13th-octave temperaments: Difference between revisions

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{{Fractional-octave navigation|13}}
{{Technical data page}}
{{Infobox fractional-octave|13}}
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.
{{Navbox fractional-octave}}
 
== 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

Latest revision as of 03:52, 21 July 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

← 12th-octave • 13th-octave • 14th-octave →

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.

Temperaments discussed elsewhere are aluminium, tridecatonic, trideci, and triskaidekic.

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