70ed6: Difference between revisions

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'''[[Ed6|Division of the sixth harmonic]] into 70 equal parts''' (70ED6) is very nearly identical to [[27edo|27 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 3.5316 [[cent]]s [[stretched and compressed tuning|compressed]] and the step size is about 44.3136 cents. 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 44.3071 cents, making 70ed6 very close to optimal for 27edo.

==~~Harmonics~~==

== Theory ==

70ed6 is closely related to [[27edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just, which [[stretched and compressed tuning|compresses the octave]] by about 3.53{{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.

[[Category:~~Edonoi~~]]

=== 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 ==

== Scales ==

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

== See also ==

* [[16edf]] – relative edf

* [[27edo]] – relative edo

* [[43edt]] – relative edt

* [[90ed10]] – relative ed10

* [[97ed12]] – relative ed12

[[Category:27edo]]

[[Category:Zeta-optimized tunings]]

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 {{Infobox ET}}
-'''[[Ed6|Division of the sixth harmonic]] into 70 equal parts''' (70ED6) is very nearly identical to [[27edo|27 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 3.5316 [[cent]]s [[stretched and compressed tuning|compressed]] and the step size is about 44.3136 cents. 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 44.3071 cents, making 70ed6 very close to optimal for 27edo.
+{{ED intro}}
-==Harmonics==
+== Theory ==
-{{Harmonics in equal|70|6|1|prec=2|columns=15}}
+ed6 is closely related to [[27edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just, which [[stretched and compressed tuning|compresses the octave]] by about 3.53{{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.
-[[Category:Edonoi]]
+=== 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}}
+== Scales ==
+* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]]
+== See also ==
+* [[16edf]] – relative edf
+* [[27edo]] – relative edo
+* [[43edt]] – relative edt
+* [[90ed10]] – relative ed10
+* [[97ed12]] – relative ed12
+[[Category:27edo]]
+[[Category:Zeta-optimized tunings]]