"Badness" is a function of the complexity and error of a temperament, which increases if you increase either complexity or error. A common example of a badness function is C e · err, where C is the complexity and e is a fixed exponent. The idea of a badness function is to compare and rank temperaments, with a lower badness number being better.
A logflat badness measure chooses the exponent e of complexity C so that there is a badness such that below it an infinite number of temperaments can be found, but if e were to be raised, only a finite number could be found below any badness cutoff. If L is a regular temperament of rank r (or dimension r - 1), so that:
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