Amity family: Difference between revisions

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{{see also|Ragismic microtemperaments #Amity}}
{{see also|Ragismic microtemperaments #Amity}}


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|Ragismic microtemperaments #Hitchcock}}
{{see also|Ragismic microtemperaments #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


=Accord=
=Accord=

Revision as of 02:23, 18 April 2021

The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. 99edo is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.

Temperaments not discussed here include amicable and chromat.

Amity

Main article: Amity
See also: Ragismic microtemperaments § Amity

Comma: 1600000/1594323

Mapping: [<1 3 6|, <0 -5 -13|]

POTE generator: ~243/200 = 339.519

Vals: Template:Val list

Badness: 0.021960

7-limit

Comma list: 4375/4374, 5120/5103

Mapping: [<1 3 6 -2|, <0 -5 -13 17|]

Wedgie: <<5 13 -17 9 -41 -76||

POTE generator: ~128/105 = 339.432

Vals: Template:Val list

Badness: 0.023649

11-limit

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

Vals: Template:Val list

Badness: 0.031506

13-limit

Comma list: 352/351, 540/539, 625/624, 847/845

Mapping: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]

POTE generator: ~128/105 = 339.481

Vals: Template:Val list

Badness: 0.028008

Hitchcock

See also: Ragismic microtemperaments § Hitchcock

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

Mapping: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]

POTE generator: ~11/9 = 339.390

Vals: Template:Val list

Badness: 0.035187

13-limit

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

Vals: Template:Val list

Badness: 0.022448

Hemiamity

Comma list: 3025/3024, 4375/4374, 5120/5103

Mapping: [<2 1 -1 13 13|, <0 5 13 -17 -14|]

POTE generator: ~64/55 = 339.439

Vals: Template:Val list

Badness: 0.031307

Accord

Commas: 126/125, 100352/98415

POTE generator: ~243/200 = 338.993

Map: [<1 3 6 11|, <0 -5 -13 -29|]

Wedgie: <<5 13 29 9 32 31||

EDOs: 7d, 46, 131c, 177c

Badness: 0.0956

11-limit

Commas: 121/120, 126/125, 896/891

POTE generator: ~11/9 = 339.047

Map: [<1 3 6 11 6|, <0 -5 -13 -29 -9|]

EDOs: 7d, 46, 177c, 223bc, 269bce

Badness: 0.0425

Bamity

Commas: 245/243, 64827/64000

POTE generator: ~7/6 = 260.402

Map: [<2 1 -1 3|, <0 5 13 6|]

Wedgie: <<10 26 12 18 -9 -45||

EDOs: 46, 60, 106d

Badness: 0.0836

11-limit

Commas: 121/120, 245/243, 441/440

POTE generator: ~7/6 = 260.393

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

EDOs: 14c, 46, 60e, 106de

Badness: 0.0355

13-limit

Commas: 91/90, 121/120, 245/243, 441/440

POTE generator: ~7/6 = 260.618

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

EDOs: 46, 106def, 152def

Badness: 0.0309

Hamity

Commas: 2430/2401, 4000/3969

POTE generator: ~9/7 = 430.219

Map: [<1 8 19 15|, <0 -10 -26 -19|]

Wedgie: <<10 26 19 18 2 -29||

EDOs: 14c, 39d, 53

Badness: 0.0740

11-limit

Commas: 99/98, 121/120, 4000/3969

POTE generator: ~9/7 = 430.192

Map: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]

EDOs: 14c, 39d, 53

Badness: 0.0429

13-limit

Commas: 99/98, 121/120, 275/273, 572/567

POTE generator: ~9/7 = 430.216

Map: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|]

EDOs: 14cf, 53

Badness: 0.0298

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