554432

41: 34171875/33554432, 32805/32768

13-limit

Commas: 105/104, 196/195, 352/351

Map: [<1 0 0 -5 -13 -8|, <0 1 0 2 6 3|, <0 0 1 2 3 3|]

EDOs: 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef

Badness: 0.000736

Prodigious

Commas: 225/224, 441/440, 364/363

Map: [<1 0 0 -5 -13 -23|, <0 1 0 2 6 11|, <0 0 1 2 3 4|]

EDOs: 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf

Badness: 0.000900

Prodigal

Commas: 225/224, 441/440, 351/350

Map: [<1 0 0 -5 -13 -4|, <0 1 0 2 6 -1|, <0 0 1 2 3 4|]

EDOs: 31, 72, 103, 175f

Badness: 0.000889

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