10th-octave temperaments: Difference between revisions

(3 intermediate revisions by 3 users not shown)

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: [[~~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: [[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. 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]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888~~

~~{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}~~

~~[[Badness]]: 0.206596~~

[[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: [[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: [[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. 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]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888
-{{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}
-[[Badness]]: 0.206596
 {{Navbox fractional-octave}}
 [[Category:10edo]]