In an analytical vignette, David Lewin (1998) creates a musical space to trace occurrences of a particular motive in the opening of J.S. Bach's Fugue in F# minor from Book 1 of the Well-Tempered Clavier. The space organizes all possible versions of trichord (013)—some configuration of a semitone within a minor third—so that adjacent versions share some interval. Lewin suggests that the reader explore the implications of his approach through an analysis of “Durch Adams Fall ist ganz verderbt,” BWV 637. Although Reed and Bain (2007) rework Lewin's rather old-fashioned-looking analysis of the fugue using 3D geometry, no one has pursued Lewin's suggestion with the chorale prelude.

Part 1 of my presentation takes up Lewin's challenge, tracing occurrences of the same (013) motive in “Durch Adams Fall” on Lewin's map. The (013) idea engages what Peter Williams (2003, 304) calls the motivating chromatic “passus” or “step” figure of the piece. The resulting musical map of the (013) motive offers a starting point for a broader analysis of the piece, which explores the absence of the intervallic motive in the pedal, and its rarity in the chorale melody. I propose that the presence or absence of the motive relates to the “corruption” of the piece's title—an aspect which is easily overlooked given the extravagant “falling” in the pedal.

Part 2 of the presentation expands Lewin's approach to consider the narrative possibilities of motivic tetrachords in the cantatas and other organ works. For example, in the terzetto “Zerdern müssen von den Winden” from BWV 150, a series of tetrachords serve as cadential gestures. The text compares the faithful to sturdy cedars, buffeted—and sometimes overcome—by violent winds. As the cedars are blown by the winds, the tetrachords are blown through their various intervallic orderings. I offer further demonstrations of motivic tetrachords in BWV 82 and tetrachords and hexachords in BWV 612.

More broadly, my presentation models a way by which technical analysis can engage questions of musical meaning and narrative—a connection that is common in other repertoires but is less established in contemporary Anglo-American studies of Bach's music. The issue becomes especially acute in the music theory classroom, where due to curriculum or time, study of Bach's music in particular and the Baroque in general is frequently limited to the classification of formal genres, harmony labeling, or text-painting. Building on the transformational approaches to intervallic modeling of Steven Rings and Dmitri Tymoczko, I argue that technical but accessible visualizations of intervallic processes may offer a solution—and illuminate a fascinating aspect of Bach's compositional technique.

Select Bibliography

Lewin, David. 1998. “Notes on the Opening of the F# minor Fugue from WTC1.” Journal of Music Theory 42 (2): 235-239.

Reed, Jacob Rosenthal and Matthew Neil Bain. 2007. “A Tetrahelix Animates Bach: Revisualization of David Lewin's Analysis of the Opening of the F# Minor Fugue from WTC I.” Music Theory Online 13 (4). https://www.mtosmt.org/issues/mto.07.13.4/mto.07.13.4.reed_bain.html

Williams, Peter. 2003. The Organ Music of J.S. Bach. Cambridge University Press.