76ed80: Difference between revisions
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== 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}}, making 76ed80 extremely close to optimal for 12edo. | |||
=== Harmonics === | |||
{{Harmonics in equal|76|80|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|76|80|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 76ed80 (continued)}} | |||
== See also == | |||
* [[12edo]] – relative edo | |||
* [[19edt]] – relative edt | |||
* [[28ed5]] – relative ed5 | |||
* [[31ed6]] – relative ed6 | |||
* [[40ed10]] – relative ed10 | |||
* [[43ed12]] – relative ed12 | |||
[[Category:12edo]] | |||
[[Category:Zeta-optimized tunings]] | |||