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 | 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 | ||
Comma list: {{ | [[Comma list]]: {{monzo| 21 60 -50 }} | ||
{{Mapping|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): ~{{ | [[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888 | ||
{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }} | |||
[[Badness]]: 0.206596 | |||
{{Navbox fractional-octave}} | |||
[[Category:10edo]] | [[Category:10edo]] | ||