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{{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]] 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.


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* [[7-odd-limit]]: 3 and 5 1/4-comma flat, 7 just
* [[7-odd-limit]]: 3 and 5 1/4-comma flat, 7 just
: {{monzo list| 1 0 0 0 | 5/4 1/2 -1/2 1/4 | 5/4 -1/2 1/2 1/4  | 0 0 0 1 }}
: {{monzo list| 1 0 0 0 | 5/4 1/2 -1/2 1/4 | 5/4 -1/2 1/2 1/4  | 0 0 0 1 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7
* [[9-odd-limit]]: 3 1/6-comma flat, 5 1/3-comma flat, 7 just
* [[9-odd-limit]]: 3 1/6-comma flat, 5 1/3-comma flat, 7 just
: {{monzo list| 1 0 0 0 | 5/6 2/3 -1/3 1/6 | 5/3 -2/3 1/3 1/3 | 0 0 0 1 }}
: {{monzo list| 1 0 0 0 | 5/6 2/3 -1/3 1/6 | 5/3 -2/3 1/3 1/3 | 0 0 0 1 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.7


{{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 }}
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* ''[[Supernatural]]'' (+245/243) → [[Keemic family #Supernatural|Keemic family]]
* ''[[Supernatural]]'' (+245/243) → [[Keemic family #Supernatural|Keemic family]]
* ''[[Artemis]]'' (+121/120) → [[Biyatismic clan #Artemis|Biyatismic clan]]
* ''[[Artemis]]'' (+121/120) → [[Biyatismic clan #Artemis|Biyatismic clan]]
* ''[[Spectacle]]'' (+243/242) → [[Rastmic rank three clan #Spectacle|Rastmic rank-3 clan]]
* ''[[Spectacle]]'' (+243/242) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]]
* ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank three clan #Spectacle|Rastmic rank-3 clan]]
* ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]]


== Undecimal marvel (unimarv) ==
== Undecimal marvel (unimarv) ==
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* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{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 }}]
: [{{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 basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11/9
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/9


{{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 }}
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Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]


{{Databox|Hobbit bases|
{{Databox|[[Hobbit]] bases|
2.3.5 subgroup
2.3.5 subgroup
* 12: 128/125, 2048/2025
* 12: 128/125, 2048/2025
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Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/9
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.11/9.13/9
* 15-odd-limit eigenmonzo (unchanged-interval) 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: {{Optimal ET sequence| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}
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Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.13/5
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.13/5
* 15-odd-limit eigenmonzo (unchanged-interval) 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: {{Optimal ET sequence| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}
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Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.11/9
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/5.11/9
* 15-odd-limit eigenmonzo (unchanged-interval) 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: {{Optimal ET sequence| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}
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Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/11
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13/11
* 15-odd-limit eigenmonzo (unchanged-interval) 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: {{Optimal ET sequence| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}
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* [[CWE]]: ~2 = 1\1, ~3/2 = 700.301, ~5/4 = 386.579
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.301, ~5/4 = 386.579


[[Minimax tuning]]: [[11-odd-limit]] [[eigenmonzo basis|eigenmonzo (unchanged-interval) 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| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}
{{Optimal ET sequence|legend=1| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}
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Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/7
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.11/9.13/7
* 15-odd-limit eigenmonzo (unchanged-interval) 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: {{Optimal ET sequence| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}
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* [[CWE]]: ~2 = 1\1, ~3/2 = 703.461, ~5/4 = 381.507
* [[CWE]]: ~2 = 1\1, ~3/2 = 703.461, ~5/4 = 381.507


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) 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 }}
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[[Associated temperament]]: [[magic]]
[[Associated temperament]]: [[magic]]


;Scales
Scales: [[apollo wholetone]], [[indigo17]]
* [[Apollo wholetone]]
* [[Indigo17]]


=== 13-limit ===
=== 13-limit ===
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* CWE: ~2 = 1\1, ~3/2 = 703.985, ~5/4 = 381.358
* CWE: ~2 = 1\1, ~3/2 = 703.985, ~5/4 = 381.358


Minimax tuning: 13-odd-limit eigenmonzo (unchanged-interval) 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: {{Optimal ET sequence| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
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* [[CWE]]: ~2 = 1\1, ~3/2 = 696.059, ~5/4 = 384.947
* [[CWE]]: ~2 = 1\1, ~3/2 = 696.059, ~5/4 = 384.947


[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) 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 }}
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Minimax tuning:  
Minimax tuning:  
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/9
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13/9
* 15-odd-limit eigenmonzo (unchanged-interval) 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: {{Optimal ET sequence| 9, 10, 12f, 19, 31e, 50e }}
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* [[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|eigenmonzo (unchanged-interval) 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 }}
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Badness: 0.916 × 10<sup>-3</sup>
Badness: 0.916 × 10<sup>-3</sup>
== Subgroup extensions ==
=== Char ===
Subgroup: 2.3.5.7.17
Comma list: 120/119, 225/224
Mapping: {{mapping| 1 0 0 -5 8 | 0 1 0 2 -1 | 0 0 1 2 -1 }}
Optimal tuning:
* CTE: ~2 = 1\1, ~3/2 = 701.244, ~5/4 = 384.789
{{Optimal ET sequence| legend=1 | 9, 10, 12, 19, 22, 31, 41, 53 }}
=== Devimarvel ===
Subgroup: 2.3.5.7.19
Comma list: 225/224, 400/399
Mapping: {{mapping| 1 0 0 -5 9 | 0 1 0 2 -3 | 0 0 1 2 0 }}
Optimal tuning:
* CTE: ~2 = 1\1, ~3/2 = 701.904, ~5/4 = 384.260
{{Optimal ET sequence| legend=1 | 10, 12, 19, 22, 31, 41, 53, 72, 94 }}


== Notes ==
== Notes ==


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Marvel family| ]] <!-- main article -->
[[Category:Marvel family| ]] <!-- main article -->
[[Category:Marvel| ]] <!-- key article -->
[[Category:Marvel| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
<references />
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