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Marvel temperaments: Difference between revisions

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Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)


=Negri=
= Negri =
{{main|Negri}}
{{main| Negri }}


==5-limit==
== 5-limit ==
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|Comma]]s: 16875/16384
Comma list: 16875/16384


[[POTE_tuning|POTE temperament]]: ~15/14 = 125.7549
[[POTE generator]]: ~15/14 = 125.7549


[[Map|Map]]: [<1 2 2|, <0 -4 3|]
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]


[[wedgie|Wedgie]]: <<4 -3 -14||
[[Wedgie]]: {{wedgie| 4 -3 -14 }}


EDOs: {{EDOs|9, 10, 19, 86}}
{{Val list|legend=1| 9, 10, 19, 86 }}


==7-limit==
== 7-limit ==
[[Comma|Comma]]s: 49/48, 225/224
Comma list: 49/48, 225/224


[[POTE_tuning|POTE temperament]]: ~15/14 = 125.608
[[POTE generator]]: ~15/14 = 125.608


[[Map|Map]]: [<1 2 2 3|, <0 -4 3 -2|]
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]


[[wedgie|Wedgie]]: <<4 -3 2 -14 -8 13||
[[Wedgie]]: {{wedgie| 4 -3 2 -14 -8 13 }}


EDOs: {{EDOs|9, 10, 19, 86}}
{{Val list|legend=1| 9, 10, 19, 86 }}


==11-limit==
== 11-limit ==
Commas: 45/44, 49/48, 56/55
Comma list: 45/44, 49/48, 56/55


[[POTE_tuning|POTE generator]]: ~15/14 = 126.474
[[POTE generator]]: ~15/14 = 126.474


Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]


EDOs: {{EDOs|9, 10, 19}}
{{Val list|legend=1| 9, 10, 19 }}


[[Badness|Badness]]: 0.0262
[[Badness]]: 0.0262


=== 13-limit ===
=== 13-limit ===
Commas: 45/44, 49/48, 56/55, 78/77
Comma list: 45/44, 49/48, 56/55, 78/77


[[POTE_tuning|POTE generator]]: ~14/13 = 126.431
[[POTE generator]]: ~14/13 = 126.431


Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]
Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]


EDOs: {{EDOs|9, 10, 19}}
{{Val list|legend=1| 9, 10, 19 }}


== Negril ==
== Negril ==
Commas: 49/48, 100/99, 225/224
Comma list: 49/48, 100/99, 225/224


POTE generator: ~15/14 = 124.767
POTE generator: ~15/14 = 124.767


Map: [<1 2 2 3 2|, <0 -4 3 -2 14|]
Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]


EDOs: {{EDOs|19, 29, 48df, 77cdf}}
{{Val list|legend=1| 19, 29, 48df, 77cdf }}


Badness: 0.0387
Badness: 0.0387


=== 13-limit ===
=== 13-limit ===
Commas: 49/48, 65/64, 91/90, 875/858
Comma list: 49/48, 65/64, 91/90, 875/858


POTE generator: ~15/14 = 124.716
POTE generator: ~15/14 = 124.716


Map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]
Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]


EDOs: {{EDOs|9, 10, 19, 29, 48, 77}}
{{Val list|legend=1| 9, 10, 19, 29, 48, 77 }}


Badness: 0.0244
Badness: 0.0244


== Negric ==
== Negric ==
Commas: 33/32, 49/48, 77/75
Comma list: 33/32, 49/48, 77/75


POTE generator: ~15/14 = 127.039
POTE generator: ~15/14 = 127.039


Map: [<1 2 2 3 3|, <0 -4 3 -2 4|]
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]


EDOs: {{EDOs|9, 19, 85}}
{{Val list|legend=1| 9, 19, 85 }}


Badness: 0.0306
Badness: 0.0306


=== 13-limit ===
=== 13-limit ===
Commas: 33/32, 49/48, 65/64, 91/90
Comma list: 33/32, 49/48, 65/64, 91/90


POTE generator: ~15/14 = 127.039
POTE generator: ~15/14 = 127.039


Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]


EDOs: {{EDOs|9, 19, 85}}
{{Val list|legend=1| 9, 19, 85 }}


Badness: 0.0202
Badness: 0.0202


== Negroni ==
== Negroni ==
Commas: 49/48, 55/54, 225/224
Comma list: 49/48, 55/54, 225/224


POTE generator: ~15/14 = 124.539
POTE generator: ~15/14 = 124.539


Map: [<1 2 2 3 5|, <0 -4 3 -2 -15|]
Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]


EDOs: {{EDOs|10, 19e, 29, 77cde}}
{{Val list|legend=1| 10, 19e, 29, 77cde }}


Badness: 0.0353
Badness: 0.0353


=== 13-limit ===
=== 13-limit ===
Commas: 49/48, 55/54, 65/64, 91/90
Comma list: 49/48, 55/54, 65/64, 91/90


POTE generator: ~15/14 = 124.545
POTE generator: ~15/14 = 124.545


Map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|]
Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]


EDOs: {{EDOs|10, 19e, 29, 77cdef}}
{{Val list|legend=1| 10, 19e, 29, 77cdef }}


Badness: 0.0216
Badness: 0.0216
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