25th-octave temperaments: Difference between revisions
Created page with "{{Fractional-octave navigation|25}} == Manganese == ''Manganese'' is the simplest 5-limit 25th-octave temperament by TE simple badness at 0.1 cent error <ref>http://x31eq..." |
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=== Semimanganese === | === Semimanganese === | ||
While manganese is a rather bulky temperament, splitting the generator in half lends itself to a high-limit interpretaton, which can be described as the 525 & 2000 temperament. | While manganese is a rather bulky temperament, splitting the generator in half lends itself to a high-limit interpretaton, which can be described as the 525 & 2000 temperament. | ||
==== 23-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17.19.23 | |||
Comma list: 4096/4095, 6175/6174, 8625/8624, 10626/10625, 14400/14399, 67392/67375, 89376/89375 | |||
{{Mapping|legend=1| 25 2 43 89 15 164 121 46 162 | 0 10 4 -5 19 -19 -5 16 -13 }} | |||
: mapping generators: ~3213/3125 = 1\25, ~272/245 = 180.598 | |||
[[Optimal tuning]] ([[CTE]]): ~272/245 = 180.598 | |||
[[Support]]ing [[ET]]s: {{EDOs|525, 1475, 2000, 2525, 3475}} | |||
== References == | == References == | ||
Revision as of 21:44, 22 October 2023
Template:Fractional-octave navigation
Manganese
Manganese is the simplest 5-limit 25th-octave temperament by TE simple badness at 0.1 cent error [1].
Subgroup: 2.3.5
Comma list: [211 50 -125⟩
Mapping: [⟨25 2 43], ⟨0 5 2]]
- mapping generators: ~[76 18 -45⟩ = 1\25, ~[54 13 -32⟩ = 361.189
Optimal tuning (CTE): ~[54 13 -32⟩ = 361.189
Supporting ETs: 525, 1000, ...
Semimanganese
While manganese is a rather bulky temperament, splitting the generator in half lends itself to a high-limit interpretaton, which can be described as the 525 & 2000 temperament.
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 4096/4095, 6175/6174, 8625/8624, 10626/10625, 14400/14399, 67392/67375, 89376/89375
Mapping: [⟨25 2 43 89 15 164 121 46 162], ⟨0 10 4 -5 19 -19 -5 16 -13]]
- mapping generators: ~3213/3125 = 1\25, ~272/245 = 180.598
Optimal tuning (CTE): ~272/245 = 180.598
Supporting ETs: 525, 1475, 2000, 2525, 3475