The Harmonic Syntax of Post-Tonal Music: A Digital Approach

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Harmony in non-tonal works is a common analytical preoccupation: from pitch-class set theory to charting the manipulation of serial rows, it has been widely discussed in the literature. With the advent of digital tools, however, it is possible to apply innovative new strategies to this area, particularly in gathering large amounts of data as the basis for the discussion, and thus grounding the analysis in a somewhat 'objective' context. Indeed, by doing so, it is possible to use statistical analysis and digital data-collection to interrogate stylistic practice, and develop an accurate sense of what composers were doing, rather than only focussing on individual passages or works, and extrapolating from these.The repertoire under review in this project is the non-tonal works of the Second Viennese school, and the focus is on considering the harmonic language employed by these composers. The primary research question considers chords: are there certain chord-types and chord-sequences that occur more often than others? Contextualising these chords, subsequent questions explore other aspects of harmony: whether particular chord-types are associated with specific pitches or registers, and whether they tend to be voiced in similar ways. The overarching questions resulting from these investigations is whether there are chronological trends within particular composers' work, and to what extent these harmonic entities are brought to light in the surface of the music.The methodology for compiling the data is largely digital, and will take a variety of forms, depending on those harmonic elements under investigation. Nonetheless, the author has already developed code for their M. Phil. research, written with music21 (a Python-based library of tools for computational musicology), which will certainly be pertinent. This code finds those chord-types and chord-sequences most frequently used in given works, and provides a useful example of the author's intended approach.This digital process amasses large quantities of data about the given repertoire, drawing attention to chord-types and chord-sequences of particular interest. Though the examples above only concern chord-types and chord-sequences, it is quite possible that over the course of the PhD further digital tools will be developed to amass data on a wider range of harmonic elements. Of course, few of the relevant works are presently encoded as computer-readable files and publicly accessible, and so before any data-collection can commence, the author will have to encode relevant works for the corpus. This will be carried out with the help of OMR ('optical music recognition'), or done manually. Though this is time-consuming, the author has experience in this sort of encoding, and is confident that this is viable within the given time-frame.Those works that are out of copyright (by the end of the project, all works of Schoenberg, Berg, and Webern) will be published online, allowing other scholars to benefit from the encoding. Similarly, any code written and used for the project will be published online in an open-source manner. Not only does this allow for constructive discussion and improvement, but it allows other musicologists to use these tools in their own work, making a positive social contribution to broader musicology. As many of these tools are relevant to a wide range of repertoire, they will be accompanied by clear instructions, enabling musicologists who are digitally inexperienced to employ them, as well as specialists.Following the process of data-collection, the results will be presented and discussed, both in terms of different composers, and chronologically. Indeed, this comparative approach is one of the most significant extensions of the initial research question: how similar is the harmonic syntax between these composers, how consistent are their individual harmonic languages, and how did they change over time?