Definitions

Max diff

The largest cent difference between corresponding tones when comparing two scales of the same length. For example, the max diff between the just major scale 0, 203.9, 386.3, 498.0, 702.0, 884.4, 1088.3, 1200 and the equal-tempered major scale 0, 200, 400, 500, 700, 900, 1100, 1200 is 15.6¢, since abs(884.4 - 900) = 15.6.

Period

The interval after which a scale repeats — often the octave (2/1), but can be any interval (e.g. 3/1 for Bohlen-Pierce).

Rotation

A mode of a scale formed by starting on a different note. Rotation 0 is the scale itself; rotation k means the scale starting on its (k+1)th note, wrapping at the period.

Similar scales

Two scales are similar if a rotation of the second scale approximates the first scale. For example, the just major pentatonic 0, 203.9, 386.3, 702.0, 884.4, 1200 and the equal-tempered minor pentatonic 0, 300, 500, 700, 1000, 1200 are similar with rotation 1 and max diff 15.6¢.

Parent and child scales

If a larger scale contains an approximation of a smaller scale, both starting on the same root, we say the smaller scale is a child of the larger, and the larger a parent of the smaller. For example, the equal-tempered major pentatonic scale 0, 200, 400, 700, 900, 1200 is a child of the equal-tempered major scale 0, 200, 400, 500, 700, 900, 1100, 1200 with max diff 0¢, and a child of the just major scale 0, 203.9, 386.3, 498.0, 702.0, 884.4, 1088.3, 1200 with max diff 15.6¢.