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Marvel family: Difference between revisions

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{{interwiki
{{interwiki
| en = Marvel family
| de = Marvel
| de = Marvel
| en = Marvel family
| es =  
| es =  
| ja =  
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}}
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{{Technical data page}}
{{Technical data page}}
The '''marvel family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] tempers out the [[7-limit]] marvel comma, [[225/224]] = {{monzo| -5 2 2 -1 }}, which is also known as ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common [[equal temperament|equal]] and [[rank-2 temperament]]s.
The '''marvel family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[7-limit]] [[marvel comma]] ([[ratio]]: [[225/224]], {{monzo|legend=1| -5 2 2 -1 }}), also known as ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common [[equal temperament|equal]] and [[rank-2 temperament]]s.


The marvel comma can also be viewed as a comma of the 2.9.25.7 [[subgroup]]. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] (when using the 34d val) which temper out the marvel comma.
The marvel comma can also be viewed as a comma of the 2.9.25.7 [[subgroup]]. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] (when using the 34d val) which temper out the marvel comma.
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{{Main| Marvel }}
{{Main| Marvel }}


The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[normal lists|normal generator list]] 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]].
The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[normal lists|normal generator list]] 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]], with which it shares the [[optimal patent val]]. Another temperament which does little damage to tuning accuracy is [[compton]], for which [[240edo]] may be used. See [[marvel temperaments]] for some other rank-2 temperaments.  
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[catakleismic]], with which it shares the [[optimal patent val]]. Another temperament which does little damage to tuning accuracy is [[compton]], for which [[240edo]] may be used. See [[marvel temperaments]] for some other rank-2 temperaments.  
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{{Mapping|legend=1| 1 0 0 -5 | 0 1 0 2 | 0 0 1 2 }}
{{Mapping|legend=1| 1 0 0 -5 | 0 1 0 2 | 0 0 1 2 }}
: mapping generators: ~2, ~3, ~5
: mapping generators: ~2, ~3, ~5


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Lattice basis:  
Lattice basis:  
: secor length = 1.256, 3/2 length = 1.369
: ~15/14 length = 1.256, ~3/2 length = 1.369
: Angle (secor, 3/2) = 106.958 degrees
: Angle (~15/14, ~3/2) = 106.958 degrees


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 700.974, ~5/4 = 384.208
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.974{{c}}, ~5/4 = 384.208{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.622, ~5/4 = 383.854
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.622{{c}}, ~5/4 = 383.854{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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{{Optimal ET sequence|legend=1| 9, 10, 12, 19, 31, 41, 53, 72, 197, 269c }}
{{Optimal ET sequence|legend=1| 9, 10, 12, 19, 31, 41, 53, 72, 197, 269c }}


[[Badness]]: 0.0365 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.0365 × 10<sup>-3</sup>


[[Projection pair]]s: 7 225/32
[[Projection pair]]s: <code>7 225/32</code>


[[Complexity spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9
[[Complexity spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9
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Lattice basis:  
Lattice basis:  
: secor length = 1.0364, 5/4 length = 1.0759
: ~15/14 length = 1.0364, ~5/4 length = 1.0759
: Angle (secor, 5/4) = 104.028 degrees
: angle (~15/14, ~5/4) = 104.028 degrees


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.373, ~5/4 = 383.146
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.373{{c}}, ~5/4 = 383.146{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.605, ~5/4 = 383.454
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.605{{c}}, ~5/4 = 383.454{{c}}


[[Minimax tuning]]:
[[Minimax tuning]]:
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{{Optimal ET sequence|legend=1| 9, 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 238c, 269ce, 341ce }}
{{Optimal ET sequence|legend=1| 9, 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 238c, 269ce, 341ce }}


[[Badness]]: 0.255 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.255 × 10<sup>-3</sup>


[[Projection pair]]s: 7 225/32 11 4096/375
[[Projection pair]]s: <code>7 225/32 11 4096/375</code>


