Dr. Ross W. Duffin

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The Major and Minor tones are both part of the harmonic series and the Just scale. The usual whole tone in Just has the harmonic ratio 9:8, but to go from a 9:8 whole tone to a pure major 3rd above the starting note, a smaller tone is needed. That smaller tone has the harmonic ratio 10:9, representing the difference between the 5:4 (10:8) pure Major 3rd and the 9:8 whole tone. Its use in the Just scale thus depends on the context, with a tendency towards alternation in stepwise progressions. With a C-D Majortone, for example, we would expect to find E a Minor tone above D (a pure M3rd above C), and with a C-D Minor tone, we would expect to find Bb a Major tone below C (a pure M3rd below D). Meantone systems average the size of the two tones contained in the M3rd and thus have no Major or Minor forms.

Page last modified: March 25, 2015