70ed6: Difference between revisions
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== Theory == | == Theory == | ||
70ed6 is | 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. | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|70|6|1}} | {{Harmonics in equal|70|6|1|intervals=integer|columns=11}} | ||
{{Harmonics in equal|70|6|1| | {{Harmonics in equal|70|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 70ed6 (continued)}} | ||
=== Subsets and supersets === | === 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 }}. | 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 == | == Intervals == | ||
{{Interval table}} | {{Interval table}} | ||
== Scales == | |||
* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]] | |||
== See also == | == See also == | ||
* [[16edf]] – relative edf | |||
* [[27edo]] – relative edo | * [[27edo]] – relative edo | ||
* [[43edt]] – relative edt | * [[43edt]] – relative edt | ||
* [[90ed10]] – relative ed10 | |||
* [[97ed12]] – relative ed12 | * [[97ed12]] – relative ed12 | ||
[[Category:27edo]] | |||
[[Category:Zeta-optimized tunings]] | |||