Ragismic microtemperaments: Difference between revisions

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= Amity =

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, {{multival|5 13 -17 9 -41 -76}}~~. [[99edo|99EDO]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 39, 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 the 6/5 just 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. [[99edo|99EDO]] is a good tuning for amity, with generator 28\99, and MOS of 11, 18, 25, 32, 39, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.

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)<sup>1/13</sup>, which gives pure major thirds.

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

~~[[Mapping]]: [{{val|1 3 6}}, {{val|0 -5 -13}}]~~

~~[[POTE generator]]: ~243/200 = 339.519~~

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

~~[[Badness]]: 0.021960~~

~~== 7-limit ==~~

[[Comma list]]: 4375/4374, 5120/5103

[[Mapping]]: [{{val|1 3 6 -2}}, {{val|0 -5 -13 17}}]

[[Mapping]]: [{{val| 1 3 6 -2 }}, {{val| 0 -5 -13 17 }}]

~~[[Wedgie]]:~~ {{~~multival~~|5 13 -17 9 -41 -76}}

[[POTE generator]]: ~128/105 = 339.432

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

{{Val list|legend=1| 7, 32c, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}

[[Badness]]: 0.023649

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POTE generator: ~128/105 = 339.464

Vals: {{Val list| 53, 99e, 152, 555dee, 707ddee, 859bddee }}

Vals: {{Val list| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}

Badness: 0.031506

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POTE generator: ~128/105 = 339.481

Vals: {{Val list| 53, 99ef, 152f }}

Vals: {{Val list| 46ef, 53, 99ef, 152f }}

Badness: 0.028008

@@ Line 864: / Line 864: @@
 = Amity =
-{{main|Amity}}
+{{main| Amity }}
-{{see also|Amity family #Amity}}
+{{see also| Amity family #Amity }}
-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&amp;53 temperament, or by its wedgie, {{multival|5 13 -17 9 -41 -76}}. [[99edo|99EDO]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 39, 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 the 6/5 just 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&amp;53 temperament. [[99edo|99EDO]] is a good tuning for amity, with generator 28\99, and MOS of 11, 18, 25, 32, 39, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.
-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)<sup>1/13</sup>, which gives pure major thirds.
-[[Comma]]: 1600000/1594323
-[[Mapping]]: [{{val|1 3 6}}, {{val|0 -5 -13}}]
-[[POTE generator]]: ~243/200 = 339.519
-[[Vals]]: {{Val list| 7, 39, 46, 53, 152, 205, 463, 668, 873 }}
-[[Badness]]: 0.021960
-== 7-limit ==
 [[Comma list]]: 4375/4374, 5120/5103
-[[Mapping]]: [{{val|1 3 6 -2}}, {{val|0 -5 -13 17}}]
+[[Mapping]]: [{{val| 1 3 6 -2 }}, {{val| 0 -5 -13 17 }}]
-[[Wedgie]]: {{multival|5 13 -17 9 -41 -76}}
+{{Multival|legend=1| 5 13 -17 9 -41 -76 }}
 [[POTE generator]]: ~128/105 = 339.432
-[[Vals]]: {{Val list| 7, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}
+{{Val list|legend=1| 7, 32c, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}
 [[Badness]]: 0.023649
@@ Line 901: / Line 890: @@
 POTE generator: ~128/105 = 339.464
-Vals: {{Val list| 53, 99e, 152, 555dee, 707ddee, 859bddee }}
+Vals: {{Val list| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}
 Badness: 0.031506
@@ Line 912: / Line 901: @@
 POTE generator: ~128/105 = 339.481
-Vals: {{Val list| 53, 99ef, 152f }}
+Vals: {{Val list| 46ef, 53, 99ef, 152f }}
 Badness: 0.028008