59ed6: Difference between revisions

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~~{{Stub}}~~

== Theory ==

59ed6 corresponds to 22.8243…edo. It can be viewed as a stretched version of [[23edo]].

59ed6 corresponds to 22.8243…edo. It can be viewed as a [[stretched and compressed tuning|stretched]] version of [[23edo]] or a compressed version of [[36edt]].

23edo's [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] are all more than 20 cents away from just, so they exhibit very little [[consonance]]. 59ed6 improves upon all of their tunings, bringing all of them within 10 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.

The trade-off is that 59ed6's octave is significantly worse than 23edo. It has just over 9 cents of error, compared to none. For some composers, 9 cents error on the octave may be unacceptable, but for others, it may be considered still close enough for consonance and [[octave equivalence]] to be well preserved, and they may see it a worthwhile sacrifice to unlock so many warm [[11-limit]] harmonies.

=== Harmonics ===

{{Harmonics in equal|59|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59ed6 (continued)}}

=== Subsets and supersets ===

59ed6 is the 17th [[prime equal division|prime ed6]], so it does not contain any nontrivial subset ed6's.

== Intervals ==

== Scales ==

* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]]

== See also ==

* [[36edt]] – relative edt

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-{{Stub}}
 {{Infobox ET}}
 {{ED intro}}
 == Theory ==
-ed6 corresponds to 22.8243…edo. It can be viewed as a stretched version of [[23edo]].
+ed6 corresponds to 22.8243…edo. It can be viewed as a [[stretched and compressed tuning|stretched]] version of [[23edo]] or a compressed version of [[36edt]].
+edo's [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] are all more than 20 cents away from just, so they exhibit very little [[consonance]]. 59ed6 improves upon all of their tunings, bringing all of them within 10 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.
+The trade-off is that 59ed6's octave is significantly worse than 23edo. It has just over 9 cents of error, compared to none. For some composers, 9 cents error on the octave may be unacceptable, but for others, it may be considered still close enough for consonance and [[octave equivalence]] to be well preserved, and they may see it a worthwhile sacrifice to unlock so many warm [[11-limit]] harmonies.
 === Harmonics ===
 {{Harmonics in equal|59|6|1|intervals=integer|columns=11}}
 {{Harmonics in equal|59|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59ed6 (continued)}}
+=== Subsets and supersets ===
+ed6 is the 17th [[prime equal division|prime ed6]], so it does not contain any nontrivial subset ed6's.
 == Intervals ==
 {{Interval table}}
+== Scales ==
+* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]]
+== See also ==
+* [[36edt]] – relative edt