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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|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.
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, {{monzo|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 {{multival|13 14 35 -8 19 42}} and adding 3136/3125 and 4375/4374, and the 11-limit wedgie {{multival|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


[[Mapping]]: [<1 5 6|, <0 -13 -14|]
[[Mapping]]: [{{val|1 5 6}}, {{val|0 -13 -14}}]


[[POTE tuning|POTE generator]]: ~6/5 = 315.240
[[POTE generator]]: ~6/5 = 315.240


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


[[Badness]]: 0.043279
[[Badness]]: 0.043279
Line 959: Line 959:
[[Comma list]]: 3136/3125, 4375/4374
[[Comma list]]: 3136/3125, 4375/4374


[[Mapping]]: [<1 5 6 12|, <0 -13 -14 -35|]
[[Mapping]]: [{{val|1 5 6 12}}, {{val|0 -13 -14 -35}}]


[[Wedgie]]: <<13 14 35 -8 19 42||
[[Wedgie]]: {{multival|13 14 35 -8 19 42}}


[[POTE tuning|POTE generator]]: ~6/5 = 315.181
[[POTE generator]]: ~6/5 = 315.181


[[EDO|Vals]]: {{Val list| 19, 80, 99, 217, 316, 415 }}
[[Vals]]: {{Val list| 19, 80, 99, 217, 316, 415 }}


[[Badness]]: 0.027431
[[Badness]]: 0.027431
Line 972: Line 972:
Comma list: 385/384, 3136/3125, 4375/4374
Comma list: 385/384, 3136/3125, 4375/4374


Mapping: [<1 5 6 12 -6|, <0 -13 -14 -35 36|]
Mapping: [{{val|1 5 6 12 -6}}, {{val|0 -13 -14 -35 36}}]


POTE generator: ~6/5 = 315.251
POTE generator: ~6/5 = 315.251
Line 983: Line 983:
Comma list: 176/175, 1375/1372, 2200/2187
Comma list: 176/175, 1375/1372, 2200/2187


Mapping: [<1 5 6 12 20|, <0 -13 -14 -35 -63|]
Mapping: [{{val|1 5 6 12 20}}, {{val|0 -13 -14 -35 -63}}]


POTE generator: ~6/5 = 315.060
POTE generator: ~6/5 = 315.060
Line 994: Line 994:
Comma list: 169/168, 176/175, 325/324, 1375/1372
Comma list: 169/168, 176/175, 325/324, 1375/1372


Mapping: [<1 5 6 12 20 10|, <0 -13 -14 -35 -63 -24|]
Mapping: [{{val|1 5 6 12 20 10}}, {{val|0 -13 -14 -35 -63 -24}}]


POTE generator: ~6/5 = 315.075
POTE generator: ~6/5 = 315.075
Line 1,005: Line 1,005:
Comma list: 540/539, 896/891, 3136/3125
Comma list: 540/539, 896/891, 3136/3125


Mapping: [<1 5 6 12 -1|, <0 -13 -14 -35 17|]
Mapping: [{{val|1 5 6 12 -1}}, {{val|0 -13 -14 -35 17}}]


POTE generator: ~6/5 = 315.096
POTE generator: ~6/5 = 315.096
Line 1,016: Line 1,016:
Comma list: 169/168, 325/324, 540/539, 832/825
Comma list: 169/168, 325/324, 540/539, 832/825


Mapping: [<1 5 6 12 -1 10|, <0 -13 -14 -35 17 -24|]
Mapping: [{{val|1 5 6 12 -1 10}}, {{val|0 -13 -14 -35 17 -24}}]


POTE generator: ~6/5 = 315.080
POTE generator: ~6/5 = 315.080
Line 1,027: Line 1,027:
Comma list: 3025/3024, 3136/3125, 4375/4374
Comma list: 3025/3024, 3136/3125, 4375/4374


Mapping: [<2 10 12 24 19|, <0 -13 -14 -35 -23|]
Mapping: [{{val|2 10 12 24 19}}, {{val|0 -13 -14 -35 -23}}]


POTE generator: ~6/5 = 315.181
POTE generator: ~6/5 = 315.181
Line 1,038: Line 1,038:
Comma list: 352/351, 1001/1000, 3025/3024, 4375/4374
Comma list: 352/351, 1001/1000, 3025/3024, 4375/4374


Mapping: [<2 10 12 24 19 -1|, <0 -13 -14 -35 -23 16|]
Mapping: [{{val|2 10 12 24 19 -1}}, {{val|0 -13 -14 -35 -23 16}}]


POTE generator: ~6/5 = 315.156
POTE generator: ~6/5 = 315.156
Line 1,049: Line 1,049:
Comma list: 169/168, 325/324, 364/363, 3136/3125
Comma list: 169/168, 325/324, 364/363, 3136/3125


Mapping: [<2 10 12 24 19 20|, <0 -13 -14 -35 -23 -24|]
Mapping: [{{val|2 10 12 24 19 20}}, {{val|0 -13 -14 -35 -23 -24}}]


POTE generator: ~6/5 = 315.184
POTE generator: ~6/5 = 315.184
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