21st-octave temperaments: Difference between revisions
Add a strong temperament |
→Blackmagic: note primes 17 and 19, etymology |
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== Blackmagic == | == Blackmagic == | ||
Blackmagic is the 63 & 84 temperament, merging two systems which cover many large primes.{{Todo|review}} | Blackmagic is the 63 & 84 temperament, merging two systems which cover many large primes. It was named by [[User:Overthink|Overthink]] in 2026 as a twist on "blackjack" (which itself already refers to the 21-note [[MOS scale|mos]] of [[miracle]]), as well as because of its higher-limit properties. {{Todo|review}} | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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{{Optimal ET sequence|legend=1|21, 63, 84, 147}} | {{Optimal ET sequence|legend=1|21, 63, 84, 147}} | ||
[[Badness]] (Sintel): 5.605 | |||
=== 2.3.5.7.11.13.23.29.31.43 subgroup === | === 2.3.5.7.11.13.23.29.31.43 subgroup === | ||
Primes 17 and 19 could be included by mapping them to -1 and 1 generators respectively, though in practice this mapping only works in [[84edo]]. | |||
Subgroup: 2.3.5.7.11.13.23.29.31.43 | Subgroup: 2.3.5.7.11.13.23.29.31.43 | ||
Comma list: 155/154, | 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|legend=1| 21 0 82 59 106 111 95 102 104 114 | 0 1 -1 0 -1 -1 0 0 0 0 }} | ||
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: Mapping generators: ~16807/16384 = 1\21, ~3 | : Mapping generators: ~16807/16384 = 1\21, ~3 | ||
Optimal tuning ([[CWE]]): ~3/2 = 701.742{{C}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0|21, 63, 84, 147}} | ||
Badness (Sintel): 1.317 | |||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||