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== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit results in the rank-6 '''fidesmic''' temperament, or in the the 3.5.7.17 subgroup, the rank-3 '''fidic''' temperament. | Tempering out this comma in the 17-limit results in the rank-6 '''fidesmic''' temperament, or in the the 3.5.7.17 subgroup, the rank-3 '''fidic''' temperament. | ||
=== Fidic === | |||
[[Subgroup]]: 2.3.5.7.17 | |||
{{Mapping|legend=2| 1 0 0 2 | 0 1 0 1 | 0 0 2 -1 }} | |||
: mapping generators: ~3, ~5, ~45/17 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~3 = 1901.8290{{c}}, ~5/3 = 884.3495{{c}}, ~45/17 = 1684.4623{{c}} | |||
* [[CWE]]: ~3 = 1901.9550{{c}}, ~5/3 = 884.3084{{c}}, ~45/17 = 1684.5363{{c}} | |||
[[Optimal ET sequence]]: [[17edt|b17]], [[26edt|b26]], [[62edt|b62]], [[88edt|b88]], [[114edt|b114]], [[245edt|b245]], [[271edt|b271]], [[385edt|b385]], [[630edt|b630]], [[656edt|b656]], [[1015edt|b1015]], [[1400edt|b1400g]], [[2415edt|b2415g]], [[2686edt|b2686gg]], [[3071edt|b3071dgg]] | |||
[[Badness]] (Sintel): 0.0269 | |||
=== Fidesmic === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Mapping]]:<br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 2 || 0 || 0 || -1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | |||
|} | |||
: mapping generators: ~2, ~3, ~5, ~45/17, ~11, ~13 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8290{{c}}, ~5/4 = 386.1785{{c}}, ~45/34 = 484.4623{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5276{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8290{{c}}, ~5/4 = 386.1785{{c}}, ~45/34 = 484.4623{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5276{{c}} | |||
{{Optimal ET sequence|legend=1| 17cg, 22, 27eg, 34d, 38df, 45efg, 49fg, 50, 60e, 72, 111, 121, 149, 159, 171, 183, 243e, 270, 354, 414, 441, 525, 597, 624, 684, 867, 966g, 1038, 1308g, 1402, 1833g, 2026g, 2551g }} * | |||
<nowiki/>* [[optimal patent val]]: [[1905edo|1905]] | |||
[[Badness]] (Sintel): 2.53 | |||
== Etymology == | == Etymology == | ||