10th-octave temperaments

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

Fractional-octave temperaments

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← 9th-octave • 10th-octave • 11th-octave →

10edo is notable for having close approximations of 15/14 to one step, the associated comma being the linus comma 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, decile, decimetra, decistearn, decavish, and linus (the 15/14 relationship mentioned above).

Neon

For extensions, see Ragismic microtemperaments #Deca, Landscape microtemperaments #Zinc, and 20th-octave temperaments #Calcium.

Neon tempers out the neon comma, [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.

Extending neon with ragisma, or equivalently with the linus comma, produces deca.

Subgroup: 2.3.5

Comma list: [21 60 -50⟩

Mapping: [⟨10 4 9], ⟨0 5 6]]

mapping generators: ~3125/2916, [10 29 -24⟩

Optimal tunings:

• WE: ~3125/2916 = 119.9999 ¢, [10 29 -24⟩ = 284.3890 ¢

error map: ⟨-0.001 -0.011 +0.019]

• CWE: ~3125/2916 = 120.0000 ¢, [10 29 -24⟩ = 284.3891 ¢

error map: ⟨0.000 -0.010 +0.021]

Optimal ET sequence: 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650

Badness (Sintel): 4.85