Xenharmonic Wiki

Ragismic microtemperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
No edit summary
Line 348: Line 348:


= Deca =
= Deca =
Deca temperament has a period of 1/10 octave and tempers out the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}} and {{monzo|12 -3 -14 9}} = 165288374272/164794921875 (satritrizo-asepbigu).
[[Comma list]]: 4375/4374, 165288374272/164794921875
[[Comma list]]: 4375/4374, 165288374272/164794921875


[[Mapping]]: [<10 4 9 2|, <0 5 6 11|]
[[Mapping]]: [{{val|10 4 9 2}}, {{val|0 5 6 11}}]


[[Wedgie]]: <<50 60 110 -21 34 87||
[[Wedgie]]: {{multival|50 60 110 -21 34 87}}


[[POTE tuning|POTE generator]]: ~6/5 = 315.577
[[POTE generator]]: ~6/5 = 315.577


[[EDO|Vals]]: {{Val list| 80, 190, 270, 1270, 1540, 1810, 2080 }}
[[Vals]]: {{Val list| 80, 190, 270, 1270, 1540, 1810, 2080 }}


[[Badness]]: 0.080637
[[Badness]]: 0.080637
Line 363: Line 365:
Comma list: 3025/3024, 4375/4374, 422576/421875
Comma list: 3025/3024, 4375/4374, 422576/421875


Mapping: [<10 4 9 2 18|, <0 5 6 11 7|]
Mapping: [{{val|10 4 9 2 18}}, {{val|0 5 6 11 7}}]


POTE generator: ~6/5 = 315.582
POTE generator: ~6/5 = 315.582
Line 374: Line 376:
Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374
Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374


Mapping: [<10 4 9 2 18 37|, <0 5 6 11 7 0|]
Mapping: [{{val|10 4 9 2 18 37}}, {{val|0 5 6 11 7 0}}]


POTE generator: ~6/5 = 315.602
POTE generator: ~6/5 = 315.602
Line 387: Line 389:
[[Comma list]]: 4375/4374, 2100875/2097152
[[Comma list]]: 4375/4374, 2100875/2097152


[[Mapping]]: [<1 -1 -3 6|, <0 17 35 -21|]
[[Mapping]]: [{{val|1 -1 -3 6}}, {{val|0 17 35 -21}}]


[[Wedgie]]: <<17 35 -21 16 -81 -147||
[[Wedgie]]: {{val|17 35 -21 16 -81 -147}}


[[POTE tuning|POTE generator]]: ~10/9 = 182.458
[[POTE generator]]: ~10/9 = 182.458


[[EDO|Vals]]: {{Val list| 46, 125, 171 }}
[[Vals]]: {{Val list| 46, 125, 171 }}


[[Badness]]: 0.025184
[[Badness]]: 0.025184
Line 400: Line 402:
[[Comma list]]: 4375/4374, 64827/64000
[[Comma list]]: 4375/4374, 64827/64000


[[Mapping]]: [<1 2 3 3|, <0 -19 -31 -9|]
[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -19 -31 -9}}]


[[Wedgie]]: <<19 31 9 5 -39 -66||
[[Wedgie]]: {{multival|19 31 9 5 -39 -66}}


[[POTE tuning|POTE generator]]: ~49/48 = 26.287
[[POTE generator]]: ~49/48 = 26.287


[[EDO|Vals]]: {{Val list| 45, 46, 91, 137d }}
[[Vals]]: {{Val list| 45, 46, 91, 137d }}


[[Badness]]: 0.123291
[[Badness]]: 0.123291
Line 413: Line 415:
Comma list: 121/120, 441/440, 4375/4374
Comma list: 121/120, 441/440, 4375/4374


Mapping: [<1 2 3 3 4|, <0 -19 -31 -9 -25|]
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -19 -31 -9 -25}}]


POTE generator: ~49/48 = 26.286
POTE generator: ~49/48 = 26.286
Line 424: Line 426:
Comma list: 121/120, 169/168, 325/324, 441/440
Comma list: 121/120, 169/168, 325/324, 441/440


Mapping: [<1 2 3 3 4 4|, <0 -19 -31 -9 -25 -14|]
Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -19 -31 -9 -25 -14}}]


POTE generator: ~49/48 = 26.310
POTE generator: ~49/48 = 26.310
Line 435: Line 437:
Comma list: 385/384, 2401/2376, 4375/4374
Comma list: 385/384, 2401/2376, 4375/4374


Mapping: [<1 2 3 3 3|, <0 -19 -31 -9 21|]
Mapping: [{{val|1 2 3 3 3}}, {{val|0 -19 -31 -9 21}}]


POTE generator: ~49/48 = 26.246
POTE generator: ~49/48 = 26.246
Line 446: Line 448:
Comma list: 196/195, 364/363, 385/384, 4375/4374
Comma list: 196/195, 364/363, 385/384, 4375/4374


Mapping: [<1 2 3 3 3 3|, <0 -19 -31 -9 21 32|]
Mapping: [{{val|1 2 3 3 3 3}}, {{val|0 -19 -31 -9 21 32}}]


POTE generator: ~49/48 = 26.239
POTE generator: ~49/48 = 26.239
Line 457: Line 459:
[[Comma list]]: 4375/4374, 2147483648/2144153025
[[Comma list]]: 4375/4374, 2147483648/2144153025


[[Mapping]]: [<2 7 13 -1|, <0 -11 -24 19|]
[[Mapping]]: [{{val|2 7 13 -1}}, {{val|0 -11 -24 19}}]


