60ed6: Difference between revisions

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== Theory ==

60ed6 can be viewed as [[23edo]] with the [[~~2/1|~~octave]] being [[stretched and compressed tuning|compressed]] by 10.9 cents, and with the 6th harmonic being [[just]], instead of the octave being just.

60ed6 can be viewed as [[23edo]] with the [[octave]] being [[stretched and compressed tuning|compressed]] by 10.9 cents, and with the 6th harmonic being [[just]], instead of the octave being just.

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]]. 60ed6 improves upon all of their tunings, bringing all of them within 16 cents of just, and bringing 3, 5 and 7 within 11 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.

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{{Harmonics in equal|60|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60ed6 (continued)}}

=== Subsets and supersets ===

60ed6 is the 9th [[highly composite equal division|highly composite ed6]], with subset ed6's {{EDs|equave=6| 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 }}.

== Intervals ==

~~{{todo|expand}}~~

== See also ==

* [[37edt]] – relative edt

[[Category:23edo]]

@@ Line 3: / Line 3: @@
 == Theory ==
-ed6 can be viewed as [[23edo]] with the [[2/1|octave]] being [[stretched and compressed tuning|compressed]] by 10.9 cents, and with the 6th harmonic being [[just]], instead of the octave being just.
+ed6 can be viewed as [[23edo]] with the [[octave]] being [[stretched and compressed tuning|compressed]] by 10.9 cents, and with the 6th harmonic being [[just]], instead of the octave being just.
 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]]. 60ed6 improves upon all of their tunings, bringing all of them within 16 cents of just, and bringing 3, 5 and 7 within 11 cents of just. This dramatically increases the number of consonant intervals and chords available in the tuning.
@@ Line 12: / Line 12: @@
 {{Harmonics in equal|60|6|1|intervals=integer|columns=11}}
 {{Harmonics in equal|60|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60ed6 (continued)}}
+=== Subsets and supersets ===
+ed6 is the 9th [[highly composite equal division|highly composite ed6]], with subset ed6's {{EDs|equave=6| 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 }}.
 == Intervals ==
 {{Interval table}}
-{{todo|expand}}
+== See also ==
+* [[37edt]] – relative edt
 [[Category:23edo]]