76ed80: Difference between revisions

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 == Theory ==
-ed80 is closely related to [[12edo]], but with the 80th harmonic rather than the [[2/1|octave]] being just, resulting in octaves being [[stretched and compressed tuning|compressed]] by about 2.16{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch|zeta peak]] around 12 is located at 12.023183, which has a step size of 99.807{{c}} and an octave of 1197.686{{c}} (which is compressed by 2.31{{c}}), making 76ed80 very close to optimal for 12edo.
+The 80th harmonic would be extremely wide for an equivalence, so 76ed80 is better thought of as a compressed version of the ubiquitous [[12edo]]. Indeed, tuning the 80/1 ratio just instead of 2/1 results in octaves being [[stretched and compressed tuning|compressed]] by about 2.16{{c}}. The local [[The Riemann zeta function and tuning #Optimal octave stretch|zeta peak]] around 12 is located at 12.023183, which has a step size of 99.807{{c}} and an octave of 1197.686{{c}} (which is compressed by 2.31{{c}}), making 76ed80 extremely close to optimal for 12edo.
 === Harmonics ===