76ed80: Difference between revisions

ArrowHead294 (talk | contribs)
m Text replacement - "{{mathematical interest}}" to "{{Mathematical interest}}"
 
(2 intermediate revisions by one other user not shown)
Line 1: Line 1:
{{mathematical interest}}
{{Mathematical interest}}
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
{{ED intro}}


== 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}}; 76ed80's octave is off from the zeta peak by only {{frac|1|6}}{{c}} and is therefore extremely close to optimal for 12edo.
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 ===