139ed5: Difference between revisions

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 {{ED intro}}
-==== Odd harmonics ====
+== Theory ==
-{{Harmonics in equal|139|5|1}}
+ed5 is similar to [[60edo]], but with the 5th harmonic being [[just]], instead of the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 2.73 cents. Like 60edo, 139ed5 is [[consistent]] to the [[integer limit|10-integer-limit]].
+On the harmonics 2, [[3/1|3]], 5, [[7/1|7]], [[11/1|11]], 60edo has 0%, -10%, -32%, -44% and +43% relative error. On those same harmonics, 139ed5 has +14%, +12%, 0%, -6% and -10% relative error. This is a large improvement relative to the step size of the tuning if the focus is on the higher [[prime harmonic|primes]], and is the main reason why a composer might choose to use 139ed5.
-{{Stub}}
+=== Harmonics ===
+{{Harmonics in equal|139|5|1|intervals=integer|columns=11}}
+{{Harmonics in equal|139|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 139ed5 (continued)}}
+=== Subsets and supersets ===
+ed5 is the 34th [[prime equal division|prime ed5]]. It does not contain any nontrivial subset ed5's.
+== Intervals ==
+{{Interval table}}
+== See also ==
+* [[35edf]] – relative edf
+* [[60edo]] – relative edo
+* [[95edt]] – relative edt
+* [[155edt]] – relative ed6
+[[Category:60edo]]