198ed304: Difference between revisions

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+{{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]]