59edf: Difference between revisions
Every EDF up to 60 except this one had a page, so I made this one such that someone can travel between any smaller EDF and 60edf just using the info boxes; ended up discovering this is actually a pretty based stretched tuning of 101edo along the way |
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== Theory == | == Theory == | ||
59edf corresponds is [[101edo]] but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 1.65 [[cents]]. 58edf is [[consistent]] to the [[integer limit|7-integer-limit]]. In comparison, 101edo is only consistent up to the 3-integer-limit. | 59edf corresponds is [[101edo]] but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 1.65 [[cents]]. 58edf is [[consistent]] to the [[integer limit|7-integer-limit]]. In comparison, 101edo is only consistent up to the 3-integer-limit. | ||
Where each of 101edo's [[prime]]s 5, 7 and 11 have two about equally good mappings with 40-60% [[relative error]], 59edf instead has one mapping for each with 5-30% relative error, at the cost of only minimal damage to the 2 and 3. | Where each of 101edo's [[prime]]s 5, 7 and 11 have two about equally good mappings with 40-60% [[relative error]], 59edf instead has one mapping for each with 5-30% relative error, at the cost of only minimal damage to the 2 and 3. | ||
59edf is very close to [[zpi|581zpi]], the biggest of the [[Zeta]] peaks near 101edo. | |||
=== Harmonics === | === Harmonics === | ||
59edf approximates all no-19s [[29-limit]] primes with less than 30% relative error. | |||
{{Harmonics in equal|59|3|2|intervals=integer|columns=11}} | {{Harmonics in equal|59|3|2|intervals=integer|columns=11}} | ||
{{Harmonics in equal|59|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edf (continued)}} | {{Harmonics in equal|59|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edf (continued)}} | ||