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{{mathematical interest}}
{{Mathematical interest}}
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
{{ED intro}}


== Theory ==
== Theory ==
The 2560th harmonic is far too wide to be a useful equivalence, so 57ed2560 is better thought of as a compressed version of [[5edo]]. Indeed, tuning the 96/1 ratio just instead of 2/1 results in octaves being [[stretched and compressed tuning|compressed]] by about 8.237{{c}}. It is almost exactly equal to the local [[The Riemann zeta function and tuning #Optimal octave stretch|zeta peak]] around 5, with an octave only 0.000612{{c}} off from the ideal size.
The 2560th harmonic is far too wide to be a useful equivalence, so 57ed2560 is better thought of as a compressed version of [[5edo]]. Indeed, tuning the 2560/1 ratio just instead of 2/1 results in octaves being [[stretched and compressed tuning|compressed]] by about 8.237{{c}}. It is almost exactly equal to the local [[The Riemann zeta function and tuning #Optimal octave stretch|zeta peak]] around 5, with an octave only 0.000612{{c}} off from the ideal size.


=== Harmonics ===
=== Harmonics ===