10th-octave temperaments: Difference between revisions
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-linus (addressed in kalismic temperaments) |
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== Neon == | == Neon == | ||
Neon tempers out | Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]]. | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
Comma list: {{ | [[Comma list]]: {{monzo| 21 60 -50 }} | ||
{{Mapping|10 4 9|0 5 6 | {{Mapping|legend=1| 10 4 9 | 0 5 6 }} | ||
: mapping generators: ~3125/2916 | : mapping generators: ~3125/2916, {{monzo| 10 29 -24 }} | ||
Optimal tuning (CTE): ~{{ | [[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888 | ||
{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }} | |||
[[Badness]]: 0.207 | |||
[[Category:10edo]] | [[Category:10edo]] | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
Revision as of 16:26, 6 January 2024
Template:Fractional-octave navigation 10edo is notable for having close approximations of 15/14 to one step, and 13/8 to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.
Temperaments discussed elsewhere include: decoid, deca, decal, decimetra, decistearn, decavish, and linus.
Neon
Neon tempers out [21 60 -50⟩ in the 5-limit. Neon extensions discussed elsewhere include deca, calcium, and zinc.
Subgroup: 2.3.5
Comma list: [21 60 -50⟩
Mapping: [⟨10 4 9], ⟨0 5 6]]
- mapping generators: ~3125/2916, [10 29 -24⟩
Optimal tuning (CTE): ~3125/2916 = 1\10, [10 29 -24⟩ = 284.3888
Optimal ET sequence: 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650
Badness: 0.207