Double-Tonic Complexes as Bistable Phenomena in Gershwin


In this paper, I analyze double-tonic complexes as bistable phenomena that arise from the collision of two relative-related keys using Gershwin’s Concerto in F as a case study. The double-tonic complex (Bailey 1985) has inspired studies that investigate tonal pairing, juxtaposition, or conflation of more than one key at a variety of structural levels in the music of several nineteenth-century composers (e.g., Lewis 1984; Kinderman and Krebs 1996). By adapting the work of Harrison 1994 and Swinden 2005, I create a music-theoretic parallel to a neural network model developed by Stadler and Kruse 1995 that models our perception of bistable images, e.g. the rabbit-duck illusion.

I propose treating conflated double-tonics as the collision of two keys' tonics that produces two bistable tonics, for example, an F-minor seventh-chord and an added-sixth A♭-major tetrachord. I refashion Swinden’s superscript-notation to emphasize both states (e.g., Foreground-Key^Alternate-Key^). To develop further this bistable interpretation, I introduce bistable dominants and investigate their voice-leading implications in a bistable dominant-to-tonic model. A harmonic, collision-based approach accentuates the paradox of bistable keys: both keys function as stable states, but because there remains a possibility of switching between them, the stability of each key is partially undermined by the other. Treating conflated, double-tonic complexes as bistable phenomena inspires compelling narratives for interpreting Gershwin’s Concerto and other pieces that have similar double-tonic complexes.