Advanced Theory
In the German theory by or derived from Hugo Riemann, the minor mode is considered the inverse of the major mode, an upside down major scale based on (theoretical) undertones rather than (actual) overtones (harmonics) (See also: Utonality). The "root" of the minor triad is thus considered the top of the fifth, which, in the United States, is called "the" fifth. So in C minor, the tonic root is actually G, and the leading tone is A♭ (a halfstep), rather than, in major, the root being C and the leading tone B (a halfstep). Also, since all chords are analyzed as having a tonic, subdominant, or dominant function, with, for instance, in C, A-minor being considered the tonic parallel (US relative), Tp, the use of minor mode root chord progressions in major such as A♭-major—B♭-major—C-major is analyzed as sP—dP—T, the minor subdominant parallel, the minor dominant parallel, and the major tonic. (Gjerdingen, 1990)
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