13th-octave temperaments: Difference between revisions
Switch to Sintel's badness, WE & CWE tunings |
per discussion on discord: for the same logic as neon should belong in 10th-octave, aluminium similarly should be placed here. besides it adds to this page as opposed to just listing "discussed elsewhere". |
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{{Infobox fractional-octave|13}} | {{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. | 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. | ||
Furthermore, one step of 13edo is very close to [[135/128]], a notable 5-limit interval, in fact it is a semiconvergent to the said representation. Hence, considered below is aluminium. | |||
Temperaments discussed elsewhere are [[octagar temperaments #Tridecatonic|tridecatonic]], [[ragismic microtemperaments #Trideci|trideci]], and [[orwellismic temperaments #Triskaidekic|triskaidekic]]. | |||
== Aluminium == | == Aluminium == | ||
: ''For extensions, see [[Ragismic microtemperaments #Aluminium]].'' | : ''For extensions, see [[Ragismic microtemperaments #Aluminium]].'' | ||
Aluminium tempers out {{monzo| 92 -39 -13 }} in the 5-limit, and sets [[135/128]] to 1/13 of an [[octave]]. | Aluminium tempers out {{monzo| 92 -39 -13 }} in the 5-limit, and sets [[135/128]] to 1/13 of an [[octave]]. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Badness]] (Sintel): 2.89 | [[Badness]] (Sintel): 2.89 | ||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||