[[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
[[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
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 700.182, ~5/4 = 384.400
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 700.182{{c}}, ~5/4 = 384.400{{c}}
* CWE: ~2 = 1\1, ~3/2 = 699.811, ~5/4 = 384.118
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 699.811{{c}}, ~5/4 = 384.118{{c}}


Minimax tuning:  
Minimax tuning:  
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* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.15/11.15/13
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.15/11.15/13


Optimal ET sequence: {{Optimal ET sequence| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}
{{Optimal ET sequence|legend=0| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}


Badness: 0.690 × 10<sup>-3</sup>
Badness (Smith): 0.690 × 10<sup>-3</sup>


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
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
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.563, ~5/4 = 383.015
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.563{{c}}, ~5/4 = 383.015{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.100, ~5/4 = 383.132
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.100{{c}}, ~5/4 = 383.132{{c}}


Minimax tuning:  
Minimax tuning:  
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* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/13
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/13


Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}
{{Optimal ET sequence|legend=0| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}


Badness: 0.721 × 10<sup>-3</sup>
Badness (Smith): 0.721 × 10<sup>-3</sup>


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


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
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
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Comma list: 225/224, 325/324, 385/384, 400/399
Comma list: 225/224, 325/324, 385/384, 400/399


Sval mapping: {{mapping| 1 0 0 -5 12 2 9 | 0 1 0 2 -1 4 -3 | 0 0 1 2 -3 -2 0 }}
Subgroup-val mapping: {{mapping| 1 0 0 -5 12 2 9 | 0 1 0 2 -1 4 -3 | 0 0 1 2 -3 -2 0 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.424, ~5/4 = 383.029
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.424{{c}}, ~5/4 = 383.029{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.200, ~5/4 = 383.114
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.200{{c}}, ~5/4 = 383.114{{c}}


Optimal ET sequence: {{Optimal ET sequence| 41, 53, 72, 94, 113, 166 }}
Optimal ET sequence: {{Optimal ET sequence| 41, 53, 72, 94, 113, 166 }}


Badness: 0.773 × 10<sup>-3</sup>
Badness (Smith): 0.773 × 10<sup>-3</sup>


==== Apotropaia ====
==== Apotropaia ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.586, ~5/4 = 382.733
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.586{{c}}, ~5/4 = 382.733{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.088, ~5/4 = 382.971
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.088{{c}}, ~5/4 = 382.971{{c}}


Optimal ET sequence: {{Optimal ET sequence| 41, 53g, 72, 166g, 238cfg }}
{{Optimal ET sequence|legend=0| 41, 53g, 72, 166g, 238cfg }}


Badness: 0.869 × 10<sup>-3</sup>
Badness (Smith): 0.869 × 10<sup>-3</sup>


===== 19-limit =====
===== 19-limit =====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.443, ~5/4 = 382.739
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.443{{c}}, ~5/4 = 382.739{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.201, ~5/4 = 382.940
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.201{{c}}, ~5/4 = 382.940{{c}}


Optimal ET sequence: {{Optimal ET sequence| 41, 53g, 72, 94, 113, 166g }}
{{Optimal ET sequence|legend=0| 41, 53g, 72, 94, 113, 166g }}


Badness: 0.978 × 10<sup>-3</sup>
Badness (Smith): 0.978 × 10<sup>-3</sup>


==== Enodia ====
==== Enodia ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.627, ~5/4 = 383.346
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.627{{c}}, ~5/4 = 383.346{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.095, ~5/4 = 383.314
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.095{{c}}, ~5/4 = 383.314{{c}}


Optimal ET sequence: {{Optimal ET sequence| 41g, 53, 72, 166g, 238cfg }}
{{Optimal ET sequence|legend=0| 41g, 53, 72, 166g, 238cfg }}


