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== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 17-limit results in the rank-6 '''chlorismic''' temperament, or in the 2.3.7.17 subgroup, the rank-3 '''chloric''' temperament. In either case it equates a stack of three [[9/7]] supermajor thirds with [[17/8]], the 17th harmonic minus three octaves. [[80edo]] represents both 9/7 and 17/8 within 0.1 cents, so it and many [[80th-octave temperaments]] temper out the chlorisma. | [[Tempering out]] this comma in the 17-limit results in the rank-6 '''chlorismic''' temperament, or in the 2.3.7.17 subgroup, the rank-3 '''chloric''' temperament. In either case it equates a stack of three [[9/7]] supermajor thirds with [[17/8]], the 17th harmonic minus three octaves. [[80edo]] represents both 9/7 and 17/8 within 0.1 cents, so it and many [[80th-octave temperaments]] temper out the chlorisma. | ||
=== Chloric === | |||
[[Subgroup]]: 2.3.7.17 | |||
{{Mapping|legend=2| 1 0 0 3 | 0 1 0 6 | 0 0 1 -3 }} | |||
: mapping generators: ~2, ~3, ~7 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~7/4 = 968.8729{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~7/4 = 968.8712{{c}} | |||
{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 99, 130, 135, 171, 364, 400, 571, 971, 2378, 2549, 2949, 3920 }} | |||
[[Badness]] (Sintel): 0.0174 | |||
=== Chlorismic === | |||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[Mapping]]: <br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 3 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 6 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -3 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | |||
|} | |||
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~5/4 = 386.3232{{c}}, ~7/4 = 968.8729{{c}}, ~11/8 = 551.3322{{c}}, ~13/8 = 840.5419{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~5/4 = 386.3194{{c}}, ~7/4 = 968.8712{{c}}, ~11/8 = 551.3264{{c}}, ~13/8 = 840.5367{{c}} | |||
{{Optimal ET sequence|legend=1| 19, 22, 27eg, 41, 49fg, 50, 58, 72, 121, 149, 166g, 171, 193, 198g, 224g, 243e, 270, 364, 373g, 400, 422, 494, 742, 764, 814, 935, 1084, 1106, 1178, 1236, 1506, 2000, 2414, 2684, 3178, 3920, 4684, 5498, 10182d, 14102dg, 14174d, 15680dg, 19600dg, }} * | |||
<nowiki/> * [[optimal patent val]]: [[14916edo|14916]] | |||
[[Badness]] (Sintel): 1.13 | |||
== Etymology == | == Etymology == | ||