10th-octave temperaments: Difference between revisions
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{{ | {{Technical data page}} | ||
{{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. | ||
Temperaments discussed elsewhere include: [[ | Temperaments discussed elsewhere include: [[Quintosec family #Decoid|decoid]], [[Ragismic microtemperaments #Deca|deca]], [[Quintile family #Decile|decile]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnuzmic family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]]. | ||
== Neon == | == Neon == | ||
Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]]. | Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]]. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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{{Mapping|legend=1| 10 4 9 | 0 5 6 }} | {{Mapping|legend=1| 10 4 9 | 0 5 6 }} | ||
: | : Mapping generators: ~3125/2916, {{monzo| 10 29 -24 }} | ||
[[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888 | [[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888 | ||
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{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }} | {{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.206596 | ||
{{Navbox fractional-octave}} | |||
[[Category:10edo]] | [[Category:10edo]] | ||
Latest revision as of 18:13, 4 August 2025
- 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, deca, decile, decimetra, decistearn, decavish, and linus.
Neon
Neon tempers out [21 60 -50⟩ in the 5-limit, equating 3125/2916 with one step of 10edo. 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: 0.206596