90ed10: Difference between revisions

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== Theory ==

90ed10 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 4.11{{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 90ed10 very close to optimal for 27edo.

90ed10 is closely related to [[27edo]], but with the 10th harmonic rather than the [[octave]] being just, which [[stretched and compressed tuning|compresses the octave]] by about 4.11{{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 90ed10 very close to optimal for 27edo.

=== Harmonics ===

{{Harmonics in equal|90|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 90ed10 (continued)}}

{{Harmonics in equal|90|10|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 90ed10 (continued)}}

== Intervals ==

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* [[27edo]] – relative edo

* [[43edt]] – relative edt

* [[70ed6]] – relative ed6

* [[97ed12]] – relative ed12

[[Category:27edo]]

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 == Theory ==
-ed10 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 4.11{{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 90ed10 very close to optimal for 27edo.
+ed10 is closely related to [[27edo]], but with the 10th harmonic rather than the [[octave]] being just, which [[stretched and compressed tuning|compresses the octave]] by about 4.11{{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 90ed10 very close to optimal for 27edo.
 === Harmonics ===
-{{Harmonics in equal|90|5|1|intervals=integer|columns=11}}
+{{Harmonics in equal|90|10|1|intervals=integer|columns=11}}
-{{Harmonics in equal|90|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 90ed10 (continued)}}
+{{Harmonics in equal|90|10|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 90ed10 (continued)}}
 == Intervals ==
@@ Line 16: / Line 16: @@
 * [[27edo]] – relative edo
 * [[43edt]] – relative edt
+* [[70ed6]] – relative ed6
 * [[97ed12]] – relative ed12
 [[Category:27edo]]