Ragismic microtemperaments: Difference between revisions
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== Deca == | == Deca == | ||
Deca temperament has a period of 1/10 octave and tempers out the [[15/14ths equal temperament #Linus temperaments|linus comma]], {{monzo|11 -10 -10 10}} and {{monzo|12 -3 -14 9}} = 165288374272/164794921875 (satritrizo-asepbigu). | Deca temperament has a period of 1/10 octave and tempers out the [[15/14ths equal temperament #Linus temperaments|linus comma]], {{monzo|11 -10 -10 10}} and {{monzo|12 -3 -14 9}} = 165288374272/164794921875 (satritrizo-asepbigu). | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== 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 {{monzo|-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. | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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== Brahmagupta == | == Brahmagupta == | ||
The brahmagupta temperament has a period of 1/7 octave, tempering out the [[akjaysma]], {{monzo|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. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Semidimfourth == | == Semidimfourth == | ||
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. | 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. | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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Aside from the ragisma, the seniority temperament (26&145) tempers out the wadisma, 201768035/201326592. It is so named because the senior comma ({{monzo|-17 62 -35}}, quadla-sepquingu) is tempered out. | Aside from the ragisma, the seniority temperament (26&145) tempers out the wadisma, 201768035/201326592. It is so named because the senior comma ({{monzo|-17 62 -35}}, quadla-sepquingu) is tempered out. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Chlorine temperament has a period of 1/17 octave. It tempers out the septendecima, {{monzo|-52 -17 34}}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289&323 temperament, which tempers out {{monzo|-49 4 22 -3}} as well as the ragisma. | Chlorine temperament has a period of 1/17 octave. It tempers out the septendecima, {{monzo|-52 -17 34}}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289&323 temperament, which tempers out {{monzo|-49 4 22 -3}} as well as the ragisma. | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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Palladium temperament has a period of 1/46 octave. It tempers out the 46-9/5-comma, {{monzo|-39 92 -46}}, by which 46 minortones (10/9) fall short of seven octaves. This temperament can be described as 46&414 temperament, which tempers out {{monzo|-51 8 2 12}} as well as the ragisma. | Palladium temperament has a period of 1/46 octave. It tempers out the 46-9/5-comma, {{monzo|-39 92 -46}}, by which 46 minortones (10/9) fall short of seven octaves. This temperament can be described as 46&414 temperament, which tempers out {{monzo|-51 8 2 12}} as well as the ragisma. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Monzism == | == Monzism == | ||
The ''monzism'' temperament (53&612) 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) 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]]. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Badness: 0.053780 | Badness: 0.053780 | ||
== Quindro == | |||
The ''quindro'' temperament (205&217) is an extension of the [[28ed5 #Regular temperaments|''quindromeda'' temperament]] which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079). | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4375/4374, 72057594037927936/71489976421753125 | |||
[[Mapping]]: [{{val|1 2 0 15}}, {{val|0 -5 28 -147}}] | |||
{{Multival|legend=1| 5 -28 147 -56 219 420 }} | |||
[[POTE generator]]: ~4428675/4194304 = 99.529 | |||
{{Val list|legend=1| 205, 217, 422, 639, 1061 }} | |||
[[Badness]]: 0.316850 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 4375/4374, 5632/5625, 25165824/25109315 | |||
Mapping: [{{val|1 2 0 15 -5}}, {{val|0 -5 28 -147 102}}] | |||
POTE generator: ~17325/16384 = 99.529 | |||
Vals: {{Val list| 205, 217, 422, 639, 1061e }} | |||
Badness: 0.085219 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 2080/2079, 4375/4374, 5632/5625, 20480/20449 | |||
Mapping: [{{val|1 2 0 15 -5 11}}, {{val|0 -5 28 -147 102 -88}}] | |||
POTE generator: ~4096/3861 = 99.529 | |||
Vals: {{Val list| 205, 217, 422, 639, 1061ef }} | |||
Badness: 0.039203 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 1156/1155, 2080/2079, 2431/2430, 4375/4374, 5632/5625 | |||
Mapping: [{{val|1 2 0 15 -5 11 5}}, {{val|0 -5 28 -147 102 -88 -11}}] | |||
POTE generator: ~18/17 = 99.529 | |||
Vals: {{Val list| 205, 217, 422, 639, 1061ef }} | |||
Badness: 0.024110 | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 1156/1155, 1216/1215, 1445/1444, 2080/2079, 2376/2375, 2431/2430 | |||
Mapping: [{{val|1 2 0 15 -5 11 5 4}}, {{val|0 -5 28 -147 102 -88 -11 3}}] | |||
POTE generator: ~18/17 = 99.529 | |||
Vals: {{Val list| 205, 217, 422, 639h, 1061efh }} | |||
Badness: 0.016764 | |||
[[Category:Abigail]] | [[Category:Abigail]] | ||