Therefore, the enigmatic scale is not proper. Diatonic scale theory Balzano introduced the idea of attempting to characterize the diatonic scale in terms of propriety. There are no strictly proper seven-note scales in 12 equal temperament; however, there are five proper scales, one of which is the diatonic scale. Here transposition and modes are not counted separately, so that diatonic scale encompasses both the major diatonic scale and the natural minor scale beginning with any pitch. Each of these scales, if spelled correctly, has a version in any meantone tuning, and when the fifth is flatter than 700 cents, they all become strictly proper. In particular, five of the seven strictly proper seven-note scales in 19 equal temperament are one of these scales. The five scales are: Diatonic: C D E F G A B Melodic/ascending minor/jazz minor: C D E F G A B Harmonic minor: C D E F G A B Harmonic major: C D E F G A B Major Locrian: C D E F G A B In any meantone system with fifths flatter than 700 cents, one also has the following strictly proper scale: C D E F G A B (which is Phrygian Dominant 4 scale). The diatonic, ascending minor, harmonic minor, harmonic major and this last unnamed scale all contain complete circles of three major and four minor thirds, variously arranged. The Locrian major scale has a circle of four major and two minor thirds, along with a diminished third, which in septimal meantone temperament approximates a septimal major second of ratio . The other scales are all of the scales with a complete circle of three major and four minor thirds, which since ()3 ()4 = , tempered to two octaves in meantone, is indicative of meantone. The first three scales are of basic importance to common practice music, and the harmonic major scale often used, and that the diatonic scale is not singled out by propriety is perhaps less interesting than that the backbone scales of diatonic practice all are. See also Deep scale property References Further reading Gerald J. Balzano, The Group-Theoretic Description of 12-fold and Microtonal Pitch Systems, Computer Music Journal 4/4 (1980) 66–84 Gerald J. Balzano, The Pitch Set as a Level of Description for Studying Musical Pitch Perception, in Music, Mind, and Brain, Manfred Clynes, ed., Plenum Press, 1982 David Rothenberg, A Model for Pattern Perception