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* [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]]


= 11-limit (Unimarv) =
= 11-limit (unimarv) =
[[Commas]]: 225/224, 385/384
[[Comma list]]: 225/224, 385/384


Related linear temperament: [[catakleismic temperament]]
[[Associated temperament]]: [[catakleismic]]


[[Minimax tuning]]:
Lattice basis:  
: secor length = 1.0364, 5/4 length = 1.0759
: Angle (secor, 5/4) = 104.028 degrees


[|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>,
Map to lattice: [{{val| 0 -1 0 -2 1 }}, {{val| 0 -1 1 0 -2 }}]
|3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>]


[[Eigenmonzo subgroup]]: 2.9/5.11/9
Mapping: [{{val| 1 0 0 -5 12 }}, {{val| 0 1 0 2 -1 }}, {{val| 0 0 1 2 -3 }}]


Lattice basis: secor length 1.0364 5/4 length 1.0759
Mapping generators: ~2, ~3, ~5


Angle(secor, 5/4) = 104.028 degrees
[[Minimax tuning]]:
 
* 11-odd-limit
Map to lattice: [<0 -1 0 -2 1|, <0 -1 1 0 -2|]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 8/9 -1/3 0 -1/9 }}, {{monzo| 8/3 -2/9 1/3 0 -2/9 }}, {{monzo| 3 4/3 0 0 -2/3 }}, {{monzo| 8/3 -2/9 -2/3 0 7/9 }}]
: [[Eigenmonzo subgroup]]: 2.9/5.11/9


Map: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]
{{Val list|legend=1| 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 269ce, 341ce }}
 
[[Generator]]s: 2, 3, 5
 
{{EDOs|legend=1| 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 269ce, 341ce }}


Badness: 0.000255
Badness: 0.000255
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[[Projection pair]]s: 7 225/32 11 4096/375
[[Projection pair]]s: 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
[[Complexity 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]]
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]
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== 13-limit ==
== 13-limit ==
Commas: 225/224, 385/384, 351/350
Comma list: 225/224, 385/384, 351/350


13-limit eigenmonzo subgroup: 2.11/9.13/9
Mapping: [{{val| 1 0 0 -5 12 -4 }}, {{val| 0 1 0 2 -1 -1 }}, {{val| 0 0 1 2 -3 4 }}]


15-limit eigenmonzo subgroup: 2.15/11.15/13
Minimax tuning:
* 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9
* 15-odd-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|]
{{Val list|legend=1| 19, 22, 31, 50, 53, 72, 103, 175f, 300cef, 403bcef }}
 
{{EDOs|legend=1| 19, 22, 31, 50, 53, 72, 103, 175f, 300cef, 403bcef }}


Badness: 0.000690
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
[[Complexity 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
Comma list: 225/224, 385/384, 325/324
 
13-limit eigenmonzo subgroup: 2.7.13/5


15-limit eigenmonzo subgroup: 2.7.15/13
Mapping: [{{val| 1 0 0 -5 12 2 }}, {{val| 0 1 0 2 -1 4 }}, {{val| 0 0 1 2 -3 -2 }}]


Map: [<1 0 0 -5 12 2|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -2|]
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup: 2.7.13/5
* 15-odd-limit eigenmonzo subgroup: 2.7.15/13


{{EDOs|legend=1| 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef }}
{{Val list|legend=1| 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef }}


Badness: 0.000721
Badness: 0.000721
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Projection pairs: 7 225/32 11 4096/375 13 324/25
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
[[Complexity 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 ===
=== 17-limit ===
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