Chromatic block analysis: a practical approach to atonal harmony and counterpoint for the undergraduate classroom and beyond

Abstract

Typically, analyses of the music of the Second Viennese School prioritize the horizontal/linear logic of the music and de-emphasize the vertical/harmonic logic. Chords are usually explained as simultaneous expressions of a motive or row instead of fundamental harmonic units. However, such an approach does not answer an essential question: why is this line sounding with this one? What I propose in this presentation is to break away from the traditionally linear analysis of atonal music, setting aside motives and rows and instead forming a new methodology to examine harmonic logic on its own terms. This logic can be understood through what I call chromatic “blocks,” each of which connect all the various voices and chords within it, regardless of their horizontal origins. Blocks typically consist of four or more notes, most of which are “complemented” by a note a half-step away (whether literally or in a different register). The purpose of these blocks is to define zones of half-step complementarity, clarifying the chromatic voice-leading by analyzing it harmonically; in this way, it is analogous to figured bass theory in the Baroque, which is also a method of simplifying units of voice-leading by wrapping them up in a harmonic package. To support this, I will first trace the origins of half-step complementarity back to Wagnerian voice-leading; then, I will give examples of chromatic block analysis of both serial and “freely atonal” works and propose that this method is potentially more clear and pedagogically helpful for students of theory than existing models.