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Ragismic microtemperaments: Difference between revisions

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[[Comma list]]: 4375/4374, 1483154296875/1473173782528
[[Comma list]]: 4375/4374, 1483154296875/1473173782528


[[Mapping]]: [<2 7 7 23|, <0 -13 -8 -59|]
[[Mapping]]: [{{val|2 7 7 23}}, {{val|0 -13 -8 -59}}]


[[Wedgie]]: <<26 16 118 -35 114 229||
[[Wedgie]]: {{multival|26 16 118 -35 114 229}}


[[POTE tuning|POTE generator]]: ~448/405 = 176.805
[[POTE generator]]: ~448/405 = 176.805


[[EDO|Vals]]: {{Val list| 190, 224, 414, 638, 1052c, 1690bcc }}
[[Vals]]: {{Val list| 190, 224, 414, 638, 1052c, 1690bcc }}


[[Badness]]: 0.175982
[[Badness]]: 0.175982
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Comma list: 3025/3024, 4375/4374, 1265625/1261568
Comma list: 3025/3024, 4375/4374, 1265625/1261568


Mapping: [<2 7 7 23 19|, <0 -13 -8 -59 -41|]
Mapping: [{{val|2 7 7 23 19}}, {{val|0 -13 -8 -59 -41}}]


POTE generator: ~448/405 = 176.806
POTE generator: ~448/405 = 176.806
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Comma list: 625/624, 729/728, 1575/1573, 2200/2197
Comma list: 625/624, 729/728, 1575/1573, 2200/2197


Mapping: [<2 7 7 23 19 13|, <0 -13 -8 -59 -41 -19|]
Mapping: [{{val|2 7 7 23 19 13}}, {{val|0 -13 -8 -59 -41 -19}}]


POTE generator: ~195/176 = 176.804
POTE generator: ~195/176 = 176.804
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= Octoid =
= Octoid =
The '''octoid''' temperament has a period of 1/8 octave and tempers out 4375/4374 ([[4375/4374|ragisma]]) and 16875/16807 ([[16875/16807|mirkwai]]). In the 11-limit, it tempers out 540/539, 1375/1372, and 6250/6237. In this temperament, one period gives both 12/11 and 49/45, two gives 25/21, three gives 35/27, and four gives both 99/70 and 140/99.
[[Comma list]]: 4375/4374, 16875/16807
[[Comma list]]: 4375/4374, 16875/16807


Line 800: Line 802:
* strict range:  [582.512, 584.359]
* strict range:  [582.512, 584.359]


[[Mapping]]: [<8 1 3 3|, <0 3 4 5|]
[[Mapping]]: [{{val|8 1 3 3}}, {{val|0 3 4 5}}]


[[Wedgie]]: <<24 32 40 -5 -4 3||
[[Wedgie]]: {{multival|24 32 40 -5 -4 3}}


Mapping generators: ~49/45, ~7/5
Mapping generators: ~49/45, ~7/5


[[POTE tuning|POTE generator]]: ~7/5 = 583.940
[[POTE generator]]: ~7/5 = 583.940


[[EDO|Vals]]: {{Val list| 8d, 72, 152, 224 }}
[[Vals]]: {{Val list| 8d, 72, 152, 224 }}


[[Badness]]: 0.042670
[[Badness]]: 0.042670
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* strict range: [582.512, 585.084]
* strict range: [582.512, 585.084]


Mapping: [<8 1 3 3 16|, <0 3 4 5 3|]
Mapping: [{{val|8 1 3 3 16}}, {{val|0 3 4 5 3}}]


POTE generator: ~7/5 = 583.962
POTE generator: ~7/5 = 583.962
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Comma list: 540/539, 1375/1372, 4000/3993, 625/624
Comma list: 540/539, 1375/1372, 4000/3993, 625/624


Mapping: [<8 1 3 3 16 -21|, <0 3 4 5 3 13|]
Mapping: [{{val|8 1 3 3 16 -21}}, {{val|0 3 4 5 3 13}}]


POTE generator: ~7/5 = 583.905
POTE generator: ~7/5 = 583.905
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=== Music ===
=== Music ===
* [http://www.archive.org/details/Dreyfus http://www.archive.org/details/Dreyfus]
* [http://www.archive.org/details/Dreyfus http://www.archive.org/details/Dreyfus] [http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play]
* [http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play]


== Octopus ==
== Octopus ==
Comma list: 169/168, 325/324, 364/363, 540/539
Comma list: 169/168, 325/324, 364/363, 540/539


Mapping: [<8 1 3 3 16 14|, <0 3 4 5 3 4|]
Mapping: [{{val|8 1 3 3 16 14}}, {{val|0 3 4 5 3 4}}]


POTE generator: ~7/5 = 583.892
POTE generator: ~7/5 = 583.892
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{{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&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, {{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.


