Amity family: Difference between revisions

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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.
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]].  
Temperaments not discussed here include [[Breedsmic temperament|amicable]] and [[Hemimean clan|chromat]].  


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


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== Hitchcock ==
== Hitchcock ==
{{see also|Ragismic microtemperaments #Hitchcock}}
Comma list: 121/120, 176/175, 2200/2187
Comma list: 121/120, 176/175, 2200/2187


Line 88: Line 84:
Badness: 0.031307
Badness: 0.031307


=Accord=
= Accord =
Commas: 126/125, 100352/98415
[[Comma list]]: 126/125, 100352/98415
 
[[Mapping]]: [<1 3 6 11|, <0 -5 -13 -29|]


POTE generator: ~243/200 = 338.993
[[Wedgie]]: <<5 13 29 9 32 31||


Map: [<1 3 6 11|, <0 -5 -13 -29|]
[[POTE tuning|POTE generator]]: ~243/200 = 338.993


Wedgie: <<5 13 29 9 32 31||
[[EDO|Vals]]: {{Val list| 7d, 46, 131c, 177c }}


EDOs: 7d, 46, 131c, 177c
[[Badness]]: 0.095612


Badness: 0.0956
== 11-limit ==
Comma list: 121/120, 126/125, 896/891


==11-limit==
Mapping: [<1 3 6 11 6|, <0 -5 -13 -29 -9|]
Commas: 121/120, 126/125, 896/891


POTE generator: ~11/9 = 339.047
POTE generator: ~11/9 = 339.047


Map: [<1 3 6 11 6|, <0 -5 -13 -29 -9|]
Vals: {{Val list| 7d, 46, 177c, 223bc, 269bce }}


EDOs: 7d, 46, 177c, 223bc, 269bce
Badness: 0.042468


Badness: 0.0425
= Bamity =
[[Comma list]]: 245/243, 64827/64000


=Bamity=
[[Mapping]]: [<2 1 -1 3|, <0 5 13 6|]
Commas: 245/243, 64827/64000


POTE generator: ~7/6 = 260.402
[[Wedgie]]: <<10 26 12 18 -9 -45||


Map: [<2 1 -1 3|, <0 5 13 6|]
[[POTE tuning|POTE generator]]: ~7/6 = 260.402


Wedgie: <<10 26 12 18 -9 -45||
[[EDO|Vals]]: {{Val list| 46, 60, 106d }}


EDOs: 46, 60, 106d
[[Badness]]: 0.083601


Badness: 0.0836
== 11-limit ==
Comma list: 121/120, 245/243, 441/440


==11-limit==
Mapping: [<2 1 -1 3 3|, <0 5 13 6 9|]
Commas: 121/120, 245/243, 441/440


POTE generator: ~7/6 = 260.393
POTE generator: ~7/6 = 260.393


Map: [<2 1 -1 3 3|, <0 5 13 6 9|]
Vals: {{Val list| 14c, 46, 60e, 106de }}


EDOs: 14c, 46, 60e, 106de
Badness: 0.035504


Badness: 0.0355
== 13-limit ==
Comma list: 91/90, 121/120, 245/243, 441/440


==13-limit==
Mapping: [<2 1 -1 3 3 0|, <0 5 13 6 9 17|]
Commas: 91/90, 121/120, 245/243, 441/440


POTE generator: ~7/6 = 260.618
POTE generator: ~7/6 = 260.618


Map: [<2 1 -1 3 3 0|, <0 5 13 6 9 17|]
Vals: {{Val list| 46, 106def, 152def }}


EDOs: 46, 106def, 152def
Badness: 0.030885


Badness: 0.0309
= Hamity =
[[Comma list]]: 2430/2401, 4000/3969


=Hamity=
[[Mapping]]: [<1 8 19 15|, <0 -10 -26 -19|]
Commas: 2430/2401, 4000/3969


POTE generator: ~9/7 = 430.219
[[Wedgie]]: <<10 26 19 18 2 -29||


Map: [<1 8 19 15|, <0 -10 -26 -19|]
[[POTE tuning|POTE generator]]: ~9/7 = 430.219


Wedgie: <<10 26 19 18 2 -29||
[[EDO|Vals]]: {{Val list| 14c, 39d, 53 }}


EDOs: 14c, 39d, 53
[[Badness]]: 0.073956


Badness: 0.0740
== 11-limit ==
Comma list: 99/98, 121/120, 4000/3969


==11-limit==
Mapping: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]
Commas: 99/98, 121/120, 4000/3969


POTE generator: ~9/7 = 430.192
POTE generator: ~9/7 = 430.192


Map: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]
Vals: {{Val list| 14c, 39d, 53 }}


EDOs: 14c, 39d, 53
Badness: 0.042947


Badness: 0.0429
== 13-limit ==
Comma list: 99/98, 121/120, 275/273, 572/567


==13-limit==
Mapping: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|]
Commas: 99/98, 121/120, 275/273, 572/567


POTE generator: ~9/7 = 430.216
POTE generator: ~9/7 = 430.216


Map: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|]
Vals: {{Val list| 14cf, 53 }}
 
EDOs: 14cf, 53


Badness: 0.0298
Badness: 0.029753


[[Category:Theory]]
[[Category:Theory]]

Revision as of 10:41, 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

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

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

Comma list: 126/125, 100352/98415

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

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

POTE generator: ~243/200 = 338.993

Vals: Template:Val list

Badness: 0.095612

11-limit

Comma list: 121/120, 126/125, 896/891

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

POTE generator: ~11/9 = 339.047

Vals: Template:Val list

Badness: 0.042468

Bamity

Comma list: 245/243, 64827/64000

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

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

POTE generator: ~7/6 = 260.402

Vals: Template:Val list

Badness: 0.083601

11-limit

Comma list: 121/120, 245/243, 441/440

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

POTE generator: ~7/6 = 260.393

Vals: Template:Val list

Badness: 0.035504

13-limit

Comma list: 91/90, 121/120, 245/243, 441/440

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

POTE generator: ~7/6 = 260.618

Vals: Template:Val list

Badness: 0.030885

Hamity

Comma list: 2430/2401, 4000/3969

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

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

POTE generator: ~9/7 = 430.219

Vals: Template:Val list

Badness: 0.073956

11-limit

Comma list: 99/98, 121/120, 4000/3969

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

POTE generator: ~9/7 = 430.192

Vals: Template:Val list

Badness: 0.042947

13-limit

Comma list: 99/98, 121/120, 275/273, 572/567

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

POTE generator: ~9/7 = 430.216

Vals: Template:Val list

Badness: 0.029753

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