Badness: 0.917 × 10<sup>-3</sup>
Badness (Smith): 0.917 × 10<sup>-3</sup>


===== 19-limit =====
===== 19-limit =====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.479, ~5/4 = 383.379
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.479{{c}}, ~5/4 = 383.379{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.211, ~5/4 = 383.305
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.211{{c}}, ~5/4 = 383.305{{c}}


Optimal ET sequence: {{Optimal ET sequence| 41g, 53, 72, 94, 125f, 166g }}
{{Optimal ET sequence|legend=0| 41g, 53, 72, 94, 125f, 166g }}


Badness: 1.03 × 10<sup>-3</sup>
Badness (Smith): 1.03 × 10<sup>-3</sup>


=== Marvell ===
=== Marvell ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.385, ~5/4 = 383.208
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.385{{c}}, ~5/4 = 383.208{{c}}
* CWE: ~2 = 1\1, ~3/2 = 700.611, ~5/4 = 383.493
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 700.611{{c}}, ~5/4 = 383.493{{c}}


Minimax tuning:  
Minimax tuning:  
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* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/13
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/13


Optimal ET sequence: {{Optimal ET sequence| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}
{{Optimal ET sequence|legend=0| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}


Badness: 0.862 × 10<sup>-3</sup>
Badness (Smith): 0.862 × 10<sup>-3</sup>


=== Isis ===
=== Isis ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.997, ~5/4 = 383.134
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.997{{c}}, ~5/4 = 383.134{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.928, ~5/4 = 383.228
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.928{{c}}, ~5/4 = 383.228{{c}}


Optimal ET sequence: {{Optimal ET sequence| 10, 19f, 22, 31, 41, 53, 94 }}
{{Optimal ET sequence|legend=0| 10, 19f, 22, 31, 41, 53, 94 }}


Badness: 0.866 × 10<sup>-3</sup>
Badness (Smith): 0.866 × 10<sup>-3</sup>


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


=== Deecee ===
=== Deecee ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.702, ~5/4 = 382.074
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.702{{c}}, ~5/4 = 382.074{{c}}
* CWE: ~2 = 1\1, ~3/2 = 700.718, ~5/4 = 382.661
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 700.718{{c}}, ~5/4 = 382.661{{c}}


Minimax tuning:  
Minimax tuning:  
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* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.3.13/5
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.3.13/5


Optimal ET sequence: {{Optimal ET sequence| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}
{{Optimal ET sequence|legend=0| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}


Badness: 0.920 × 10<sup>-3</sup>
Badness (Smith): 0.920 × 10<sup>-3</sup>


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


=== Tripod ===
=== Tripod ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 700.028, ~5/4 = 382.694
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 700.028{{c}}, ~5/4 = 382.694{{c}}
* CWE: ~2 = 1\1, ~3/2 = 699.404, ~5/4 = 382.917
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 699.404{{c}}, ~5/4 = 382.917{{c}}


Minimax tuning:  
Minimax tuning:  
Line 316: Line 315:
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.13/11
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.13/11


Optimal ET sequence: {{Optimal ET sequence| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}
{{Optimal ET sequence|legend=0| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}


Badness: 0.745 × 10<sup>-3</sup>
Badness (Smith): 0.745 × 10<sup>-3</sup>


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


=== Marvelcat ===
=== Marvelcat ===
Line 328: Line 327:


Mapping: {{mapping| 1 0 0 -5 12 -1 | 0 2 0 4 -2 3 | 0 0 1 2 -3 1 }}
Mapping: {{mapping| 1 0 0 -5 12 -1 | 0 2 0 4 -2 3 | 0 0 1 2 -3 1 }}
: mapping generators: ~2, ~26/15, ~5
: mapping generators: ~2, ~26/15, ~5


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~26/15 = 950.961, ~5/4 = 383.088
* CTE: ~2 = 1200.000{{c}}, ~26/15 = 950.961{{c}}, ~5/4 = 383.088{{c}}
* CWE: ~2 = 1\1, ~26/15 = 950.426, ~5/4 = 383.479
* CWE: ~2 = 1200.000{{c}}, ~26/15 = 950.426{{c}}, ~5/4 = 383.479{{c}}


