13/12: Difference between revisions

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In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

~~The neutral second in~~ [[~~17edo~~]] ~~is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate~~ 3~~/2 and 12\17 taken to approximate 13/8, you can generate a 13~~-~~limit harmonic triad that approximates an 8:12:13 chord with a good 13/12~~.

== Approximation ==

It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].

{{Interval edo approximation|{{PAGENAME}}}}

~~It is approximated~~ to ~~within about 0~~.11 [[~~cents~~]] ~~by the 3-step interval of~~ [[~~26edo~~]].

== Temperaments ==

13/12 can be used to generate [[bleu]] temperament in the 2.3.7.11.13 subgroup, mapping [[3/2]] to +5 generators, [[7/4]] to +7 generators, [[11/8]] to +4 generators, and [[13/8]] to +6 generators.

A slightly sharp 13/12 generates [[glacier]] temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu.

== See also ==

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 In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).
-The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.
+== Approximation ==
+It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].
+{{Interval edo approximation|{{PAGENAME}}}}
-It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].
+== Temperaments ==
+/12 can be used to generate [[bleu]] temperament in the 2.3.7.11.13 subgroup, mapping [[3/2]] to +5 generators, [[7/4]] to +7 generators, [[11/8]] to +4 generators, and [[13/8]] to +6 generators.
+A slightly sharp 13/12 generates [[glacier]] temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu.
 == See also ==