Consistent circle: Difference between revisions

Godtone (talk | contribs)
m Examples: tildes & better notation
Godtone (talk | contribs)
m Definition: add "strong circle"
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: |''N''<sup>2</sup> log<sub>2</sub>(a/b) / GCD(''k'',''N'')| < 1/2
: |''N''<sup>2</sup> log<sub>2</sub>(a/b) / GCD(''k'',''N'')| < 1/2


And is a ''weak circle'' if it is < 1 instead.
And is a ''weak circle'' if it is < 1 instead, or a ''strong circle'' if it is < 1/4.


=== Weak circle ===
=== Weak circle ===
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This is a much more common type of circle that is still generally reliable for most purposes, hence useful to distinguish.
This is a much more common type of circle that is still generally reliable for most purposes, hence useful to distinguish.
=== Strong circle ===
A strong circle is a circle with closing error of less than a quarter of an EDOstep, so that it is in some sense as reliable as you could possibly ask of it.
This is useful because it means that when you tune perfectly, it will have significantly more plausible "closure" than a non-strong circle.
For example, [[12edo]], [[53edo]] and [[665edo]] are the first three strong circles of ~3/2, given that the remnant is less than a quarter of an edostep in each case.


=== Is vs. has ===
=== Is vs. has ===