Mu badness: Difference between revisions

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-WIP
+μ always provides a value between 1 and ζ(2) = (π^2)/6 ≈ 1.6449, as such, the final "mu badness" result can be obtained by
+<math>\mu_{s}\left(x\right)=1-\frac{\mu\left(x\right)-1}{\left(\frac{\pi^{2}}{6}\right)-1}</math>
+This also flips the result so that higher values represent worse tunings, as would be expected from a "badness" function.
+{| class="wikitable"
+|+Mu badness (μ<sub>s</sub>(x)) for edos, calculated up to k=100
+!Edo
+!Badness
+|-
+|5
+|0.182
+|-
+|7
+|0.184
+|-
+|12
+|0.126
+|-
+|13
+|0.311
+|-
+|15
+|0.227
+|-
+|16
+|0.278
+|-
+|17
+|0.191
+|-
+|19
+|0.175
+|-
+|22
+|0.163
+|-
+|23
+|0.369
+|-
+|24
+|0.147
+|-
+|25
+|0.278
+|-
+|26
+|0.239
+|-
+|27
+|0.253
+|-
+|29
+|0.177
+|-
+|31
+|0.139
+|-
+|34
+|0.170
+|-
+|41
+|0.108
+|-
+|53
+|0.086
+|}
+One can also define mu peaks, similar to zeta peaks. The mu peak integer edos (ignoring zero) calculated up to k=100 include 1, 2, 3, 5, 12, 41, 53, 441, 494, 612, 2460, 3125, 6079... Note that this may differ slightly from the true list, because I am using only the first 100 terms of μ.
+The mu valley edos calculated up to k=100 include 1, 8, 11, 18, 23, 76, 194, 247...