10th-octave temperaments: Difference between revisions

Eliora (talk | contribs)
Neon: explain what exactly makes this notable
Review, switch to Sintel's badness, WE & CWE tunings
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== Neon ==
== Neon ==
Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].
Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. It was named by [[Eliora]] in 2023 after the 10th element. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
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{{Mapping|legend=1| 10 4 9 | 0 5 6 }}
{{Mapping|legend=1| 10 4 9 | 0 5 6 }}
: Mapping generators: ~3125/2916, {{monzo| 10 29 -24 }}
: Mapping generators: ~3125/2916, {{monzo| 10 29 -24 }}


[[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888
[[Optimal tuning]]s:
* [[WE]]: ~3125/2916 = 119.9999{{c}}, {{monzo| 10 29 -24 }} = 284.3890{{c}}
: [[error map]]: {{val| -0.001 -0.011 +0.019 }}
* [[CWE]]: ~3125/2916 = 120.0000{{c}}, {{monzo| 10 29 -24 }} = 284.3891{{c}}
: error map: {{val| 0.000 -0.010 +0.021 }}


{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}
{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}


[[Badness]]: 0.206596
[[Badness]] (Sintel): 4.85


{{Navbox fractional-octave}}
{{Navbox fractional-octave}}


[[Category:10edo]]
[[Category:10edo]]