10th-octave temperaments: Difference between revisions

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Review, switch to Sintel's badness, WE & CWE tunings
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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: [[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]].  
Temperaments discussed elsewhere include: [[Miscellaneous 5-limit temperaments #Neon|neon]]/[[Ragismic microtemperaments #Deca|deca]], [[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 ==
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. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].
 
[[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]]

Latest revision as of 07:48, 5 July 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: neon/deca, decoid, decile, decimetra, decistearn, decavish, and linus.

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