198ed304: Difference between revisions
m Text replacement - "{{infobox et}}↵{{ed intro}}" to "{{Infobox ET}} {{ED intro}}" |
m Text replacement - "[[The Riemann zeta function and tuning #" to "[[Riemann zeta function #" |
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{{ | {{Mathematical interest}} | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
== Theory == | == Theory == | ||
The 304th harmonic is far too wide to be a useful equivalence, so 198ed304 is better thought of as a compressed version of [[24edo]]. Indeed, tuning the 304/1 ratio just instead of 2/1 results in octaves being [[stretched and compressed tuning|stretched]] by about 0.301{{c}}. The local [[ | The 304th harmonic is far too wide to be a useful equivalence, so 198ed304 is better thought of as a compressed version of [[24edo]]. Indeed, tuning the 304/1 ratio just instead of 2/1 results in octaves being [[stretched and compressed tuning|stretched]] by about 0.301{{c}}. The local [[Riemann zeta function #Optimal octave stretch|zeta peak]] around 24 is located at 24.005742, which has a step size of 49.98804{{c}} and an octave of 1199.713{{c}} (which is compressed by 0.287{{c}}), making 198ed304 extremely close to optimal for 24edo. | ||
=== Harmonics === | === Harmonics === | ||