Chapter 7 considers how to integrate dissonant tetrachords into a model that focuses on triads. In order to disable the requirement that an analytic approach to dissonance must be internally consistent, the chapter begins by showing that Rameau’s theory of dissonance is based on four partly incommensurate principles, each of which is present in current classical theories of dissonance. The chapter then develops two incommensurate ways to integrate dissonance into pan-triadic syntax. The first way, proceeding by extension, involves reducing a chord to its consonant subset, if the latter is unique. The technique enriches a motivic and hermeneutic analysis of Wagner’s Parsifal by enlarging its scope. The second way, proceeding by analogy, groups dominant and half-diminished-seventh chords into a single Tristan genus, on the basis that they are minimal perturbation so the perfectly equal fully-diminished seventh chord. Geometric layouts (Douthett’s Power Towers) and transformations, analogous to the triadic case, are developed for charting progressions within the Tristan genus. The chapter concludes with an extended analysis of Chopin’s e-minor prelude.
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