Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

@ 00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Login   |  Encyclopedia Index

Badness

"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.

Logflat Badness

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:

and so forth. If d is the number of primes in the prime limit p, so that d = pi(p), then the exponent e should be chosen as d / (d - r) to achieve logflatness.

[Gene Ward SmithYahoo tuning-math message 11108]
. . . . . . . . .

The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.

support level