Ragismic microtemperaments: Difference between revisions
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== | == Monzismic == | ||
{{See also| Very high accuracy temperaments #Monzismic }} | |||
The ''monzismic'' temperament (53&612) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}, and in the 7-limit, the [[nanisma]], {{monzo| 109 -67 0 -1 }}, as well as the ragisma, [[4375/4374]]. | |||
[[ | [[Subgroup]]: 2.3.5.7 | ||
[[ | [[Comma list]]: 4375/4374, {{monzo| -55 30 2 1 }} | ||
[[ | [[Mapping]]: [{{val| 1 2 10 -25 }}, {{val| 0 -2 -37 134 }}] | ||
{{Multival|legend=1| 2 37 -134 54 -218 -415 }} | |||
{{Val list|legend=1| 53, 559, 612, 1277, 1889 }} | [[Optimal tuning]] ([[POTE]]): ~310078125/268435456 = 249.0207 | ||
{{Val list|legend=1| 53, …, 559, 612, 1277, 1889 }} | |||
[[Badness]]: 0.046569 | [[Badness]]: 0.046569 | ||
=== | === Monzism === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 4375/4374, 41503/41472, 184549376/184528125 | Comma list: 4375/4374, 41503/41472, 184549376/184528125 | ||
Mapping: [{{val|1 2 10 -25 46}}, {{val|0 -2 -37 134 -205}}] | Mapping: [{{val| 1 2 10 -25 46 }}, {{val| 0 -2 -37 134 -205 }}] | ||
POTE | Optimal tuning (POTE): ~231/200 = 249.0193 | ||
Optimal GPV sequence: {{Val list| 53, 559, 612 }} | Optimal GPV sequence: {{Val list| 53, 559, 612 }} | ||
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Badness: 0.057083 | Badness: 0.057083 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625 | Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625 | ||
Mapping: [{{val|1 2 10 -25 46 23}}, {{val|0 -2 -37 134 -205 -93}}] | Mapping: [{{val| 1 2 10 -25 46 23 }}, {{val| 0 -2 -37 134 -205 -93 }}] | ||
POTE | Optimal tuning (POTE): ~231/200 = 249.0199 | ||
Optimal GPV sequence: {{Val list| 53, 559, 612 }} | Optimal GPV sequence: {{Val list| 53, 559, 612 }} | ||