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, the associated comma being the [[linus comma]] 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: [[quintosec family #Decoid|decoid]], [[quintile family #Decile|decile]], [[metric microtemperaments #Decimetra|decimetra]], [[trisedodge family #Decistearn|decistearn]], [[vishnu family #Decavish|decavish]], and [[kalismic temperaments #Linus|linus]] (the 15/14 relationship mentioned above).

== 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~~]].

: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''

Neon tempers out the [[neon comma]], {{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.

Extending neon with [[ragisma]], or equivalently with the linus comma, produces [[deca]].

[[Subgroup]]: 2.3.5

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: ~~Mapping~~ generators: ~3125/2916, {{monzo| 10 29 -24 }}

: mapping generators: ~3125/2916, {{monzo| 10 29 -24 }}

[[Optimal tuning]]s:

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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, the associated comma being the [[linus comma]] 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: [[quintosec family #Decoid|decoid]], [[quintile family #Decile|decile]], [[metric microtemperaments #Decimetra|decimetra]], [[trisedodge family #Decistearn|decistearn]], [[vishnu family #Decavish|decavish]], and [[kalismic temperaments #Linus|linus]] (the 15/14 relationship mentioned above).
 == 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]].
+: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''
+Neon tempers out the [[neon comma]], {{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.
+Extending neon with [[ragisma]], or equivalently with the linus comma, produces [[deca]].
 [[Subgroup]]: 2.3.5
@@ Line 13: / Line 17: @@
 {{Mapping|legend=1| 10 4 9 | 0 5 6 }}
-: Mapping generators: ~3125/2916, {{monzo| 10 29 -24 }}
+: mapping generators: ~3125/2916, {{monzo| 10 29 -24 }}
 [[Optimal tuning]]s: