Hugo Riemann

Riemann and dualism:

• Major and minor chords are inversionally related forms of the consonant triad

• Riemann believed in the existence of an undertone series up to 1905 "Das Problem des harmonischen Dualismus"

• For the major triad, the proportion relates to frequency and, for the minor, wavelength

The Development of Riemann's Theory of Harmonic Function:

• I : Thesis

• IV - I6/4 : Antithesis

• V - I : Synthesis

Digest of Daniel Harrison's Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents.

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