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Marvel temperaments: Difference between revisions

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This page discusses some of the temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the [[Marvel_family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone family #Septimal meantone|meantone]], [[Gamelismic clan #Miracle|miracle]], [[Magic family|magic]], [[Diaschismic family #Pajara|pajara]], [[orwell]], [[Kleismic family #Catakleismic|catakleismic]], [[Schismatic family #Garibaldi|garibaldi]], [[Augmented family #August|august]], [[Pythagorean family #Compton|compton]], [[Dicot family #Sharp|sharp]], [[Escapade family #Escapade|escapade]] and [[Pelogic family #Mavila|mavila]].
This page discusses some of the temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the [[Marvel_family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone family #Septimal meantone|meantone]], [[Gamelismic clan #Miracle|miracle]], [[Magic family|magic]], [[Diaschismic family #Pajara|pajara]], [[orwell]], [[Kleismic family #Catakleismic|catakleismic]], [[Schismatic family #Garibaldi|garibaldi]], [[Augmented family #August|august]], [[Pythagorean family #Compton|compton]], [[Dicot family #Sharp|sharp]], [[Escapade family #Escapade|escapade]] and [[Pelogic family #Mavila|mavila]].


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Note that this is technically not a marvel temperament until the 7-limit, but also placed here for reference.  
Note that this is technically not a marvel temperament until the 7-limit, but also placed here for reference.  


Comma list: 16875/16384
[[Comma list]]: 16875/16384


[[POTE generator]]: ~15/14 = 125.7549
[[POTE generator]]: ~15/14 = 125.7549
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== 7-limit ==
== 7-limit ==
Comma list: 49/48, 225/224
[[Comma list]]: 49/48, 225/224


[[POTE generator]]: ~15/14 = 125.608
[[POTE generator]]: ~15/14 = 125.608
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Badness: 0.0751
Badness: 0.0751


=Wizard=
= Wizard =
Comma: 2197265625/2147483648
== 5-limit ==
Comma list: 2197265625/2147483648


POTE generator: ~5/4 = 383.212
POTE generator: ~5/4 = 383.212


Map: [<2 1 5|, <0 6 -1|]
Mapping: [{{val| 2 1 5 }}, {{val| 0 6 -1 }}]


EDOs: {{EDOs|22, 50, 72, 166, 238c, 310c, 548bc}}
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}


Badness: 0.3864
Badness: 0.3864


==7-limit==
== 7-limit ==
Commas: 225/224, 118098/117649
Comma list: 225/224, 118098/117649


[[POTE_tuning|POTE temperament]]: 383.256
[[POTE generator]]: ~5/4 = 383.256


Map: [<2 1 5 2|, <0 6 -1 10|]
Mapping: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]


Wedgie: <<12 -2 20 -31 -2 52||
Wedgie: {{wedgie| 12 -2 20 -31 -2 52 }}


EDOs: {{EDOs|22, 50, 72, 94, 166, 238c, 310c, 382c}}
{{Val list|legend=1| 22, 50, 72, 94, 166, 238c, 310c, 382c }}


Badness: 0.0408
Badness: 0.0408


==11-limit==
== 11-limit ==
Commas: 225/224, 385/384, 4000/3993
Comma list: 225/224, 385/384, 4000/3993


[[POTE_tuning|POTE temperament]]: 383.232
[[POTE generator]]: ~5/4 = 383.232


Map: [<2 1 5 2 8|, <0 6 -1 10 -3|]
Mapping: [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3 }}]


EDOs: {{EDOs|22, 50, 72, 94, 166, 238c, 310c}}
{{Val list|legend=1| 22, 50, 72, 94, 166, 238c, 310c }}


Badness: 0.0185
Badness: 0.0185


=== Lizard ===
=== Lizard ===
Commas: 225/224, 351/350, 364/363, 385/384
Comma list: 225/224, 351/350, 364/363, 385/384


[[POTE_tuning|POTE temperament]]: 383.389
[[POTE generator]]: ~5/4 = 383.389


Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|]
Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 0 6 -1 10 -3 -10 }}]


EDOs: {{EDOs|22, 50, 72, 122, 194df}}
{{Val list|legend=1| 22, 50, 72, 122, 194df }}


Badness: 0.0218
Badness: 0.0218


==== 17-limit ====
==== 17-limit ====
Commas: 221/220, 273/272, 289/288, 351/350, 375/374
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374


[[POTE_tuning|POTE temperament]]: 383.381
[[POTE generator]]: ~5/4 = 383.381


Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|]
Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]


EDOs: {{EDOs|22, 50, 72, 122g, 194dfg}}
{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }}


Badness: 0.0145
Badness: 0.0145


==== 19-limit ====
==== 19-limit ====
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


[[POTE_tuning|POTE generator]]: ~5/4 = 383.477
[[POTE generator]]: ~5/4 = 383.477


Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|]
Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]


EDOs: {{EDOs|22h, 50, 72, 122g, 194dfg}}
{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }}


Badness: 0.0157
Badness: 0.0157


=== Gizzard ===
=== Gizzard ===
Commas: 225/224, 385/384, 325/324, 1573/1568
Comma list: 225/224, 385/384, 325/324, 1573/1568


POTE generator: ~5/4 = 383.170
POTE generator: ~5/4 = 383.170


Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|]
Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]


EDOs: {{EDOs|22, 72, 94, 166, 238cf}}
{{Val list|legend=1| 22, 72, 94, 166, 238cf }}


Badness: 0.0203
Badness: 0.0203


==== 17-limit ====
==== 17-limit ====
Commas: 225/224, 289/288, 325/324, 375/374, 385/384
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384


POTE generator: ~5/4 = 383.175
POTE generator: ~5/4 = 383.175


Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|]
Mapping: [{{val| 2 1 5 2 8 -2 6 }}, {{val| 0 6 -1 10 -3 26 6 }}]


EDOs: {{EDOs|22f, 72, 94, 166g, 238cfg}}
{{Val list|legend=1| 22f, 72, 94, 166g, 238cfg }}


Badness: 0.0136
Badness: 0.0136


==== 19-limit ====
==== 19-limit ====
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399
Comma list: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399


POTE generator: ~5/4 = 383.138
POTE generator: ~5/4 = 383.138


Map: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|]
Mapping: [{{val| 2 1 5 2 8 -2 6 15 }}, {{val| 0 6 -1 10 -3 26 6 -18 }}]


EDOs: {{EDOs|22f, 72, 94, 166g}}
{{Val list|legend=1| 22f, 72, 94, 166g }}


Badness: 0.0148
Badness: 0.0148


== Mage ==
== Mage ==
Commas: 99/98, 176/175, 1331/1296
Comma list: 99/98, 176/175, 1331/1296


POTE generator: ~55/48 = 216.876
POTE generator: ~55/48 = 216.876


Map: [<2 1 5 2 4|, <0 6 -1 10 8|]
Map: [{{val| 2 1 5 2 4 }}, {{val| 0 6 -1 10 8 }}]


EDOs: {{EDOs|22, 72e, 94e}}
{{Val list|legend=1| 22, 72e, 94e }}


Badness: 0.0578
Badness: 0.0578
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