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Ragismic microtemperaments: Difference between revisions

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= Parakleismic =
= Parakleismic =
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13>, with the [[118edo]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 give 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being <<13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie <<13 14 35 -36 ...|| adding 385/384. For the 7-limit [[99edo]] may be preferred, but in the 11-limit it is best to stick with 118.
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13>, with the [[118edo|118EDO]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 give 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being <<13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie <<13 14 35 -36 -8 19 -102 42 -132 -222|| adding 385/384. For the 7-limit [[99edo|99EDO]] may be preferred, but in the 11-limit it is best to stick with 118.


Comma: 124440064/1220703125
[[Comma]]: 124440064/1220703125


POTE generator: ~6/5 = 315.240
[[Mapping]]: [<1 5 6|, <0 -13 -14|]


Map: [<1 5 6|, <0 -13 -14|]
[[POTE tuning|POTE generator]]: ~6/5 = 315.240


EDOs: 19, 61, 80, 99, 118, 453, 571, 689, 1496
[[EDO|Vals]]: {{Val list| 19, 61, 80, 99, 118, 453, 571, 689, 1496 }}


Badness: 0.0433
[[Badness]]: 0.043279


==7-limit==
== 7-limit ==
Commas: 3136/3125, 4375/4374
[[Comma list]]: 3136/3125, 4375/4374


POTE generator: ~6/5 = 315.181
[[Mapping]]: [<1 5 6 12|, <0 -13 -14 -35|]
 
[[Wedgie]]: <<13 14 35 -8 19 42||
 
[[POTE tuning|POTE generator]]: ~6/5 = 315.181


Map: [<1 5 6 12|, <0 -13 -14 -35|]
[[EDO|Vals]]: {{Val list| 19, 80, 99, 217, 316, 415 }}


EDOs: 19, 80, 99, 217, 316, 415
[[Badness]]: 0.027431


Badness: 0.0274
== 11-limit ==
Comma list: 385/384, 3136/3125, 4375/4374


==11-limit==
Mapping: [<1 5 6 12 -6|, <0 -13 -14 -35 36|]
Commas: 385/384, 3136/3125, 4375/4374


POTE generator: ~6/5 = 315.251
POTE generator: ~6/5 = 315.251


Map: [<1 5 6 12 -6|, <0 -13 -14 -35 36|]
Vals: {{Val list| 19, 99, 118 }}


EDOs: 19, 99, 118
Badness: 0.049711


Badness: 0.0497
== Parkleismic ==
Comma list: 176/175, 1375/1372, 2200/2187


==Parkleismic==
Mapping: [<1 5 6 12 20|, <0 -13 -14 -35 -63|]
Commas: 176/175, 1375/1372, 2200/2187


POTE generator: ~6/5 = 315.060
POTE generator: ~6/5 = 315.060


Map: [<1 5 6 12 20|, <0 -13 -14 -35 -63|]
Vals: {{Val list| 19e, 80, 179, 259cd }}


EDOs: 80, 179, 259cd
Badness: 0.055884


Badness: 0.0559
=== 13-limit ===
Comma list: 169/168, 176/175, 325/324, 1375/1372


===13-limit===
Mapping: [<1 5 6 12 20 10|, <0 -13 -14 -35 -63 -24|]
Commas: 169/168, 176/175, 325/324, 1375/1372


POTE generator: ~6/5 = 315.075
POTE generator: ~6/5 = 315.075


Map: [<1 5 6 12 20 10|, <0 -13 -14 -35 -63 -24|]
Vals: {{Val list| 19e, 80, 179 }}


EDOs: 15, 19, 80, 179
Badness: 0.036559


Badness: 0.0366
== Paradigmic ==
Comma list: 540/539, 896/891, 3136/3125


==Paradigmic==
Mapping: [<1 5 6 12 -1|, <0 -13 -14 -35 17|]
Commas: 540/539, 896/891, 3136/3125


POTE generator: ~6/5 = 315.096
POTE generator: ~6/5 = 315.096


Map: [<1 5 6 12 -1|, <0 -13 -14 -35 17|]
Vals: {{Val list| 19, 61d, 80, 99e, 179e }}


EDOs: 19, 80, 99e, 179e
Badness: 0.041720


Badness: 0.0417
=== 13-limit ===
Comma list: 169/168, 325/324, 540/539, 832/825


===13-limit===
Mapping: [<1 5 6 12 -1 10|, <0 -13 -14 -35 17 -24|]
Commas: 169/168, 325/324, 540/539, 832/825


POTE generator: ~6/5 = 315.080
POTE generator: ~6/5 = 315.080


Map: [<1 5 6 12 -1 10|, <0 -13 -14 -35 17 -24|]
Vals: {{Val list| 19, 61d, 80, 99e, 179e }}


EDOs: 19, 80, 99e, 179e
Badness: 0.035781


Badness: 0.0358
== Semiparakleismic ==
Comma list: 3025/3024, 3136/3125, 4375/4374


== Semiparakleismic ==
Mapping: [<2 10 12 24 19|, <0 -13 -14 -35 -23|]
Commas: 3025/3024, 3136/3125, 4375/4374


POTE generator: ~6/5 = 315.181
POTE generator: ~6/5 = 315.181


Map: [<2 10 12 24 19|, <0 -13 -14 -35 -23|]
Vals: {{Val list| 80, 118, 198, 316, 514c, 830c }}
 
EDOs: 80, 118, 198, 316, 514c, 830c


Badness: 0.0342
Badness: 0.034208


=== 13-limit ===
=== 13-limit ===
Commas: 352/351, 1001/1000, 3025/3024, 4375/4374
Comma list: 352/351, 1001/1000, 3025/3024, 4375/4374


POTE generator: ~6/5 = 315.1563
Mapping: [<2 10 12 24 19 -1|, <0 -13 -14 -35 -23 16|]


Map: [<2 10 12 24 19 -1|, <0 -13 -14 -35 -23 16|]
POTE generator: ~6/5 = 315.156


EDOs: {{EDOs|80, 118, 198}}
Vals: {{Val list| 80, 118, 198 }}


Badness: 0.0338
Badness: 0.033775


=== Gentsemiparakleismic ===
=== Gentsemiparakleismic ===
Commas: 169/168, 325/324, 364/363, 3136/3125
Comma list: 169/168, 325/324, 364/363, 3136/3125


POTE generator: ~6/5 = 315.1839
Mapping: [&lt;2 10 12 24 19 20|, &lt;0 -13 -14 -35 -23 -24|]


Map: [<2 10 12 24 19 20|, <0 -13 -14 -35 -23 -24|]
POTE generator: ~6/5 = 315.184


EDOs: {{EDOs|80, 118f, 198f}}
Vals: {{Val list| 80, 118f, 198f }}


Badness: 0.0405
Badness: 0.040467


=Quincy=
=Quincy=
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