Optimal ET sequence: {{Optimal ET sequence| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}
{{Optimal ET sequence|legend=0| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}


Badness: 0.9997 × 10<sup>-3</sup>
Badness (Smith): 0.9997 × 10<sup>-3</sup>


== Minerva ==
== Minerva ==
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Lattice basis:  
Lattice basis:  
: 16/15 length = 0.8997, 5/4 length = 1.0457
: ~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


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 700.379, ~5/4 = 386.617
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.379{{c}}, ~5/4 = 386.617{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.301, ~5/4 = 386.579
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.301{{c}}, ~5/4 = 386.579{{c}}


[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9
Line 360: Line 358:
{{Optimal ET sequence|legend=1| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}
{{Optimal ET sequence|legend=1| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}


[[Badness]]: 0.381 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.381 × 10<sup>-3</sup>


[[Projection pair]]s: 7 225/32 11 5625/512
[[Projection pair]]s: <code>7 225/32 11 5625/512</code>


Scales: [[minerva12]], [[minerva22x]]
Scales: [[minerva12]], [[minerva22x]]
Line 376: Line 374:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.179, ~5/4 = 385.888
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.179{{c}}, ~5/4 = 385.888{{c}}
* CWE: ~2 = 1\1, ~3/2 = 701.214, ~5/4 = 385.934
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 701.214{{c}}, ~5/4 = 385.934{{c}}


Minimax tuning:  
Minimax tuning:  
Line 383: Line 381:
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.11/9.13/7
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.11/9.13/7


Optimal ET sequence: {{Optimal ET sequence| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}
{{Optimal ET sequence|legend=0| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}


Badness: 0.818 × 10<sup>-3</sup>
Badness (Smith): 0.818 × 10<sup>-3</sup>


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


== Apollo ==
== Apollo ==
Line 399: Line 397:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 703.418, ~5/4 = 381.331
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.418{{c}}, ~5/4 = 381.331{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 703.461, ~5/4 = 381.507
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.461{{c}}, ~5/4 = 381.507{{c}}


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9


{{Optimal ET sequence|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}
{{Optimal ET sequence|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}


[[Projection pair]]s: 7 225/32 11 100/9
[[Projection pair]]s: <code>7 225/32 11 100/9</code>


[[Associated temperament]]: [[magic]]
[[Associated temperament]]: [[magic]]
Line 420: Line 418:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 703.959, ~5/4 = 381.001
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 703.959{{c}}, ~5/4 = 381.001{{c}}
* CWE: ~2 = 1\1, ~3/2 = 703.985, ~5/4 = 381.358
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 703.985{{c}}, ~5/4 = 381.358{{c}}


Minimax tuning: 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.11/9.13/9
Minimax tuning: 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.11/9.13/9


Optimal ET sequence: {{Optimal ET sequence| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
{{Optimal ET sequence|legend=0| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}


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


== Potassium ==
== Potassium ==
Line 437: Line 435:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 695.937, ~5/4 = 384.836
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 695.937{{c}}, ~5/4 = 384.836{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 696.059, ~5/4 = 384.947
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.059{{c}}, ~5/4 = 384.947{{c}}


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11
[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11


{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}
{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}


[[Badness]]: 0.464 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.464 × 10<sup>-3</sup>


[[Projection pair]]s: 7 225/32 11 45/4
[[Projection pair]]s: <code>7 225/32 11 45/4</code>


=== 13-limit ===
=== 13-limit ===
Line 456: Line 454:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.894, ~5/4 = 384.602
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 695.894{{c}}, ~5/4 = 384.602{{c}}
* CWE: ~2 = 1\1, ~3/2 = 695.948, ~5/4 = 384.637
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 695.948{{c}}, ~5/4 = 384.637{{c}}


