79ed12: Difference between revisions

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79ed12 is ~~very nearly identical~~ to [[22edo]], but with the [[12/1]] ~~rather than the 2/1~~ being just, resulting in octaves being [[stretched and compressed tuning|compressed]] by about 1.99{{c}}. The local [[~~The_Riemann_zeta_function_and_tuning~~#~~Optimal_octave_stretch~~|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 ~~extremely~~ close to optimal for 22edo.

== Theory ==

79ed12 is closely related to [[22edo]], but with the 12th harmonic rather than the [[2/1|octave]] being just, resulting in octaves being [[stretched and compressed tuning|compressed]] by about 1.99{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 very close to optimal for 22edo.

== Harmonics ==

=== Harmonics ===

{{Harmonics in equal|79|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 79ed12 (continued)}}

[[~~Category:Edonoi~~]]

=== Subsets and supersets ===

79ed12 is the 22nd [[prime equal division|prime ed12]], so it does not contain any nontrivial subset ed12's.

== See also ==

* [[22edo]] – relative edo

* [[35edt]] – relative edt

* [[57ed6]] – relative ed6

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 {{ED intro}}
-ed12 is very nearly identical to [[22edo]], but with the [[12/1]] rather than the 2/1 being just, resulting in octaves being [[stretched and compressed tuning|compressed]] by about 1.99{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 extremely close to optimal for 22edo.
+== Theory ==
+ed12 is closely related to [[22edo]], but with the 12th harmonic rather than the [[2/1|octave]] being just, resulting in octaves being [[stretched and compressed tuning|compressed]] by about 1.99{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch|zeta peak]] around 22 is located at 22.025147, which has a step size of 54.483{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 79ed12 very close to optimal for 22edo.
-== Harmonics ==
+=== Harmonics ===
-{{Harmonics in equal|79|12|1|prec=2|columns=15}}
+{{Harmonics in equal|79|12|1|intervals=integer|columns=11}}
+{{Harmonics in equal|79|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 79ed12 (continued)}}
-[[Category:Edonoi]]
+=== Subsets and supersets ===
+ed12 is the 22nd [[prime equal division|prime ed12]], so it does not contain any nontrivial subset ed12's.
+== See also ==
+* [[22edo]] – relative edo
+* [[35edt]] – relative edt
+* [[57ed6]] – relative ed6