Badness: Difference between revisions

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'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. in terms of both [[complexity]] and [[error]], two measures that usually vary in opposite directions.

Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.

Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error. A temperament is said to be '''efficient''' if it achieves low badness.

Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]]. Some also have several normalizing coefficients.

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 '''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. in terms of both [[complexity]] and [[error]], two measures that usually vary in opposite directions.
-Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.
+Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error. A temperament is said to be '''efficient''' if it achieves low badness.
 Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]]. Some also have several normalizing coefficients.