10th-octave temperaments: Difference between revisions
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{{ | {{Infobox fractional-octave|10}} | ||
[[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. | [[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. | ||
Revision as of 03:43, 14 February 2025
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