10th-octave temperaments: Difference between revisions
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declutter miscellaneous 5-limit - neon is of importance to 10edo and fractional octave theory. see discord conversation |
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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. | [[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: | Temperaments discussed elsewhere include: [[Quintosec family #Decoid|decoid]], [[Quintile family #Decile|decile]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnu family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]]. | ||
== Neon == | |||
: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].'' | |||
{{See also| Neon comma }} | |||
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. | |||
Extending neon with [[ragisma]], or equivalently with the linus comma, produces [[deca]]. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| 21 60 -50 }} | |||
{{Mapping|legend=1| 10 4 9 | 0 5 6 }} | |||
: mapping generators: ~3125/2916, {{monzo| 10 29 -24 }} | |||
[[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 }} | |||
[[Badness]] (Sintel): 4.85 | |||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||
[[Category:10edo]] | [[Category:10edo]] | ||
Revision as of 19:06, 1 August 2026
- 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.
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, decile, decimetra, decistearn, decavish, and linus.
Neon
- For extensions, see Ragismic microtemperaments #Deca, Landscape microtemperaments #Zinc, and 20th-octave temperaments #Calcium.
Neon tempers out [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⟩
- 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