20th-octave temperaments: Difference between revisions
→19-limit: facts |
→Soviet Ferris wheel: +5-limit, +7-limit |
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== Soviet Ferris wheel == | == Soviet Ferris wheel == | ||
Defined as the 320 & 460 temperament, and named because it's a period-20 temperament, and there are 20 cabins on a standard ferris wheel found throughout most of Eastern Europe and Central Asia (as in abandoned Pripyat wheel, for example). | Defined as the 320 & 460 temperament, and named because it's a period-20 temperament, and there are 20 cabins on a standard ferris wheel found throughout most of Eastern Europe and Central Asia (as in abandoned Pripyat wheel, for example). | ||
Subgroup: 2.3.5 | |||
Comma list: {{monzo|-171 20 60}} | |||
Mapping: {{val|20 0 57}}, {{val|0 3 -1}} | |||
Mapping generators: ~{{monzo|77 -9 -27}} = 1\20, ~208568572998046875/144115188075855872 = 633.970 | |||
Optimal tuning (CTE): ~208568572998046875/144115188075855872 = 633.970 | |||
Vals: {{EDOs|40, 140, 180, 320, 460, 600, 740, 780, 1060, 1240, 1520}}, ... | |||
=== 7-limit === | |||
Subgroup: 2.3.5.7 | |||
Comma list: 65625/65536, 1977326743/1968300000 | |||
Mapping: {{val|20 0 57 35}}, {{val|0 3 -1 2}} | |||
Mapping generators: ~16807/16200 = 1\20, ~3456/2401 = 634.023 | |||
Optimal tuning (CTE): ~3456/2401 = 634.023 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Vals: {{EDOs|140, 320, 460}} | Vals: {{EDOs|140, 320, 460}} | ||
==Calcium== | ==Calcium== | ||
A highly precise and high-limit 2000 & 2460 temperament, named after the 20th element following the convention of naming some fractional-octave temperaments after chemical elements. | A highly precise and high-limit 2000 & 2460 temperament, named after the 20th element following the convention of naming some fractional-octave temperaments after chemical elements. | ||