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)^(1/13), which gives pure major thirds.
Line 864: Line 865:
[[Comma]]: 1600000/1594323
[[Comma]]: 1600000/1594323


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


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


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


[[Badness]]: 0.021960
[[Badness]]: 0.021960
Line 875: Line 876:
[[Comma list]]: 4375/4374, 5120/5103
[[Comma list]]: 4375/4374, 5120/5103


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


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


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


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


[[Badness]]: 0.023649
[[Badness]]: 0.023649
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Comma list: 540/539, 4375/4374, 5120/5103
Comma list: 540/539, 4375/4374, 5120/5103


Mapping: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]
Mapping: [{{val|1 3 6 -2 21}}, {{val|0 -5 -13 17 -62}}]


POTE generator: ~128/105 = 339.464
POTE generator: ~128/105 = 339.464
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Comma list: 352/351, 540/539, 625/624, 847/845
Comma list: 352/351, 540/539, 625/624, 847/845


Mapping: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]
Mapping: [{{val|1 3 6 -2 21 17}}, {{val|0 -5 -13 17 -62 -47}}]


POTE generator: ~128/105 = 339.481
POTE generator: ~128/105 = 339.481
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Comma list: 121/120, 176/175, 2200/2187
Comma list: 121/120, 176/175, 2200/2187


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


POTE generator: ~11/9 = 339.390
POTE generator: ~11/9 = 339.390
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Comma list: 121/120, 169/168, 176/175, 325/324
Comma list: 121/120, 169/168, 176/175, 325/324


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


POTE generator: ~11/9 = 339.419
POTE generator: ~11/9 = 339.419
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Comma list: 3025/3024, 4375/4374, 5120/5103
Comma list: 3025/3024, 4375/4374, 5120/5103


Mapping: [<2 1 -1 13 13|, <0 5 13 -17 -14|]
Mapping: [{{val|2 1 -1 13 13}}, {{val|0 5 13 -17 -14}}]


POTE generator: ~64/55 = 339.439
POTE generator: ~64/55 = 339.439
Line 1,059: Line 1,060:
[[Comma list]]: 4375/4374, 823543/819200
[[Comma list]]: 4375/4374, 823543/819200


[[Mapping]]: [<1 2 3 3|, <0 -30 -49 -14|]
[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -30 -49 -14}}]


[[Wedgie]]: <<30 49 14 8 -62 -105||
[[Wedgie]]: {{multival|30 49 14 8 -62 -105}}


[[POTE tuning|POTE generator]]: ~1728/1715 = 16.613
[[POTE generator]]: ~1728/1715 = 16.613


[[EDO|Vals]]: {{Val list| 72, 217, 289 }}
[[Vals]]: {{Val list| 72, 217, 289 }}


[[Badness]]: 0.079657
[[Badness]]: 0.079657
Line 1,072: Line 1,073:
Comma list: 441/440, 4000/3993, 4375/4374
Comma list: 441/440, 4000/3993, 4375/4374


Mapping: [<1 2 3 3 4|, <0 -30 -49 -14 -39|]
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -30 -49 -14 -39}}]


POTE generator: ~100/99 = 16.613
POTE generator: ~100/99 = 16.613
Line 1,083: Line 1,084:
Comma list: 364/363, 441/440, 676/675, 4375/4374
Comma list: 364/363, 441/440, 676/675, 4375/4374


Mapping: [<1 2 3 3 4 5|, <0 -30 -49 -14 -39 -94|]
Mapping: [{{val|1 2 3 3 4 5}}, {{val|0 -30 -49 -14 -39 -94}}]


POTE generator: ~100/99 = 16.602
POTE generator: ~100/99 = 16.602
Line 1,094: Line 1,095:
Comma list: 364/363, 441/440, 595/594, 676/675, 1156/1155
Comma list: 364/363, 441/440, 595/594, 676/675, 1156/1155


Mapping: [<1 2 3 3 4 5 5|, <0 -30 -49 -14 -39 -94 -66|]
Mapping: [{{val|1 2 3 3 4 5 5}}, {{val|0 -30 -49 -14 -39 -94 -66}}]


