10th-octave temperaments

Fractional-octave temperaments

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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