13th-octave temperaments: Difference between revisions

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Although [[13edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are.

A 13th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 13. Although [[13edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are.

~~Discussed~~ elsewhere are:

Temperaments discussed elsewhere are [[ragismic microtemperaments #Aluminium|aluminium]], [[octagar temperaments #Tridecatonic|tridecatonic]], [[ragismic microtemperaments #Trideci|trideci]], and [[orwellismic temperaments #Triskaidekic|triskaidekic]].

* ''[[~~Aluminium]]'', → [[Ragismic~~ microtemperaments#Aluminium|~~Ragismic microtemperaments~~]], ~~which is notable as [[135/128]] is a [[semiconvergent]] to 1\13 as well as a 5-limit interval.~~

~~== Tridecatonic ==~~

~~: ''See also:~~ [[~~Octagar~~ temperaments #Tridecatonic]], [[~~Ragismic~~ microtemperaments #Trideci]], and [[~~26th-octave~~ temperaments~~]]''~~

~~''Tridecatonic'' tempers out the devil's tridecalimma, the comma which associates the [[10/9]] minor tone with 2 steps of 13edo.~~

~~Subgroup: 2.3.5~~

~~[[Comma]]: 2541865828329/2500000000000~~

~~[[Mapping]]: [{{Val| 13 21 31 }}, {{Val~~| ~~0 -1 -2 }}]~~

~~[[POTE generator]]: ~3/2 = 701.0837~~

~~{{Optimal ET sequence|legend=1| 26, 39, 65, 286, 351, 416, 481, 546 }}~~

~~[[Badness~~]]~~: 0~~.~~437494~~

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+{{Technical data page}}
 {{Infobox fractional-octave|13}}
-Although [[13edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are.
+A 13th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 13. Although [[13edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are.
-Discussed elsewhere are:
+Temperaments discussed elsewhere are [[ragismic microtemperaments #Aluminium|aluminium]], [[octagar temperaments #Tridecatonic|tridecatonic]], [[ragismic microtemperaments #Trideci|trideci]], and [[orwellismic temperaments #Triskaidekic|triskaidekic]].
-* ''[[Aluminium]]'', → [[Ragismic microtemperaments#Aluminium|Ragismic microtemperaments]], which is notable as [[135/128]] is a [[semiconvergent]] to 1\13 as well as a 5-limit interval.
-== Tridecatonic ==
-: ''See also: [[Octagar temperaments #Tridecatonic]], [[Ragismic microtemperaments #Trideci]], and [[26th-octave temperaments]]''
-''Tridecatonic'' tempers out the devil's tridecalimma, the comma which associates the [[10/9]] minor tone with 2 steps of 13edo.
-Subgroup: 2.3.5
-[[Comma]]: 2541865828329/2500000000000
-[[Mapping]]: [{{Val| 13 21 31 }}, {{Val| 0 -1 -2 }}]
-[[POTE generator]]: ~3/2 = 701.0837
-{{Optimal ET sequence|legend=1| 26, 39, 65, 286, 351, 416, 481, 546 }}
-[[Badness]]: 0.437494
 {{Navbox fractional-octave}}