44ed5: Difference between revisions

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== Theory ==

44ed5 is very similar to [[19edo]], but with the [[5/1]] rather than the 2/1 being just. The [[~~The~~ Riemann zeta function ~~and tuning~~|local zeta peak]] around 19 is located at 18.948087, which has the octave stretched by 3.2877{{c}}, and the octave of 44ed5 comes extremely close (differing by only {{sfrac|1|9}}{{c}}), thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.

44ed5 is very similar to [[19edo]], but with the [[5/1]] rather than the 2/1 being just. The [[Riemann zeta function|local zeta peak]] around 19 is located at 18.948087, which has the octave stretched by 3.2877{{c}}, and the octave of 44ed5 comes extremely close (differing by only {{sfrac|1|9}}{{c}}), thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.

Other variants (which stretch the octave by different amounts, but the differences are probably imperceptible) are [[30edt]], [[49ed6]], and [[93ed30]]. The latter of the two optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp.

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 == Theory ==
-ed5 is very similar to [[19edo]], but with the [[5/1]] rather than the 2/1 being just. The [[The Riemann zeta function and tuning|local zeta peak]] around 19 is located at 18.948087, which has the octave stretched by 3.2877{{c}}, and the octave of 44ed5 comes extremely close (differing by only {{sfrac|1|9}}{{c}}), thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.
+ed5 is very similar to [[19edo]], but with the [[5/1]] rather than the 2/1 being just. The [[Riemann zeta function|local zeta peak]] around 19 is located at 18.948087, which has the octave stretched by 3.2877{{c}}, and the octave of 44ed5 comes extremely close (differing by only {{sfrac|1|9}}{{c}}), thus minimizing relative error as much as possible. Because 19edo itself is a flat-tending system, stretching the octave improves the overall tuning accuracy.
 Other variants (which stretch the octave by different amounts, but the differences are probably imperceptible) are [[30edt]], [[49ed6]], and [[93ed30]]. The latter of the two optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp.