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.

~~== Harmonics ==~~

On the harmonics 2, [[3/1|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. 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.

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 ===

~~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.~~

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

~~60edo for comparison:~~

== Intervals ==

~~{{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.
-== Harmonics ==
+On the harmonics 2, [[3/1|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. 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.
-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}}
-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.
+{{Harmonics in equal|139|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 139ed5 (continued)}}
-{{Harmonics in equal|139|5|1|intervals=prime}}
-edo for comparison:
-{{Harmonics in equal|60|2|1|intervals=prime}}
 == Intervals ==
 {{Interval table}}
-{{todo|expand}}
 [[Category:60edo]]