70ed6: Difference between revisions

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70ed6 is ~~very nearly identical~~ to [[27edo~~|27 EDO~~]], but with the [[~~6/1~~]] ~~rather than the 2/1~~ being just, which [[stretched and compressed tuning|compresses the octave]] by 3.~~5316~~{{c}}. The local [[~~The_Riemann_zeta_function_and_tuning~~#~~Optimal_octave_stretch~~|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.

== Theory ==

70ed6 is closely related to [[27edo]], but with the 6th harmonic rather than the [[octave]] being just, which [[stretched and compressed tuning|compresses the octave]] by about 3.53{{c}}. The local [[Riemann zeta function #Optimal octave stretch|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.

=== Harmonics ===

{{Harmonics in equal|70|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 70ed6 (continued)}}

=== Subsets and supersets ===

Since 70 factors into primes as {{nowrap| 2 × 5 × 7 }}, 70ed6 has subset ed6's {{EDs|equave=6| 2, 5, 7, 10, 14, and 35 }}.

== Intervals ==

== ~~Harmonics~~ ==

== Scales ==

~~{{Harmonics in equal~~|~~70|6|1|prec~~=~~2}}~~

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

~~{{Harmonics in equal|70|6|1|prec~~=~~2|intervals~~=~~prime|start~~=~~6}}~~

== See also ==

* [[16edf]] – relative edf

* [[27edo]] – relative edo

* [[43edt]] – relative edt

* [[90ed10]] – relative ed10

* [[97ed12]] – relative ed12

[[Category:~~Edonoi~~]]

[[Category:27edo]]

[[Category:Zeta-optimized tunings]]

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 {{ED intro}}
-ed6 is very nearly identical to [[27edo|27 EDO]], but with the [[6/1]] rather than the 2/1 being just, which [[stretched and compressed tuning|compresses the octave]] by 3.5316{{c}}. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.
+== Theory ==
+ed6 is closely related to [[27edo]], but with the 6th harmonic rather than the [[octave]] being just, which [[stretched and compressed tuning|compresses the octave]] by about 3.53{{c}}. The local [[Riemann zeta function #Optimal octave stretch|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3023{{c}}, making 70ed6 very close to optimal for 27edo.
+=== Harmonics ===
+{{Harmonics in equal|70|6|1|intervals=integer|columns=11}}
+{{Harmonics in equal|70|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 70ed6 (continued)}}
+=== Subsets and supersets ===
+Since 70 factors into primes as {{nowrap| 2 × 5 × 7 }}, 70ed6 has subset ed6's {{EDs|equave=6| 2, 5, 7, 10, 14, and 35 }}.
 == Intervals ==
 {{Interval table}}
-== Harmonics ==
+== Scales ==
-{{Harmonics in equal|70|6|1|prec=2}}
+* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]]
-{{Harmonics in equal|70|6|1|prec=2|intervals=prime|start=6}}
+== See also ==
+* [[16edf]] – relative edf
+* [[27edo]] – relative edo
+* [[43edt]] – relative edt
+* [[90ed10]] – relative ed10
+* [[97ed12]] – relative ed12
-[[Category:Edonoi]]
+[[Category:27edo]]
+[[Category:Zeta-optimized tunings]]