Date of Completion


Embargo Period



Bax, Vaughan Williams, Nonatonic, Octatonic, Hexatonic, neo-Riemannian operations, transformational theory

Major Advisor

Alain Frogley

Associate Advisor

Richard Bass

Associate Advisor

Peter Kaminsky

Field of Study



Doctor of Philosophy

Open Access

Open Access


This study explores the pitch structures of passages within certain works by Ralph Vaughan Williams and Arnold Bax. A methodology that employs the nonatonic collection (set class 9-12) facilitates new insights into the harmonic language of symphonies by these two composers. The nonatonic collection has received only limited attention in studies of neo-Riemannian operations and transformational theory. This study seeks to go further in exploring the nonatonic’s potential in forming transformational networks, especially those involving familiar types of seventh chords. An analysis of the entirety of Vaughan Williams’s Fourth Symphony serves as the exemplar for these theories, and reveals that the nonatonic collection acts as a connecting thread between seemingly disparate pitch elements throughout the work. Nonatonicism is also revealed to be a significant structuring element in passages from Vaughan Williams’s Sixth Symphony and his Sinfonia Antartica.

A review of the historical context of the symphony in Great Britain shows that the need to craft a work of intellectual depth, simultaneously original and traditional, weighed heavily on the minds of British symphonists in the early twentieth century. The nonatonic collection, with its ability to bridge between tonal or modal pitch space and non-tonal or chromatic pitch space, seems to arise naturally from Vaughan Williams’s need to answer the pressures both of symphonic tradition and nascent modernism. The employment of nonatonicism is not restricted to Vaughan Williams; it is shown to be at work also in the Second and Third Symphonies of Arnold Bax. Bax gained considerable attention as a symphonist during the time that Vaughan Williams was working out his Fourth Symphony. Specific musical connections between works by Vaughan Williams and Bax have received little attention, beyond an enigmatic link between Vaughan Williams’s Piano Concerto and Bax’s Third Symphony (the original version of Vaughan Williams’s concerto contained a quotation of Bax’s symphony, but this quotation was later removed). While this study does not definitively solve the riddle connecting these two works, it does establish a shared harmonic language between Vaughan Williams and Bax, reinforcing previous suggestions that the two composers may have exchanged ideas.