Minimax tuning:  
Minimax tuning:  
Line 463: Line 461:
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13/9
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13/9


Optimal ET sequence: {{Optimal ET sequence| 9, 10, 12f, 19, 31e, 50e }}
{{Optimal ET sequence|legend=0| 9, 10, 12f, 19, 31e, 50e }}


Badness: 0.733 × 10<sup>-3</sup>
Badness (Smith): 0.733 × 10<sup>-3</sup>


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


== Malcolm ==
== Malcolm ==
Line 479: Line 477:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.322, ~5/4 = 382.976
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.322{{c}}, ~5/4 = 382.976{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.054, ~5/4 = 382.622
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.054{{c}}, ~5/4 = 382.622{{c}}


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


[[Badness]]: 1.250 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.250 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Line 494: Line 492:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 702.235, ~5/4 = 383.205
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 702.235{{c}}, ~5/4 = 383.205{{c}}
* CWE: ~2 = 1\1, ~3/2 = 702.088, ~5/4 = 383.063
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.088{{c}}, ~5/4 = 383.063{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
{{Optimal ET sequence|legend=0| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}


Badness: 1.075 × 10<sup>-3</sup>
Badness (Smith): 1.075 × 10<sup>-3</sup>


Scales: [[malco]]
Scales: [[malco]]
Line 515: Line 513:


Lattice basis:  
Lattice basis:  
: secor length = 0.9111, 3/2 length = 0.9477
: ~15/14 length = 0.9111, ~3/2 length = 0.9477
: Angle (secor, 3/2) = 65.933
: angle (~15/14, ~3/2) = 65.933


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 699.995, ~5/4 = 384.330
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 699.995{{c}}, ~5/4 = 384.330{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 699.861, ~5/4 = 383.772
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 699.861{{c}}, ~5/4 = 383.772{{c}}


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11


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


[[Badness]]: 0.344 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.344 × 10<sup>-3</sup>


[[Projection pair]]s: 7 225/32 11 91125/8192
[[Projection pair]]s: <code>7 225/32 11 91125/8192</code>


Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
Line 551: Line 549:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 700.617, ~5/4 = 382.244
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 700.617{{c}}, ~5/4 = 382.244{{c}}
* CWE: ~2 = 1\1, ~3/2 = 700.469, ~5/4 = 381.669
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 700.469{{c}}, ~5/4 = 381.669{{c}}


Optimal ET sequence: {{Optimal ET sequence| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}
{{Optimal ET sequence|legend=0| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}


Badness: 0.736 × 10<sup>-3</sup>
Badness (Smith): 0.736 × 10<sup>-3</sup>


=== Prodigious ===
=== Prodigious ===
Line 566: Line 564:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 700.305, ~5/4 = 384.075
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 700.305{{c}}, ~5/4 = 384.075{{c}}
* CWE: ~2 = 1\1, ~3/2 = 700.330, ~5/4 = 383.503
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 700.330{{c}}, ~5/4 = 383.503{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}
{{Optimal ET sequence|legend=0| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}


Badness: 0.900 × 10<sup>-3</sup>
Badness (Smith): 0.900 × 10<sup>-3</sup>


=== Prodigal ===
=== Prodigal ===
Line 581: Line 579:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 699.698, ~5/4 = 384.884
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 699.698{{c}}, ~5/4 = 384.884{{c}}
* CWE: ~2 = 1\1, ~3/2 = 699.554, ~5/4 = 384.350
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 699.554{{c}}, ~5/4 = 384.350{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}


Badness: 0.889 × 10<sup>-3</sup>
Badness (Smith): 0.889 × 10<sup>-3</sup>


=== Protannic ===
=== Protannic ===
Line 596: Line 594:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 698.947, ~5/4 = 385.480
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 698.947{{c}}, ~5/4 = 385.480{{c}}
* CWE: ~2 = 1\1, ~3/2 = 699.422, ~5/4 = 383.983
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 699.422{{c}}, ~5/4 = 383.983{{c}}


