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.

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~~

[[Category:10edo]]

@@ Line 3: / Line 3: @@
 [[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}}
 [[Category:10edo]]