Ragismic microtemperaments: Difference between revisions

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* ''[[Quindro]]'', {4375/4374, {{monzo| 56 -28 -5 }}} → [[Quindromeda family #Quindro|Quindromeda family]]
* ''[[Quindro]]'', {4375/4374, {{monzo| 56 -28 -5 }}} → [[Quindromeda family #Quindro|Quindromeda family]]


Microtemperaments considered below are ennealimmal, supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, seniority, monzismic, semidimfourth, acrokleismic, quasithird, chlorine, deca, keenanose, quatracot, and palladium.  
Microtemperaments considered below are ennealimmal, supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, quatracot, and palladium.  


Some near-microtemperaments are appended as octoid, amity, parakleismic, counterkleismic, quincy, sfourth, and trideci.  
Some near-microtemperaments are appended as octoid, amity, parakleismic, counterkleismic, quincy, sfourth, and trideci.  
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Badness: 0.021762
Badness: 0.021762
== Chlorine ==
The name of chlorine temperament comes from Chlorine, the 17th element.
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. Not only the semitwelfth, but also the ~5/4 can be used as a generator.
Subgroup: 2.3.5
[[Comma]]: {{monzo| -52 -17 34 }}
[[Mapping]]: [{{val| 17 0 26 }}, {{val| 0 2 1 }}]
Mapping generators: ~25/24, ~{{monzo| 26 9 -17 }}
[[POTE generator]]: ~{{monzo| 26 9 -17 }} = 950.9746
{{Val list|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}
[[Badness]]: 0.077072
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 4375/4374, 193119049072265625/193091834023510016
[[Mapping]]: [{{val| 17 0 26 -87 }}, {{val| 0 2 1 10 }}]
{{Multival|legend=1| 34 17 170 -52 174 347 }}
[[POTE generator]]: ~822083584/474609375 = 950.9995
{{Val list|legend=1| 289, 323, 612, 935, 1547 }}
[[Badness]]: 0.041658
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
Mapping: [{{val| 17 0 26 -87 207 }}, {{val| 0 2 1 10 -11 }}]
POTE generators: ~822083584/474609375 = 950.9749
Optimal GPV sequence: {{Val list| 289, 323, 612 }}
Badness: 0.063706


== Seniority ==
== Seniority ==
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Badness: 0.029501
Badness: 0.029501
== Chlorine ==
The name of chlorine temperament comes from Chlorine, the 17th element.
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. Not only the semitwelfth, but also the ~5/4 can be used as a generator.
Subgroup: 2.3.5
[[Comma]]: {{monzo| -52 -17 34 }}
[[Mapping]]: [{{val| 17 0 26 }}, {{val| 0 2 1 }}]
Mapping generators: ~25/24, ~{{monzo| 26 9 -17 }}
[[POTE generator]]: ~{{monzo| 26 9 -17 }} = 950.9746
{{Val list|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}
[[Badness]]: 0.077072
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 4375/4374, 193119049072265625/193091834023510016
[[Mapping]]: [{{val| 17 0 26 -87 }}, {{val| 0 2 1 10 }}]
{{Multival|legend=1| 34 17 170 -52 174 347 }}
[[POTE generator]]: ~822083584/474609375 = 950.9995
{{Val list|legend=1| 289, 323, 612, 935, 1547 }}
[[Badness]]: 0.041658
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
Mapping: [{{val| 17 0 26 -87 207 }}, {{val| 0 2 1 10 -11 }}]
POTE generators: ~822083584/474609375 = 950.9749
Optimal GPV sequence: {{Val list| 289, 323, 612 }}
Badness: 0.063706


== Deca ==
== Deca ==