139ed5: Difference between revisions

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It is similar to [[60edo]], but with the ~~octave (~~2/1) being [[~~octave stretch~~|stretched]] by about 2.7 cents, ~~and with the interval~~ [[~~5/1~~]] ~~being~~ [[~~just~~]]~~, instead of 2/1 being just~~.

== Theory ==

139ed5 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]].

~~== Harmonics ==~~

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.

On harmonics 2.3.5.7.11, 60edo has 0%, 10%, 32%, 44% and 43% relative error.

~~On those same~~ harmonics, 139ed5 ~~has 14%, 12%, 0%, 6% and 10% relative error.~~

=== Harmonics ===

{{Harmonics in equal|139|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 139ed5 (continued)}}

~~This is a large improvement relative to the step size of the tuning,~~ and is the ~~main reason why a composer might choose to use 139ed5.~~

=== Subsets and supersets ===

~~{{Harmonics in~~ equal|~~139|5|1|intervals=~~prime}}

139ed5 is the 34th [[prime equal division|prime ed5]]. It does not contain any nontrivial subset ed5's.

== Intervals ==

60edo ~~for comparison:~~

== See also ==

~~{{Harmonics in equal|60|2|1|intervals=prime}}~~

* [[35edf]] – relative edf

* [[60edo]] – relative edo

* [[95edt]] – relative edt

* [[155edt]] – relative ed6

~~== Intervals ==~~

~~{{Interval table}}~~

~~{{todo|expand}}~~

[[Category:60edo]]

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 {{ED intro}}
-It is similar to [[60edo]], but with the octave (2/1) being [[octave stretch|stretched]] by about 2.7 cents, and with the interval [[5/1]] being [[just]], instead of 2/1 being just.
+== Theory ==
+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]].
-== Harmonics ==
+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.
-On harmonics 2.3.5.7.11, 60edo has 0%, 10%, 32%, 44% and 43% relative error.
-On those same harmonics, 139ed5 has 14%, 12%, 0%, 6% and 10% relative error.
+=== 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)}}
-This is a large improvement relative to the step size of the tuning, and is the main reason why a composer might choose to use 139ed5.
+=== Subsets and supersets ===
-{{Harmonics in equal|139|5|1|intervals=prime}}
+ed5 is the 34th [[prime equal division|prime ed5]]. It does not contain any nontrivial subset ed5's.
+== Intervals ==
+{{Interval table}}
-edo for comparison:
+== See also ==
-{{Harmonics in equal|60|2|1|intervals=prime}}
+* [[35edf]] – relative edf
+* [[60edo]] – relative edo
+* [[95edt]] – relative edt
+* [[155edt]] – relative ed6
-== Intervals ==
-{{Interval table}}
-{{todo|expand}}
 [[Category:60edo]]