POTE generator: ~100/99 = 16.602
POTE generator: ~100/99 = 16.602
Line 1,105: Line 1,106:
Comma list: 343/342, 364/363, 441/440, 476/475, 595/594, 676/675
Comma list: 343/342, 364/363, 441/440, 476/475, 595/594, 676/675


Mapping: [<1 2 3 3 4 5 5 4|, <0 -30 -49 -14 -39 -94 -66 18|]
Mapping: [{{val|1 2 3 3 4 5 5 4}}, {{val|0 -30 -49 -14 -39 -94 -66 18}}]


POTE generator: ~100/99 = 16.594
POTE generator: ~100/99 = 16.594
Line 1,124: Line 1,125:
[[POTE tuning|POTE generators]]: ~25/24 = 70.5882, ~5/4 = 386.2687
[[POTE tuning|POTE generators]]: ~25/24 = 70.5882, ~5/4 = 386.2687


[[EDO|Vals]]: {{Val list| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}
[[Vals]]: {{Val list| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}


[[Badness]]: 0.077072
[[Badness]]: 0.077072
Line 1,137: Line 1,138:
[[POTE tuning|POTE generators]]: ~25/24 = 70.5882, ~5/4 = 386.2936
[[POTE tuning|POTE generators]]: ~25/24 = 70.5882, ~5/4 = 386.2936


[[EDO|Vals]]: {{Val list| 289, 323, 612, 935, 1547 }}
[[Vals]]: {{Val list| 289, 323, 612, 935, 1547 }}


[[Badness]]: 0.041658
[[Badness]]: 0.041658
Line 1,163: Line 1,164:
[[Wedgie]]: {{multival|46 92 -46 39 -202 -365}}
[[Wedgie]]: {{multival|46 92 -46 39 -202 -365}}


[[POTE tuning|POTE generator]]: ~3/2 = 701.6074
[[POTE generator]]: ~3/2 = 701.6074


[[EDO|Vals]]: {{Val list| 46, 368, 414, 460, 874d }}
[[Vals]]: {{Val list| 46, 368, 414, 460, 874d }}


[[Badness]]: 0.308505
[[Badness]]: 0.308505
Line 1,205: Line 1,206:
The ''monzism'' temperament (53&612, named by [[User:Xenllium|Xenllium]]) is a rank-two temperament which tempers out the [[monzisma]], {{monzo|54 -37 2}} and the [[nanisma]], {{monzo|109 -67 0 -1}}, as well as the ragisma, [[4375/4374]].  
The ''monzism'' temperament (53&612, named by [[User:Xenllium|Xenllium]]) is a rank-two temperament which tempers out the [[monzisma]], {{monzo|54 -37 2}} and the [[nanisma]], {{monzo|109 -67 0 -1}}, as well as the ragisma, [[4375/4374]].  


[[Comma list]]: 4375/4374, {{monzo|-55 30 2 1}}
[[Comma list]]: 4375/4374, 36030948116563575/36028797018963968


[[Mapping]]: [<1 2 10 -25|, <0 -2 -37 134|]
[[Mapping]]: [{{val|1 2 10 -25}}, {{val|0 -2 -37 134}}]


[[Wedgie]]: <<2 37 -134 54 -218 -415||
[[Wedgie]]: {{multival|2 37 -134 54 -218 -415}}


[[POTE tuning|POTE generator]]: ~310078125/268435456 = 249.0207
[[POTE generator]]: ~310078125/268435456 = 249.0207


[[EDO|Vals]]: {{Val list| 53, 559, 612, 1277, 1889 }}
[[Vals]]: {{Val list| 53, 559, 612, 1277, 1889 }}


[[Badness]]: 0.046569
[[Badness]]: 0.046569
Line 1,220: Line 1,221:
Comma list: 4375/4374, 41503/41472, 184549376/184528125
Comma list: 4375/4374, 41503/41472, 184549376/184528125


Mapping: [<1 2 10 -25 46|, <0 -2 -37 134 -205|]
Mapping: [{{val|1 2 10 -25 46}}, {{val|0 -2 -37 134 -205}}]


POTE generator: ~231/200 = 249.0193
POTE generator: ~231/200 = 249.0193
Line 1,231: Line 1,232:
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625


Mapping: [<1 2 10 -25 46 23|, <0 -2 -37 134 -205 -93|]
Mapping: [{{val|1 2 10 -25 46 23}}, {{val|0 -2 -37 134 -205 -93}}]


POTE generator: ~231/200 = 249.0199
POTE generator: ~231/200 = 249.0199
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