76ed80: Difference between revisions
ArrowHead294 (talk | contribs) m →Theory |
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== Theory == | == Theory == | ||
The 80th harmonic is too wide to be a useful 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}} | The 80th harmonic is too wide to be a useful 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}}; 76ed80's octave is off from the zeta peak by only {{frac|1|6}}{{c}} and is therefore extremely close to optimal for 12edo. | ||
=== Harmonics === | === Harmonics === | ||