10th-octave temperaments: Difference between revisions
declutter miscellaneous 5-limit - neon is of importance to 10edo and fractional octave theory. see discord conversation |
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{{Infobox fractional-octave|10}} | {{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: [[ | 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 == | ||
: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].'' | : ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].'' | ||
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 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]]. | Extending neon with [[ragisma]], or equivalently with the linus comma, produces [[deca]]. | ||