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Additional info for A theory of harmony
And curiously enough, it resolves into the natural-seventh chord: This view is at variance with Riemann's, to whom the seventh maintains its original function whether the chord is major or minor:* It seems to me that in this chord progression the seventh has to be interpreted differently. About that later (chapter 9). The natural seventh, carrying into the open the latent dynamism of the triad, may touch off a chain reaction, thereby destroying the hierarchical order: These progressions have something frightening about them, suggested by a tremendous natural driving force running loose from the ordering principles.
It represents a first organization of the tone mass, a first realization of the idea of tonality, affording numerous musical conclusions, some of which we shall now consider. Page 27 First we have to establish the series of dominantic progression according to what we have learned. We organize the succession of fifths around C as tonic in the telluric sense, while respecting the genesis of C minor as G¯º. The triads immediately flanking C± will then be G+ and F¯. ) The primary tendencies of the major and minor triads (as exemplified in the primary cadences) create two currents in opposite directions throughout the table.
This should not deceive us at the veritable reciprocals, shown in the following cadences: Here is the complete cadence (reciprocal chords are marked * and **): Page 33 The beauty of this cadence stems from the absolute reciprocity of minor and major. For the sake of comparison, play the cadence in Å: The balance is disrupted; the succession is trite and without beauty. Next in order is the tendency of the other exterior tone to become generator Note: in four-part setting it is advisable to double the tone on whose change of function the transformation depends: Instead of becoming generator, an exterior tone may become dominant: Finally, the middle tone may become determinant: Page 34 The transformations are analogous for the sixth chord( in minor ).