76ed80: Difference between revisions
m Text replacement - "{{mathematical interest}}" to "{{Mathematical interest}}" |
m Text replacement - "[[The Riemann zeta function and tuning #" to "[[Riemann zeta function #" |
||
| Line 4: | Line 4: | ||
== 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 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 [[Riemann zeta function #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 === | ||