57ed12: Difference between revisions

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== Theory ==

57ed12 is similar to [[16edo]], but has the 12th harmonic tuned just instead of the [[~~2/1|~~octave]], which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.

57ed12 is similar to [[16edo]], but has the 12th harmonic tuned just instead of the [[octave]], which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.

16edo's [[harmonic]]s 3, 11 and 17 are all more than 25 cents away from just, making them unusable for most purposes. 57ed12 improves upon all of their tunings, bringing all those harmonics within 16 cents of just, and bringing 11 and 17 within an impressive 1 cent of just. This dramatically increases the number of [[consonant]] intervals and chords available in the tuning.

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{{Harmonics in equal|57|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57ed12 (continued)}}

=== Subsets and supersets ===

Since 57 factors into primes as {{nowrap| 3 × 19 }}, 57ed12 contains subset ed12's [[3ed12]] and [[19ed12]].

== Intervals ==

== See also ==

* [[16edo]] – relative edo

* [[25edt]] – relative edt

* [[41ed6]] – relative ed6

[[Category:Mavila]]

[[Category:Pelog]]

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 == Theory ==
-ed12 is similar to [[16edo]], but has the 12th harmonic tuned just instead of the [[2/1|octave]], which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L&nbsp;5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.
+ed12 is similar to [[16edo]], but has the 12th harmonic tuned just instead of the [[octave]], which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L&nbsp;5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.
 edo's [[harmonic]]s 3, 11 and 17 are all more than 25 cents away from just, making them unusable for most purposes. 57ed12 improves upon all of their tunings, bringing all those harmonics within 16 cents of just, and bringing 11 and 17 within an impressive 1 cent of just. This dramatically increases the number of [[consonant]] intervals and chords available in the tuning.
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 {{Harmonics in equal|57|12|1|intervals=integer|columns=11}}
 {{Harmonics in equal|57|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57ed12 (continued)}}
+=== Subsets and supersets ===
+Since 57 factors into primes as {{nowrap| 3 × 19 }}, 57ed12 contains subset ed12's [[3ed12]] and [[19ed12]].
 == Intervals ==
 {{Interval table}}
+== See also ==
+* [[16edo]] – relative edo
+* [[25edt]] – relative edt
+* [[41ed6]] – relative ed6
 [[Category:Mavila]]
 [[Category:Pelog]]