21st-octave temperaments: Difference between revisions
m link, fixes |
Add a strong temperament |
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{{Mapping|legend=2|21 95}} | {{Mapping|legend=2|21 95}} | ||
: | : Mapping generator: ~529/512 = 1\21 | ||
[[Support]]ing [[ET]]s: 21N, N = 1 to 96, largest: [[2016edo]] | [[Support]]ing [[ET]]s: 21N, N = 1 to 96, largest: [[2016edo]] | ||
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{{Mapping|legend=1| 21 0 59 82 | 0 13 -4 -9 }} | {{Mapping|legend=1| 21 0 59 82 | 0 13 -4 -9 }} | ||
: | : Mapping generators: ~403368/390625 = 1\21, ~160/147 | ||
[[Optimal tuning]] ([[CTE]]): ~160/147 = 146.305 | [[Optimal tuning]] ([[CTE]]): ~160/147 = 146.305 | ||
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{{Mapping|legend=1| 21 0 59 82 24 111 114 38 95 | 0 13 -4 -9 19 -13 -11 20 0}} | {{Mapping|legend=1| 21 0 59 82 24 111 114 38 95 | 0 13 -4 -9 19 -13 -11 20 0}} | ||
: | : Mapping generators: ~216/209 = 1\21, ~160/147 | ||
[[Optimal tuning]] ([[CTE]]): ~160/147 = 146. | [[Optimal tuning]] ([[CTE]]): ~160/147 = 146.308{{C}} | ||
[[Support]]ing [[ET]]s: {{EDOs|525, 861h, 1050f, 1911}} | [[Support]]ing [[ET]]s: {{EDOs|525, 861h, 1050f, 1911}} | ||
== Blackmagic == | |||
Blackmagic is the 63 & 84 temperament, merging two systems which cover many large primes.{{Todo|review}} | |||
Subgroup: 2.3.5.7 | |||
Comma list: [[225/224]], {{Monzo|27 1 1 -11}} | |||
{{Mapping|legend=1| 21 0 82 59 | 0 1 -1 0 }} | |||
: Mapping generators: ~16807/16384 = 1\21, ~3 | |||
[[Optimal tuning]] ([[CWE]]): ~3/2 = 701.120{{C}} | |||
{{Optimal ET sequence|legend=1|21, 63, 84, 147}} | |||
=== 2.3.5.7.11.13.23.29.31.43 subgroup === | |||
Subgroup: 2.3.5.7.11.13.23.29.31.43 | |||
Comma list: 155/154, [[225/224]], [[232/231]], [[300/299]], [[364/363]], 560/559, [[640/637]], [[1716/1715]] | |||
{{Mapping|legend=1| 21 0 82 59 106 111 95 102 104 114 | 0 1 -1 0 -1 -1 0 0 0 0 }} | |||
: Mapping generators: ~16807/16384 = 1\21, ~3 | |||
[[Optimal tuning]] ([[CWE]]): ~3/2 = 701.742{{C}} | |||
{{Optimal ET sequence|legend=1|21, 63, 84, 147}} | |||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||