Badness
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 edos) typically do not have low error, and very low error temperaments (e.g. microtemperaments) 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.
Several different badness measures are in use, including Cangwu badness, TE simple badness, and TE logflat badness.
- Note: Smith TE logflat badness is the badness appearing on temperament pages, unless stated otherwise.