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Ragismic microtemperaments: Difference between revisions

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= Quasithird =
= Quasithird =
[[Comma]]: |55 -64 20>
The '''quasithird''' temperament is featured by a major third interval which is 1600000/1594323 ([[amity comma]]) or 5120/5103 ([[5120/5103|hemifamity comma]]) below the just major third [[5/4]] as a generator, five of which give a fifth with octave reduction. This temperament has a period of a quarter octave, which allows to temper out the [[4375/4374|ragisma]] and {{monzo|-60 29 0 5}}.


[[Mapping]]: [<4 0 -11|, <0 5 16|]
[[Comma]]: {{monzo|55 -64 20}}


[[Wedgie]]: <<20 64 55||
[[Mapping]]: [{{val|4 0 -11}}, {{val|0 5 16}}]


[[POTE tuning|POTE generator]]: ~1594323/1280000 = 380.395
[[POTE generator]]: ~1594323/1280000 = 380.395


[[EDO|Vals]]: {{Val list| 60, 164, 224, 388, 612, 836, 1000, 1448, 1612, 2224, 2836 }}
[[Vals]]: {{Val list| 60, 164, 224, 388, 612, 836, 1000, 1448, 1612, 2224, 2836 }}


[[Badness]]: 0.099519
[[Badness]]: 0.099519
Line 570: Line 570:
[[Comma list]]: 4375/4374, 1153470752371588581/1152921504606846976
[[Comma list]]: 4375/4374, 1153470752371588581/1152921504606846976


[[Mapping]]: [<4 0 -11 48|, <0 5 16 -29|]
[[Mapping]]: [{{val|4 0 -11 48}}, {{val|0 5 16 -29}}]


[[Wedgie]]: <<20 64 -116 55 -240 -449||
[[Wedgie]]: {{multival|20 64 -116 55 -240 -449}}


[[POTE tuning|POTE generator]]: ~5103/4096 = 380.388  
[[POTE generator]]: ~5103/4096 = 380.388  


[[EDO|Vals]]: {{Val list| 60d, 164, 224, 388, 612, 1448, 2060 }}
[[Vals]]: {{Val list| 60d, 164, 224, 388, 612, 1448, 2060 }}


[[Badness]]: 0.061813
[[Badness]]: 0.061813
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Comma list: 3025/3024, 4375/4374, 4296700485/4294967296
Comma list: 3025/3024, 4375/4374, 4296700485/4294967296


Mapping: [<4 0 -11 48 43|, <0 5 16 -29 -23|]
Mapping: [{{val|4 0 -11 48 43}}, {{val|0 5 16 -29 -23}}]


POTE generator: ~22/21 = 80.387 (or ~5103/4096 = 380.387)
POTE generator: ~22/21 = 80.387 (or ~5103/4096 = 380.387)
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Comma list: 2200/2197, 3025/3024, 4375/4374, 468512/468195
Comma list: 2200/2197, 3025/3024, 4375/4374, 468512/468195


Mapping: [<4 0 -11 48 43 11|, <0 5 16 -29 -23 3|]
Mapping: [{{val|4 0 -11 48 43 11}}, {{val|0 5 16 -29 -23 3}}]


POTE generator: ~22/21 = 80.385 (or ~5103/4096 = 380.385)
POTE generator: ~22/21 = 80.385 (or ~5103/4096 = 380.385)
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= Semidimfourth =
= Semidimfourth =
[[Comma]]: |7 41 -31>
The '''semidimifourth''' temperament is featured by a semi-diminished fourth inverval which is [[128/125]] above the pythagorean major third [[81/64]]. In the 7-limit, this temperament tempers out the ragisma and the triwellisma, 235298/234375.


[[Mapping]]: [<1 21 28|, <0 -31 -41|]
[[Comma]]: {{monzo|7 41 -31}}


[[Wedgie]]: <<31 41 -7||
[[Mapping]]: [{{val|1 21 28}}, {{val|0 -31 -41}}]


[[POTE tuning|POTE generator]]: ~162/125 = 448.449
[[POTE generator]]: ~162/125 = 448.449


[[EDO|Vals]]: {{Val list| 8, 91, 99, 190, 289, 388, 487, 677, 875, 966 }}
[[Vals]]: {{Val list| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}


[[Badness]]: 0.233376
[[Badness]]: 0.233376
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[[Comma list]]: 4375/4374, 235298/234375
[[Comma list]]: 4375/4374, 235298/234375


[[Mapping]]: [<1 21 28 36|, <0 -31 -41 -53|]
[[Mapping]]: [{{val|1 21 28 36}}, {{val|0 -31 -41 -53}}]


[[Wedgie]]: <<31 41 53 -7 -3 8||
[[Wedgie]]: {{multival|31 41 53 -7 -3 8}}


[[POTE tuning|POTE generator]]: ~35/27 = 448.456
[[POTE generator]]: ~35/27 = 448.456


[[EDO|Vals]]: {{Val list| 8d, 91, 99, 289, 388, 875, 1263d, 1651d }}
[[Vals]]: {{Val list| 8d, 91, 99, 289, 388, 875, 1263d, 1651d }}


[[Badness]]: 0.055249
[[Badness]]: 0.055249
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Comma list: 3025/3024, 4375/4374, 235298/234375
Comma list: 3025/3024, 4375/4374, 235298/234375


Mapping: [<2 11 15 19 15|, <0 -31 -41 -53 -32|]
Mapping: [{{val|2 11 15 19 15}}, {{val|0 -31 -41 -53 -32}}]


POTE generator: ~12/11 = 151.547
POTE generator: ~12/11 = 151.547
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Comma list: 847/845, 1001/1000, 3025/3024, 4375/4374
Comma list: 847/845, 1001/1000, 3025/3024, 4375/4374


