Vulture family: Difference between revisions
→Septimal vulture: being a microtemp isn't a cause of finding prime 7 at -56 gensteps. Explain how -56 can be derived from the garischisma |
→Vulture: add 2.3.5.19 vulture which is unusually low in badness as an extension and solves the interpretation of the gen very nicely |
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[[Badness]] (Smith): 0.041431 | [[Badness]] (Smith): 0.041431 | ||
Badness (Dirichlet): 0.972 | |||
=== 2.3.5.19 === | |||
It can be observed that the generator of vulture is very close to [[25/19]]; this corresponds to tempering out [[1216/1215]] = ([[19/15]])/([[9/8|18/16]])<sup>2</sup> = S16/S18. It results in a surprising decrease in Dirichlet badness, and (up to [[octave equivalence]]) finds [[19/16]] at 41 generators so that [[19/10]] is found at 20 generators, [[38/27]] is found at 18, [[19/15]] is found at 16 (as 3 is found at 4) and 76/45 is found at 12. | |||
Subgroup: 2.3.5.19 | |||
Commas: 1216/1215, 64000000/63950067 | |||
{{Mapping|legend=1| 1 0 -6 -12 | 0 4 21 41 }} | |||
[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~25/19 = 475.542 | |||
: [[error map]]: {{val| 0.000 +0.214 +0.075 -0.278 }} | |||
{{Optimal ET sequence|legend=1| 53, 164, 217, 270, 593, 863 }} | |||
Badness (Dirichlet): 0.232 | |||
== Septimal vulture == | == Septimal vulture == | ||