Rothenberg Propriety - Diatonic Scale Theory

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 we are not counting transposition separately, so that diatonic scale encompasses both the major diatonic scale and the natural minor scale. 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/major/Ionian: C D E F G A B

• Melodic/Ascending 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, we also have the following strictly proper scale: C D♭ E F♭ G A♭ B♭.

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 8/7. The other scales are all of the scales with a complete circle of three major and four minor thirds, which since (5/4)3 (6/5)4 = 81/20, 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 the fact that the diatonic scale is not singled out by propriety is perhaps less interesting than the fact that the backbone scales of diatonic practice all are.