2023/2000: Difference between revisions
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[[Tempering out]] this comma alone in the 2.5.7.17 subgroup leads to the [[pentagoth clan#Pentagoth|pentagoth]] temperament. | [[Tempering out]] this comma alone in the 2.5.7.17 subgroup leads to the [[pentagoth clan#Pentagoth|pentagoth]] temperament. | ||
== Pentagoth (rank-3) == | |||
[[Subgroup]]: 2.5.7.17 | |||
[[Comma list]]: 2023/2000 | |||
{{Mapping|legend=1| 1 2 2 4 | 0 1 1 1 | 0 0 2 -1 }} | |||
: mapping generators: ~2, ~5/4, ~20/17 | |||
[[Mapping to lattice]]: [{{val| 0 3 0 -1 }}, {{val| 0 0 1 0 }}] | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.566{{c}}, ~5/4 = 387.475{{c}}, ~20/17 = 289.545{{c}} | |||
: [[error map]]: {{val| +0.566 2.294 -1.127 -4.760}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 388.049{{c}}, ~5/4 = 289.369{{c}} | |||
: error map: {{val| 0.000 1.735 -2.038 -6.275 }} | |||
[[Badness]] (Sintel): 0.509 | |||
== Etymology == | == Etymology == | ||
As of June 6, 2026, pentagoth is the name given to the rank-3 temperament 2.5.7.17[2023/2000] by [[groundfault]]. It originally referred to a temperament now called [[vengeance]], which as a 2.5.17 temperament tempers out this comma. | As of June 6, 2026, pentagoth is the name given to the rank-3 temperament 2.5.7.17[2023/2000] by [[groundfault]]. It originally referred to a temperament now called [[vengeance]], which as a 2.5.17 temperament tempers out this comma. | ||
[[Category:Pentagoth]] | [[Category:Pentagoth]] | ||