The Riemann zeta function and tuning: Difference between revisions

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Quick info: zeta peak edos: Fix error: switched pure octaves, rewrite
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== Quick info: zeta peak edos ==
== Quick info: zeta peak edos ==
Best edos according to the zeta metric: {{EDOs|1, 2, 3, 5, 7, 10, 12, 19, 22, 31, 41, 53, 87, 118, 130, 171, 224, 270, 311}}
These lists give the best [[equal divisions of the octave]] for their size according to the zeta metric.


Best edos according to the zeta metric (assuming pure octaves): {{EDOs|1, 2, 3, 4, 5, 7, 10, 12, 19, 22, 27, 31, 41, 53, 72, 99, 118, 130, 152, 171, 217, 224, 270,}}
Zeta peak integer EDOs (Pure octaves): {{EDOs|1, 2, 3, 5, 7, 10, 12, 19, 22, 31, 41, 53, 87, 118, 130, 171, 224, 270, 311, ...}}
 
Zeta peak EDOs (Detuned octaves): {{EDOs|1, 2, 3, 4, 5, 7, 10, 12, 19, 22, 27, 31, 41, 53, 72, 99, 118, 130, 152, 171, 217, 224, 270, ...}}
 
See the [[#Zeta edo lists|section below]] for more information.


== Intuitive explanation ==
== Intuitive explanation ==