Mapping: [<2 11 15 19 15 17|, <0 -31 -41 -53 -32 -38|]
Mapping: [{{val|2 11 15 19 15 17}}, {{val|0 -31 -41 -53 -32 -38}}]


POTE generator: ~12/11 = 151.545
POTE generator: ~12/11 = 151.545
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[[Comma list]]: 4375/4374, 2202927104/2197265625
[[Comma list]]: 4375/4374, 2202927104/2197265625


[[Mapping]]: [<1 10 11 27|, <0 -32 -33 -92|]
[[Mapping]]: [{{val|1 10 11 27}}, {{val|0 -32 -33 -92}}]


[[Wedgie]]: <<32 33 92 -22 56 121||
[[Wedgie]]: {{multival|32 33 92 -22 56 121}}


[[POTE tuning|POTE generator]]: ~6/5 = 315.557
[[POTE generator]]: ~6/5 = 315.557


[[EDO|Vals]]: {{Val list| 19, 251, 270 }}
[[Vals]]: {{Val list| 19, 251, 270 }}


[[Badness]]: 0.056184
[[Badness]]: 0.056184
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Comma list: 4375/4374, 41503/41472, 172032/171875
Comma list: 4375/4374, 41503/41472, 172032/171875


Mapping: [<1 10 11 27 -16|, <0 -32 -33 -92 74|]
Mapping: [{{val|1 10 11 27 -16}}, {{val|0 -32 -33 -92 74}}]


POTE generator: ~6/5 = 315.558
POTE generator: ~6/5 = 315.558
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Comma list: 676/675, 1001/1000, 4375/4374, 10985/10976
Comma list: 676/675, 1001/1000, 4375/4374, 10985/10976


Mapping: [<1 10 11 27 -16 25|, <0 -32 -33 -92 74 -81|]
Mapping: [{{val|1 10 11 27 -16 25}}, {{val|0 -32 -33 -92 74 -81}}]


POTE generator: ~6/5 = 315.557
POTE generator: ~6/5 = 315.557
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Comma list: 4375/4374, 5632/5625, 117649/117612
Comma list: 4375/4374, 5632/5625, 117649/117612


Mapping: [<1 10 11 27 55|, <0 -32 -33 -92 -196|]
Mapping: [{{val|1 10 11 27 55}}, {{val|0 -32 -33 -92 -196}}]


POTE generator: ~6/5 = 315.553
POTE generator: ~6/5 = 315.553
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Comma list: 676/675, 1716/1715, 4225/4224, 4375/4374
Comma list: 676/675, 1716/1715, 4225/4224, 4375/4374


Mapping: [<1 10 11 27 55 25|, <0 -32 -33 -92 -196 -81|]
Mapping: [{{val|1 10 11 27 55 25}}, {{val|0 -32 -33 -92 -196 -81}}]


POTE generator: ~6/5 = 315.554
POTE generator: ~6/5 = 315.554
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[[Comma list]]: 4375/4374, 201768035/201326592
[[Comma list]]: 4375/4374, 201768035/201326592


[[Mapping]]: [<1 11 19 2|, <0 -35 -62 3|]
[[Mapping]]: [{{val|1 11 19 2}}, {{val|0 -35 -62 3}}]


[[Wedgie]]: <<35 62 -3 17 -103 -181||
[[Wedgie]]: {{multival|35 62 -3 17 -103 -181}}


[[POTE tuning|POTE generator]]: ~3087/2560 = 322.804
[[POTE generator]]: ~3087/2560 = 322.804


[[EDO|Vals]]: {{Val list| 26, 145, 171, 1513d, 1684d, 1855d, 2026d, 2197d, 2368d, 2539d, 2710d }}
[[Vals]]: {{Val list| 26, 145, 171, 1513d, 1684d, 1855d, 2026d, 2197d, 2368d, 2539d, 2710d }}


[[Badness]]: 0.044877
[[Badness]]: 0.044877
Line 725: Line 725:
[[Comma list]]: 4375/4374, 54975581388800/54936068900769
[[Comma list]]: 4375/4374, 54975581388800/54936068900769


[[Mapping]]: [<2 21 36 5|, <0 -29 -51 1|]
[[Mapping]]: [{{val|2 21 36 5}}, {{val|0 -29 -51 1}}]


[[Wedgie]]: <<58 102 -2 27 -166 -291||
[[Wedgie]]: {{multival|58 102 -2 27 -166 -291}}


[[POTE tuning|POTE generator]]: ~8/7 = 231.104
[[POTE generator]]: ~8/7 = 231.104


[[EDO|Vals]]: {{Val list| 26, 244, 270, 836, 1106, 1376, 2482 }}
[[Vals]]: {{Val list| 26, 244, 270, 836, 1106, 1376, 2482 }}


[[Badness]]: 0.040236
[[Badness]]: 0.040236
Line 738: Line 738:
Comma list: 3025/3024, 4375/4374, 5767168/5764801
Comma list: 3025/3024, 4375/4374, 5767168/5764801


Mapping: [<2 21 36 5 2|, <0 -29 -51 1 8|]
Mapping: [{{val|2 21 36 5 2}}, {{val|0 -29 -51 1 8}}]


POTE generator: ~8/7 = 231.103
POTE generator: ~8/7 = 231.103
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Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360
Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360


Mapping: [<2 21 36 5 2 24|, <0 -29 -51 1 8 -27|]
Mapping: [{{val|2 21 36 5 2 24}}, {{val|0 -29 -51 1 8 -27}}]


POTE generator: ~8/7 = 231.103
POTE generator: ~8/7 = 231.103
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