[[Wedgie]]: <<22 48 -38 25 -122 -223||
[[Wedgie]]: {{multival|22 48 -38 25 -122 -223}}


[[POTE tuning|POTE generator]]: ~6912/6125 = 208.899
[[POTE generator]]: ~6912/6125 = 208.899


[[EDO|Vals]]: {{Val list| 46, 132, 178, 224, 270, 494, 764, 1034, 1798 }}
[[Vals]]: {{Val list| 46, 132, 178, 224, 270, 494, 764, 1034, 1798 }}


[[Badness]]: 0.037000
[[Badness]]: 0.037000
Line 470: Line 472:
Comma list: 3025/3024, 4375/4374, 20614528/20588575
Comma list: 3025/3024, 4375/4374, 20614528/20588575


Mapping: [<2 7 13 -1 1|, <0 -11 -24 19 17|]
Mapping: [{{val|2 7 13 -1 1}}, {{val|0 -11 -24 19 17}}]


POTE generator: ~1155/1024 = 208.901
POTE generator: ~1155/1024 = 208.901
Line 481: Line 483:
Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095
Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095


Map: [<2 7 13 -1 1 -2|, <0 -11 -24 19 17 27|]
Mapping: [{{val|2 7 13 -1 1 -2}}, {{val|0 -11 -24 19 17 27}}]


POTE generator: ~44/39 = 208.903
POTE generator: ~44/39 = 208.903
Line 490: Line 492:


= Semidimi =
= Semidimi =
The generator of semidimi temperament is a semi-diminished fourth interval tuned between 162/125 and 35/27. It tempers out 5-limit |-12 -73 55> and 7-limit 3955078125/3954653486, as well as 4375/4374.
The generator of semidimi temperament is a semi-diminished fourth interval tuned between 162/125 and 35/27. It tempers out 5-limit {{monzo|-12 -73 55}} and 7-limit 3955078125/3954653486, as well as 4375/4374.
 
[[Comma]]: |-12 -73 55>


[[Mapping]]: [<1 36 48|, <0 -55 -73|]
[[Comma]]: {{monzo|-12 -73 55}}


[[Wedgie]]: <<55 73 -12||
[[Mapping]]: [{{val|1 36 48}}, {{val|0 -55 -73}}]


[[POTE tuning|POTE generator]]: ~162/125 = 449.1269
[[POTE generator]]: ~162/125 = 449.1269


[[EDO|Vals]]: {{Val list| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
[[Vals]]: {{Val list| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


[[Badness]]: 0.754866
[[Badness]]: 0.754866
Line 507: Line 507:
[[Comma list]]: 4375/4374, 3955078125/3954653486
[[Comma list]]: 4375/4374, 3955078125/3954653486


[[Mapping]]: [<1 36 48 61|, <0 -55 -73 -93|]
[[Mapping]]: [{{val|1 36 48 61}}, {{val|0 -55 -73 -93}}]


[[Wedgie]]: <<55 73 93 -12 -7 11||
[[Wedgie]]: {{multival|55 73 93 -12 -7 11}}


[[POTE tuning|POTE generator]]: ~35/27 = 449.1270
[[POTE generator]]: ~35/27 = 449.1270


[[EDO|Vals]]: {{Val list| 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
[[Vals]]: {{Val list| 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


[[Badness]]: 0.015075
[[Badness]]: 0.015075


= Brahmagupta =
= Brahmagupta =
The brahmagupta temperament has a period of 1/7 octave, tempering out the [[akjaysma]], |47 -7 -7 -7> = 140737488355328 / 140710042265625.
The brahmagupta temperament has a period of 1/7 octave, tempering out the [[akjaysma]], {{monzo|47 -7 -7 -7}} = 140737488355328 / 140710042265625.


[[Comma list]]: 4375/4374, 70368744177664/70338939985125
[[Comma list]]: 4375/4374, 70368744177664/70338939985125


[[Mapping]]: [<7 2 -8 53|, <0 3 8 -11|]
[[Mapping]]: [{{val|7 2 -8 53}}, {{val|0 3 8 -11}}]


[[Wedgie]]: <<21 56 -77 40 -181 -336||
[[Wedgie]]: {{multival|21 56 -77 40 -181 -336}}


[[POTE tuning|POTE generator]]: ~27/20 = 519.716
[[POTE generator]]: ~27/20 = 519.716


[[EDO|Vals]]: {{Val list| 7, 217, 224, 441, 1106, 1547 }}
[[Vals]]: {{Val list| 7, 217, 224, 441, 1106, 1547 }}


[[Badness]]: 0.029122
[[Badness]]: 0.029122
Line 535: Line 535:
Comma list: 4000/3993, 4375/4374, 131072/130977
Comma list: 4000/3993, 4375/4374, 131072/130977


Mapping: [<7 2 -8 53 3|, <0 3 8 -11 7|]
Mapping: [{{val|7 2 -8 53 3}}, {{val|0 3 8 -11 7}}]


POTE generator: ~27/20 = 519.704
POTE generator: ~27/20 = 519.704
Line 546: Line 546:
Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374
Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374


Mapping: [<7 2 -8 53 3 35|, <0 3 8 -11 7 -3|]
Mapping: [{{val|7 2 -8 53 3 35}}, {{val|0 3 8 -11 7 -3}}]


POTE generator: ~27/20 = 519.706
POTE generator: ~27/20 = 519.706
Retrieved from "https://en.xen.wiki/w/Ragismic_microtemperaments"