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Ragismic microtemperaments: Difference between revisions

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In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.


Comma: 1600000/1594323
[[Comma]]: 1600000/1594323


POTE generator: ~243/200 = 339.519
[[Mapping]]: [<1 3 6|, <0 -5 -13|]


Map: [<1 3 6|, <0 -5 -13|]
[[POTE tuning|POTE generator]]: ~243/200 = 339.519


EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873
[[EDO|Vals]]: {{Val list| 7, 39, 46, 53, 152, 205, 463, 668, 873 }}


Badness: 0.0220
[[Badness]]: 0.021960


== 7-limit ==
== 7-limit ==
Commas: 4375/4374, 5120/5103
[[Comma list]]: 4375/4374, 5120/5103


POTE generator: ~128/105 = 339.432
[[Mapping]]: [<1 3 6 -2|, <0 -5 -13 17|]


Map: [<1 3 6 -2|, <0 -5 -13 17|]
[[Wedgie]]: <<5 13 -17 9 -41 -76||


Wedgie: <<5 13 -17 9 -41 -76||
[[POTE tuning|POTE generator]]: ~128/105 = 339.432


EDOs: 7, 39, 46, 53, 99, 251, 350
[[EDO|Vals]]: {{Val list| 7, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}


Badness: 0.0236
[[Badness]]: 0.023649


== 11-limit ==
== 11-limit ==
Commas: 540/539, 4375/4374, 5120/5103
Comma list: 540/539, 4375/4374, 5120/5103
 
Mapping: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]


POTE generator: ~128/105 = 339.464
POTE generator: ~128/105 = 339.464


Map: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]
Vals: {{Val list| 53, 99e, 152, 555dee, 707ddee, 859bddee }}


EDOs: 53, 99e, 152, 555dee, 707ddee, 859bddee
Badness: 0.031506


Badness: 0.0315
=== 13-limit ===
Comma list: 352/351, 540/539, 625/624, 847/845


=== 13-limit ===
Mapping: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]
Commas: 352/351, 540/539, 625/624, 847/845


POTE generator: ~128/105 = 339.481
POTE generator: ~128/105 = 339.481


Map: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]
Vals: {{Val list| 53, 99ef, 152f }}
 
EDOS: 53, 99ef, 152f, 205


Badness: 0.0280
Badness: 0.028008


== Hitchcock ==
== Hitchcock ==
{{see also|Amity family #Hitchcock}}
{{see also|Amity family #Hitchcock}}


Commas: 121/120, 176/175, 2200/2187
Comma list: 121/120, 176/175, 2200/2187


POTE generator: ~11/9 = 339.340
Mapping: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]


Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
POTE generator: ~11/9 = 339.390


EDOs: 7, 39, 46, 53, 99
Vals: {{Val list| 7, 39, 46, 53, 99 }}


Badness: 0.0352
Badness: 0.035187


=== 13-limit ===
=== 13-limit ===
Commas: 121/120, 169/168, 176/175, 325/324
Comma list: 121/120, 169/168, 176/175, 325/324
 
Mapping: [<1 3 6 -2 6 2|, <0 -5 -13 17 -9 6|]


POTE generator: ~11/9 = 339.419
POTE generator: ~11/9 = 339.419


Map: [<1 3 6 -2 6 2|, <0 -5 -13 17 -9 6|]
Vals: {{Val list| 7, 39, 46, 53, 99 }}
 
EDOs: 7, 39, 46, 53, 99


Badness: 0.0224
Badness: 0.022448


== Hemiamity ==
== Hemiamity ==
Commas: 3025/3024, 4375/4374, 5120/5103
Comma list: 3025/3024, 4375/4374, 5120/5103


POTE generator: ~64/55 = 339.493
Mapping: [<2 1 -1 13 13|, <0 5 13 -17 -14|]


Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|]
POTE generator: ~64/55 = 339.439


EDOs: 14cde, 46, 106, 152, 350
Vals: {{Val list| 14cde, 46, 106, 152, 350, 502d }}


Badness: 0.0313
Badness: 0.031307


= Parakleismic =
= Parakleismic =
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