Reciprocity

Chapter 3 provides support for a chapter 2 premise that inverts a cardinal tenet of classical theory: that consonant triads are generated from (dissonant) augmented ones. It develops Fétis’s view that tonality and repetition (“uniformity”) stand in reciprocal relation. When repetition takes precedence over tonality, equal divisions of the octave, of which augmented triads are a species, come to the fore. The point is illustrated through passages from piano sonatas of Beethoven (Appassionata) and Schubert’s (D. 959 in A major), where consecutive transposition by major third causes an evident large-scale arpeggiation of the augmented triad rather than the consonant arpeggiation identified by Schenker as fundamental to diatonic tonality. After 1850, augmented triads sound more frequently as surface harmonies, where they can be made to sound more stable than the consonant triads with which they come into contact; examples from Liszt’s Faust Symphony, Rimsky-Korsakov’s Antar Symphony, and Fauré’s Requiem illustrate. The chapter closes with a consideration of an 1853 treatise of Weitzmann which implies that the twenty-four consonant triads are organized by their voice-leading proximity to the four augmented triads.