Mu badness: Difference between revisions
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Lériendil prefers to set the denominator to <math>\frac{\pi^{2}}{20}</math> instead, as it can be shown that this represents a stricter bound on μ and has the advantage of the maximal possible badness for an [[EDO]] being a rational number, 5/9. This also flips the result so that higher values represent worse tunings, as would be expected from a "badness" function. | Lériendil prefers to set the denominator to <math>\frac{\pi^{2}}{20}</math> instead, as it can be shown that this represents a stricter bound on μ and has the advantage of the maximal possible badness for an [[EDO]] being a rational number, 5/9. This also flips the result so that higher values represent worse tunings, as would be expected from a "badness" function. | ||
[[File:Mu badness.png|alt=Mu badness.png|1024x107px]] | [[File:Mu badness.png|alt=Mu badness.png|1024x107px]] <br /> | ||
Mu badness for equal-step tunings between 1edo and 121edo using <math>\frac{\pi^{2}}{20}</math> scaling convention. The blue and orange dotted lines represent the best possible odd ed4 and the worst possible edo, respectively. | |||
== Peaks and Valleys == | |||
{| class="wikitable" | {| class="wikitable" | ||