Optimal ET sequence: {{Optimal ET sequence| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
{{Optimal ET sequence|legend=0| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}


Badness: 0.953 × 10<sup>-3</sup>
Badness (Smith): 0.953 × 10<sup>-3</sup>


==== 17-limit ====
==== 17-limit ====
Line 611: Line 609:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 698.969, ~5/4 = 385.440
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 698.969{{c}}, ~5/4 = 385.440{{c}}
* CWE: ~2 = 1\1, ~3/2 = 699.485, ~5/4 = 383.874
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 699.485{{c}}, ~5/4 = 383.874{{c}}


Optimal ET sequence: {{Optimal ET sequence| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
{{Optimal ET sequence|legend=0| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}


Badness: 0.772 × 10<sup>-3</sup>
Badness (Smith): 0.772 × 10<sup>-3</sup>


== Fantastic ==
== Fantastic ==
Line 626: Line 624:


{{Mapping|legend=1| 2 0 0 -10 -7 | 0 1 0 2 0 | 0 0 1 2 3 }}
{{Mapping|legend=1| 2 0 0 -10 -7 | 0 1 0 2 0 | 0 0 1 2 3 }}
: mapping generators: ~99/70, ~3, ~5
: mapping generators: ~99/70, ~3, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~99/70 = 1\2, ~3/2 = 701.132, ~5/4 = 383.926
* [[CTE]]: ~99/70 = 600.000{{c}}, ~3/2 = 701.132{{c}}, ~5/4 = 383.926{{c}}
* [[CWE]]: ~99/70 = 1\2, ~3/2 = 700.816, ~5/4 = 383.535
* [[CWE]]: ~99/70 = 600.000{{c}}, ~3/2 = 700.816{{c}}, ~5/4 = 383.535{{c}}


{{Optimal ET sequence|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
{{Optimal ET sequence|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}


[[Badness]]: 0.743 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.743 × 10<sup>-3</sup>


== Hestia ==
== Hestia ==
Line 645: Line 642:


{{Mapping|legend=1| 1 0 0 -5 9 | 0 2 0 4 -7 | 0 0 1 2 0 }}
{{Mapping|legend=1| 1 0 0 -5 9 | 0 2 0 4 -7 | 0 0 1 2 0 }}
: mapping generators: ~2, ~400/231, ~5
: mapping generators: ~2, ~400/231, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~400/231 = 950.043, ~5/4 = 384.858
* [[CTE]]: ~2 = 1200.000{{c}}, ~400/231 = 950.043{{c}}, ~5/4 = 384.858{{c}}
* [[CWE]]: ~2 = 1\1, ~400/231 = 950.121, ~5/4 = 383.953
* [[CWE]]: ~2 = 1200.000{{c}}, ~400/231 = 950.121{{c}}, ~5/4 = 383.953{{c}}


{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}


[[Badness]]: 1.54 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.54 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Line 664: Line 660:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~26/15 = 950.131, ~5/4 = 385.245
* CTE: ~2 = 1200.000{{c}}, ~26/15 = 950.131{{c}}, ~5/4 = 385.245{{c}}
* CWE: ~2 = 1\1, ~26/15 = 950.211, ~5/4 = 383.949
* CWE: ~2 = 1200.000{{c}}, ~26/15 = 950.211{{c}}, ~5/4 = 383.949{{c}}


Optimal ET sequence: {{Optimal ET sequence| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
{{Optimal ET sequence|legend=0| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}


Badness: 1.062 × 10<sup>-3</sup>
Badness (Smith): 1.062 × 10<sup>-3</sup>


== Morfil ==
== Morfil ==
Line 677: Line 673:


{{Mapping|legend=1| 1 0 1 -3 -2 | 0 1 2 6 5 | 0 0 -3 -6 -4 }}
{{Mapping|legend=1| 1 0 1 -3 -2 | 0 1 2 6 5 | 0 0 -3 -6 -4 }}
: mapping generators: ~2, ~3, ~84/55
: mapping generators: ~2, ~3, ~84/55


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.459, ~84/55 = 739.747
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.459{{c}}, ~84/55 = 739.747{{c}}
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.111, ~84/55 = 739.451
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.111{{c}}, ~84/55 = 739.451{{c}}


{{Optimal ET sequence|legend=1| 29, 31, 60e, 91e, 94, 125 }}
{{Optimal ET sequence|legend=1| 29, 31, 60e, 91e, 94, 125 }}


[[Badness]]: 1.152 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.152 × 10<sup>-3</sup>


== Catakleismoid ==
== Catakleismoid ==
Line 696: Line 691:


{{Mapping|legend=1| 1 0 1 -3 0 | 0 6 5 22 0 | 0 0 0 0 1 }}
{{Mapping|legend=1| 1 0 1 -3 0 | 0 6 5 22 0 | 0 0 0 0 1 }}
: mapping generators: ~2, ~6/5, ~11
: mapping generators: ~2, ~6/5, ~11


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~6/5 = 316.834, ~11/8 = 551.318
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 316.834{{c}}, ~11/8 = 551.318{{c}}
* [[CWE]]: ~2 = 1\1, ~6/5 = 316.771, ~11/8 = 550.034
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 316.771{{c}}, ~11/8 = 550.034{{c}}


{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce }}


[[Badness]]: 1.275 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.275 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Line 715: Line 709:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~6/5 = 316.886, ~11/8 = 551.318
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 316.886{{c}}, ~11/8 = 551.318{{c}}
* CWE: ~2 = 1\1, ~6/5 = 316.794, ~11/8 = 549.590
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 316.794{{c}}, ~11/8 = 549.590{{c}}


Optimal ET sequence: {{Optimal ET sequence| 19, 34d, 53, 72, 125f, 197ef, 269cef }}
Optimal ET sequence: {{Optimal ET sequence| 19, 34d, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.916 × 10<sup>-3</sup>
Badness (Smith): 0.916 × 10<sup>-3</sup>


== Subgroup extensions ==
== Subgroup extensions ==
Line 730: Line 724:
Mapping: {{mapping| 1 0 0 -5 8 | 0 1 0 2 -1 | 0 0 1 2 -1 }}
Mapping: {{mapping| 1 0 0 -5 8 | 0 1 0 2 -1 | 0 0 1 2 -1 }}


Optimal tuning:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.244, ~5/4 = 384.789
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.244{{c}}, ~5/4 = 384.789{{c}}


{{Optimal ET sequence| legend=1 | 9, 10, 12, 19, 22, 31, 41, 53 }}
{{Optimal ET sequence|legend=0| 9, 10, 12, 19, 22, 31, 41, 53 }}


=== Devimarvel ===
=== Devimarvel ===
Line 742: Line 736:
Mapping: {{mapping| 1 0 0 -5 9 | 0 1 0 2 -3 | 0 0 1 2 0 }}
Mapping: {{mapping| 1 0 0 -5 9 | 0 1 0 2 -3 | 0 0 1 2 0 }}


Optimal tuning:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 701.904, ~5/4 = 384.260
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 701.904{{c}}, ~5/4 = 384.260{{c}}


{{Optimal ET sequence| legend=1 | 10, 12, 19, 22, 31, 41, 53, 72, 94 }}
{{Optimal ET sequence|legend=0| 10, 12, 19, 22, 31, 41, 53, 72, 94 }}


== Notes ==
== References ==
<references />


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Marvel family| ]] <!-- main article -->
[[Category:Marvel family| ]] <!-- main article -->
[[Category:Marvel| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
<references />
Retrieved from "https://en.xen.wiki/w/Marvel_family"