10th-octave temperaments: Difference between revisions

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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: [[Breedsmic temperaments #Decoid|decoid]], [[Ragismic microtemperaments #Deca|deca]], [[Pental family #Decal|decal]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnuzmic family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]].  
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 ==

Revision as of 04:12, 3 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. 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 sequence80, 190, 270, 460, 730, 1730, 2460, 3190, 5650

Badness: 0.206596

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