Consistent circle: Difference between revisions

Line 55:

== Examples ==

[[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]] (assuming 12/11 is mapped to 1\8). 80edo does ''not'' have a 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}}. (This does however mean, because 8edo is a circle of ~13/10's, that 80edo has an ~~ultraweak~~ circle of 13/10's. If 8edo had only a weak circle of ~13/10's, this would still be true.)

[[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]] (assuming 12/11 is mapped to 1\8). 80edo does ''not'' have a 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}}. (This does however mean, because 8edo is a circle of ~13/10's, that 80edo has an sub-weak circle of 13/10's. If 8edo had only a weak circle of ~13/10's, this would still be true.)

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 ~[[35/32]]'s (meaning that 31edo is a (strong) circle of [[septimal neutral second]]s), where 35/32 = (5/4)/(8/7) = 5/4 * 7/4 / 2.

@@ Line 55: / Line 55: @@
 == Examples ==
-[[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]] (assuming 12/11 is mapped to 1\8). 80edo does ''not'' have a 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}}. (This does however mean, because 8edo is a circle of ~13/10's, that 80edo has an ultraweak circle of 13/10's. If 8edo had only a weak circle of ~13/10's, this would still be true.)
+[[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]] (assuming 12/11 is mapped to 1\8). 80edo does ''not'' have a 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}}. (This does however mean, because 8edo is a circle of ~13/10's, that 80edo has an sub-weak circle of 13/10's. If 8edo had only a weak circle of ~13/10's, this would still be true.)
 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 ~[[35/32]]'s (meaning that 31edo is a (strong) circle of [[septimal neutral second]]s), where 35/32 = (5/4)/(8/7) = 5/4 * 7/4 / 2.