Consistent circle: Difference between revisions

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== Definition ==

We define a [[circle]]{{idiosyncratic}} of some [[interval]] ''a''/''b'' as an interval with such extremely low relative error with respect to ''N''-[[edo]] that when we stack it ''m'' > 0 times, where ''m'' is the minimal amount required to reach a whole number of octaves, its ~~mapping by some val deemed appropriate~~ is [[consistent]] with its actual size in [[JI]], which is to say it is off by less than 0.5\''N'' = 1200{{cent}} / ''N'' / 2 (a.k.a. 50% relative error). Note that this definition implies that the circle need not reach all notes of the EDO if the circle occurs in a subset EDO, but that the circle must have low enough error that within the full EDO it is still consistent.

We define a [[circle]]{{idiosyncratic}} of some [[interval]] ''a''/''b'' as an interval with such extremely low relative error with respect to ''N''-[[edo]] that when we stack it ''m'' > 0 times, where ''m'' is the minimal amount required to reach a whole number of octaves, its [[direct approximation]] is [[consistent]] with its actual size in [[JI]], which is to say it is off by less than 0.5\''N'' = 1200{{cent}} / ''N'' / 2 (a.k.a. 50% relative error). Note that this definition implies that the circle need not reach all notes of the EDO if the circle occurs in a subset EDO, but that the circle must have low enough error that within the full EDO it is still consistent.

=== Closing error ===

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 == Definition ==
-We define a [[circle]]{{idiosyncratic}} of some [[interval]] ''a''/''b'' as an interval with such extremely low relative error with respect to ''N''-[[edo]] that when we stack it ''m'' > 0 times, where ''m'' is the minimal amount required to reach a whole number of octaves, its mapping by some val deemed appropriate is [[consistent]] with its actual size in [[JI]], which is to say it is off by less than 0.5\''N'' = 1200{{cent}} / ''N'' / 2 (a.k.a. 50% relative error). Note that this definition implies that the circle need not reach all notes of the EDO if the circle occurs in a subset EDO, but that the circle must have low enough error that within the full EDO it is still consistent.
+We define a [[circle]]{{idiosyncratic}} of some [[interval]] ''a''/''b'' as an interval with such extremely low relative error with respect to ''N''-[[edo]] that when we stack it ''m'' > 0 times, where ''m'' is the minimal amount required to reach a whole number of octaves, its [[direct approximation]] is [[consistent]] with its actual size in [[JI]], which is to say it is off by less than 0.5\''N'' = 1200{{cent}} / ''N'' / 2 (a.k.a. 50% relative error). Note that this definition implies that the circle need not reach all notes of the EDO if the circle occurs in a subset EDO, but that the circle must have low enough error that within the full EDO it is still consistent.
 === Closing error ===