31edf: Difference between revisions
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== Theory == | == Theory == | ||
31edf is almost identical to [[53edo]], but with the 3/2 rather than the [[2/1]] being [[just]]. The octave is [[ | 31edf is almost identical to [[53edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1]] being [[just]]. The octave is [[stretched and compressed tuning|stretched]] by about 0.117 [[cents]]. Like 53edo, 31edf is [[consistent]] to the [[integer limit|10-integer-limit]]. While the [[3-limit]] part is tuned sharp plus a sharper [[7/1|7]], the [[5/1|5]], [[11/1|11]], [[13/1|13]], and [[19/1|19]] remain flat but significantly less so than in 53edo. | ||
The [[The Riemann zeta function and tuning|local zeta peak]] around 53 is located at 52.996829, which has the octave stretched by 0.0718{{c}}; the octave of 31edf comes extremely close (differing by only {{sfrac|1|22}}{{c}}), thus minimizing relative error as much as possible. | |||
=== Harmonics === | === Harmonics === | ||
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* [[84edt]] – relative edt | * [[84edt]] – relative edt | ||
* [[137ed6]] – relative ed6 | * [[137ed6]] – relative ed6 | ||
[[Category:53edo]] | |||
[[Category:Zeta-optimized tunings]] | |||