Maximal evenness

A discussion on these concepts can be found in Timothy Johnson's book on the mathematical foundations of diatonic scale theory.

[2] Jack Douthett and Richard Krantz introduced maximally even sets to the mathematics literature.

The whole-tone scale is also maximally even, but it is not well-formed since each generic interval comes in only one size.

(ibid, p.115) This nested quality resembles Fred Lerdahl's[6] "reductional format" for pitch space from the bottom up: In a dynamical approach, spinning concentric circles and iterated maximally even sets have been constructed.

[7] Emmanuel Amiot has discovered yet another way to define maximally even sets by employing discrete Fourier transforms.

The major scale is maximally even. For example, for every generic interval of a second there are only two possible specific intervals: 1 semitone (a minor second) or 2 semitones (a major second).
The harmonic minor scale is not maximally even. For the generic interval of a second rather than only two specific intervals, the scale contains three: 1, 2, and 3 ( augmented second ) semitones.