198ed304: Difference between revisions
ArrowHead294 (talk | contribs) Make page |
m Text replacement - "{{mathematical interest}}" to "{{Mathematical interest}}" |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{ | {{Mathematical interest}} | ||
{{ | {{Infobox ET}} | ||
{{ED intro}} | |||
== 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 Riemann zeta function and tuning #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 in equal|298|304|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|198|304|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 198ed304 (continued)}} | |||
== See also == | |||
* [[14edf]] – relative edf | |||
* [[24edo]] – relative edo | |||
* [[38edt]] – relative edt | |||
* [[56ed5]] – relative ed5 | |||
* [[62ed6]] – relative ed6 | |||
* [[86ed12]] – relative ed12 | |||
[[Category:24edo]] | |||
[[Category:Zeta-optimized tunings]] | |||