10th-octave temperaments: Difference between revisions
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{{Infobox fractional-octave|10}} | {{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}} | {{Navbox fractional-octave}} | ||
[[Category:10edo]] | [[Category:10edo]] | ||