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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;
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