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

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

Post-tonal analytical techniques: Stravinsky’s symphonies of wind instruments

The analysis of post-tonal music remains problematic. Analytical methodologies designed specifically for tonal or atonal music require substantial modification if they are to effectively analyse post-tonal works. Stravinsky's Symphonies of Wind Instruments is a fine model of post-tonal originality and is a difficult piece for analysis. Following a discussion of various analytical approaches, this paper presents a detailed analytical examination of Symphonies of Wind Instruments. The paper closes by developing conclusions and acknowledging the continuing advances of music analysis

Measuring Harmonic Tension in Post-Tonal Repertoire

Despite the large body of research that has examined tonal and atonal harmonies to our perception of tension, there is no work that describes or explores the perception of post-tonal chords, but more specifically, chords that contain both tonal and post-tonal features. This article applies the concept of calculating the total amount of voice-leading movement, to examine its relationship to our perception of tension and release. To do this, three neoclassical pieces are selected to analyze the relationship between theoretical and perceived tension. The findings suggest that in addition to calculating the horizontal motion between harmonies, physical and acoustical factors play a critical role in relating theoretical to perceived tension. This approach is adaptable to other neoclassical works and in addition, this study could have implications in other musical fields such as performance practices and analyzing formal functions in post-tonal repertoire

Performance Following: Real-Time Prediction of Musical Sequences Without a Score

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Perception based approach on pattern discovery and organisation of point-set data

The general topic of the thesis is computer aided music analysis on point-set data utilising theories outlined in Timo Laiho’s Analytic-Generative Methodology (AGM) [19]. The topic is in the field of music information retrieval, and is related to previous work on both pattern discovery and computational models of music. The thesis aims to provide analysis results that can be compared to existing studies. AGM introduces two concepts based on perception, sensation and cognitive processing: interval–time complex (IntiC) and musical vectors (muV). These provide a mathematical framework for the analysis of music. IntiC is a value associated with the velocity, or rate of change, between musical notes. Musical vectors are the vector representations of these rates of change. Laiho explains these attributes as meaningful for both music analysis and as tools for music generation. Both of these attributes can be computed from a point-set representation of music data. The concepts in AGM can be viewed as being related to geometric methods for pattern discovery algorithmsof Meredith, Lemström et al.[24] whointroduce afamily of ‘Structure Induction Algorithms’. These algorithms are used to find repeating patterns in multidimensional point-set data. Algorithmic implementations of intiC and muV were made for this thesis and examined in the use of rating and selecting patterns output by the pattern discovery algorithms. In addition software tools for using these concepts of AGM were created. The concepts of AGM and pattern discovery were further related to existing work in computer aided musicology

Review of The Music of Elliott Carter, Second Edition. By David Schiff.

The second edition of David Schiff's The Music of Elliott Carter differs drastically from the first.1 Gone are two lengthy chapters on musical time and musical space; both are replaced by a single, brief technical glossary. The second edition is organized by genre, not chronologically. Discussions of pieces included in the first edition have been revised. Schiff's writing has undergone a marked change as well. 'What he describes as the "rhetorical excesses of the first edition" (vii) has been exorcised in favor of a terse, occasionally hurried prose style—perhaps too strong a swing to the other side of the writing pendulum

Predictive uncertainty in auditory sequence processing

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An Analytical Dataset of Approaches to V in Mozart

Tonal functions—tonic, pre-dominant, and dominant—are a standard feature of North American music theory. The pre-dominant (PD) encompasses the largest number of chords, varying in quality and scale degrees; unlike the tonic and dominant functions, it is primarily defined by its syntactical role, preceding the arrival of the dominant. While Western harmony textbooks consistently organize PD chords according to a regulative syntax (e.g., IV goes to ii), they differ on its rationale and are rarely explicit about the repertoire(s) on which it is based. Furthermore, while the PD is thought to be an essential element of cadential closure, the role of PDs at various formal locations is underexplored, be it in textbooks or corpus studies. To facilitate exploration of these claims for future research, we analyzed all 22 sonata-allegro movements from the Mozart piano sonatas and generated a new dataset containing every occurrence of V (including the Cad6/4), the three chords preceding each V, and their formal location