Towards a Hybrid Theoretical Model for Neoclassical Music: Schenkerian, Neo-Riemannian and Pitch-Class Set Theories

Abstract

This thesis explores the necessity for theoretical hybridity as an analytical tool to overcome the challenges faced in works that embody both tonal and post-tonal elements. This hybridised model responds to the lack of a single theory that accounts for neoclassical harmonic practices: Schenkerian methods prove useful in drawing out different structural levels whilst Neo-Riemannian theory recognises non-traditional chordal relationships, and the application of set theory can fill the gaps where none of the aforementioned methods are applicable. Although some have responded to this problem by extending the individual methods’ application (e.g. Baker, 1990) or by simultaneously using more than one analytical approach (e.g. Cinnamon, 1993; Pople, 1989), none of these authors have fully integrated the methods into one unified approach. And despite the large body of research that has examined perceptions of tension in tonal (Lerdahl and Jackendoff, 1983) and atonal (Dibben 1999) harmonies, there is no work that explores the perception of post-tonal harmonies.
The project begins with an appraisal of literature surrounding the conceptual issues around hybridity within music and various existing combined approaches to analyse music. This is then followed by the methodology – Voice-leading (VL) Reduction, Rhythmic Segmentation and Calculation, Beat-Class BC Set Theory, and an experimental enquiry into the measurement of post-tonal harmonic tension – exemplified through selected sections from a small number of studies: Mathis der Mahler by Paul Hindemith, “Tanec Loutek” (No. 5) from Puppets by Bohuslav Martinu, Passacaglia by Aaron Copland, Violin Concerto in D Minor by Ralph Vaughan Williams, Sonata No. 3 by George Enescu, Sonatine by Maurice Ravel, Piano Sonata No. 2 by Paul Hindemith, and Concerto for Piano and Wind Instruments by Igor Stravinsky.
The application of the model is then carried out through two complete case studies: First Movement of Hindemith’s Second Piano Sonata, and the first movement of Stravinsky’s Concerto for Piano and Wind Instruments. My analyses first perform the three approaches separately, before synthesising the results. To determine which pitch collections will be examined, the music is segmented into its core beat classes. My voice-leading analysis overlays three systems (treble and bass voice-leading reductions, pitch collection), describing the transformation between pitch collections. Line graphs chart the voice-leading movement between pitch collections against the treble voice-leading reduction, capturing the correlation between the melodic and harmonic factors. The rhythmic-phrase analysis is then integrated into the diagrams as a set of tables detailing its different hierarchies. The results reveal the correlation between middleground layers and phrase design, and between rhythmic features and other musical parameters. In all, the detailed examination of different musical parameters reveals that this hybridised model enables a comprehensive structural narrative for each piece, filling in existing theories’ lacunae by revealing a more detailed explanation of the harmonic content, an enriched middleground chart, and its articulation in other musical parameters. This thus reveals the model’s potential to revolutionise analytical approaches to neoclassical compositions and to understand their compositional techniques. Current findings also indicate that these graphical representations account for all types of chords as pitch collections and illustrate the relationship between each vertical sonority; that the aggregated voice-leading movement (AVL) – the total amount of voice-leading movement – can better account for the identification of post-tonal closure, and the results from the empirical study suggest that external factors need to be accounted for along with the AVL in order to relate theoretical to perceived tension.
This research will therefore not only contribute to post-tonal theory and analysis but also to music perception, to understand better how we conceive harmonic tension in music that embodies tonal and atonal elements.