Consistent circle: Difference between revisions

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== Examples ==

[[80edo]] is a circle of [[12/11]]'s because [[Undecimal octatonic comma|(12/11)<sup>8</sup> / 2]] = ~5.1{{cent}} < 0.5\80 = 7.5{{cent}}. ~5.1{{cent}} (the size of the [[undecimal octatonic comma]]) is thus the ''closing error'' of the circle of 12/11's in any multiple of [[8edo]] where 12/11 is mapped ~~consistently~~ to 1\8. 80edo is ''not'' a proper circle of [[13/10]]'s, even though [[8edo]] is a circle of 13/10's (which requires that 13/10 is mapped [[consistent]]ly by the val chosen), because the accrued error exceeds 0.5\80 = 7.5{{cent}}.

[[80edo]] has a circle of [[12/11]]'s because [[Undecimal octatonic comma|(12/11)<sup>8</sup> / 2]] = ~5.1{{cent}} < 0.5\80 = 7.5{{cent}}. ~5.1{{cent}} (the size of the [[undecimal octatonic comma]]) is thus the ''closing error'' of the circle of 12/11's in any multiple of [[8edo]] where 12/11 is mapped to 1\8. 80edo does ''not'' have a proper circle of [[13/10]]'s, even though [[8edo]] is a circle of 13/10's (which requires that 13/10 is mapped to 3\8 [[consistent]]ly by the val chosen), because the accrued error exceeds 0.5\80 = 7.5{{cent}}.

Another example from before is that 31edo is a weak circle of 5/4's and 7/4's, but note that 31edo is a circle of (5/4)/(8/7) = 5/4 * 7/4 / 2 = [[35/32]]'s (meaning that 31edo is a (strong) circle of [[septimal neutral second]]s).

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 == Examples ==
-[[80edo]] is a circle of [[12/11]]'s because [[Undecimal octatonic comma|(12/11)<sup>8</sup> / 2]] = ~5.1{{cent}} < 0.5\80 = 7.5{{cent}}. ~5.1{{cent}} (the size of the [[undecimal octatonic comma]]) is thus the ''closing error'' of the circle of 12/11's in any multiple of [[8edo]] where 12/11 is mapped consistently to 1\8. 80edo is ''not'' a proper circle of [[13/10]]'s, even though [[8edo]] is a circle of 13/10's (which requires that 13/10 is mapped [[consistent]]ly by the val chosen), because the accrued error exceeds 0.5\80 = 7.5{{cent}}.
+[[80edo]] has a circle of [[12/11]]'s because [[Undecimal octatonic comma|(12/11)<sup>8</sup> / 2]] = ~5.1{{cent}} < 0.5\80 = 7.5{{cent}}. ~5.1{{cent}} (the size of the [[undecimal octatonic comma]]) is thus the ''closing error'' of the circle of 12/11's in any multiple of [[8edo]] where 12/11 is mapped to 1\8. 80edo does ''not'' have a proper circle of [[13/10]]'s, even though [[8edo]] is a circle of 13/10's (which requires that 13/10 is mapped to 3\8 [[consistent]]ly by the val chosen), because the accrued error exceeds 0.5\80 = 7.5{{cent}}.
 Another example from before is that 31edo is a weak circle of 5/4's and 7/4's, but note that 31edo is a circle of (5/4)/(8/7) = 5/4 * 7/4 / 2 = [[35/32]]'s (meaning that 31edo is a (strong) circle of [[septimal neutral second]]s).