Alphatricot family: Difference between revisions
m Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}" |
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[[Badness]] (Smith): 0.046093 | [[Badness]] (Smith): 0.046093 | ||
; Scales | |||
* [[Alphatricot17]] – proper [[2L 15s]] | |||
* [[Alphatricot19]] – improper [[17L 2s]] | |||
=== 2.3.5.13 subgroup === | === 2.3.5.13 subgroup === | ||
{{See also| No-fives subgroup temperaments #Threedic }} | {{See also| No-fives subgroup temperaments #Threedic }} | ||
This extension identifies the generator with [[13/9]] by tempering out the threedie, [[2197/2187]], providing a relatively low-complexity mapping for 13. | |||
Subgroup: 2.3.5.13 | Subgroup: 2.3.5.13 | ||
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Comma list: 2197/2187, 41067/40960 | Comma list: 2197/2187, 41067/40960 | ||
Mapping: {{mapping| 1 0 -13 0 | 0 3 29 7 }} | |||
Optimal tunings: | Optimal tunings: | ||
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{{Optimal ET sequence|legend=0| 17c, 36c, 53 }} | {{Optimal ET sequence|legend=0| 17c, 36c, 53 }} | ||
Badness (Dirichlet): 1.262 | |||
=== Catatricot === | |||
However, alphatricot in the 5-limit is far more accurate than threedic. Catatricot interprets the generator as ~[[75/52]] instead of 13/9, making the far more accurate tempering of [[140625/140608]], the catasma, instead of the threedie. It also tempers out [[256000/255879]], the phaotisma. | |||
Subgroup: 2.3.5.13 | |||
Comma list: 140628/140625, 256000/255879 | |||
Mapping: {{mapping| 1 0 -13 -28 | 0 3 29 60 }} | |||
* | |||
* | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~75/52 = 634.009 | |||
* POTE: ~2 = 1200.000, ~75/52 = 634.0108 | |||
{{Optimal ET sequence|legend=1| 17cff, 36cff, 53, 282, 335, 388, 441, 494, 935 }} | |||
Badness (Dirichlet): 0.181 | |||
== Alphatrillium == | == Alphatrillium == | ||