Why are major and minor harmonies multiple orders of magnitude more common than modal harmony?
At least for Western music of the past 300 years, it has been far more common for music to have major or minor scales as their basis of harmony, as opposed to a modal harmony. Is there a reason modal harmonies (other than aeolian or ionian) are not used more often?
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Well, harmonies cannot help being mostly major and minor. If you take a look at simple chords, there is C-E-G, F-A-C, G-B-D in the major category, D-F-A, E-G-B, A-C-E in the minor category and B-D-F as a diminuished chord. Of course, these chords can occur in the context of any church mode as well, but the chords as such fall into two categories.
A mode is only established in the context of chord patterns. Minor is actually the revolutionary here since its modifications (harmonic/melodic minor) fall outside of the church modalities and thus lead to a much stronger and less ambiguous focus on the tonic.
So Minor's modifications make it special from other modes, and the modifications are mostly borrowed from Major mode, making the two one pair working with related cadenze which are essentially tonic-leading chord sequences.
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