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

非调性作品中的和声是一个常见的分析关注点：从音高类集合理论到绘制序列行的操作，它在文献中得到了广泛的讨论。然而，随着数字化工具的出现，有可能将创新的新战略应用于这一领域，特别是在收集大量数据作为讨论的基础方面，从而在某种程度上“客观”的背景下进行分析。事实上，通过这样做，可以使用统计分析和数字数据收集来询问风格实践，并对作曲家正在做的事情有一个准确的感觉，而不仅仅是关注单个段落或作品，并从中推断。本项目正在审查的曲目是第二维也纳学派的非调性作品，而重点是考虑这些作曲家所使用的和声语言。主要的研究问题考虑和弦：是否有某些和弦类型和和弦序列比其他人更经常出现？在这些和弦的背景下，随后的问题探讨了和声的其他方面：特定的和弦类型是否与特定的音高或音域相关，以及它们是否倾向于以类似的方式发声。这些调查所产生的首要问题是，在特定作曲家的作品中是否存在时间顺序的趋势，以及这些和声实体在音乐表面的曝光程度如何。编辑数据的方法主要是数字化的，并将采取各种形式，这取决于所调查的和声元素。尽管如此，作者已经为他们的M开发了代码。腓研究，用music21（一个基于Python的计算音乐学工具库）编写，这肯定是相关的。该代码查找给定作品中最常用的和弦类型和和弦序列，并提供了作者预期方法的有用示例。该数字过程收集了有关给定曲目的大量数据，引起人们对特别感兴趣的和弦类型和和弦序列的关注。虽然上面的例子只涉及弦的类型和弦的序列，这是很有可能的，在博士课程的进一步数字化工具将被开发，以积累数据的谐波元素的范围更广。当然，目前很少有相关作品被编码为计算机可读文件并可公开访问，因此在开始任何数据收集之前，作者必须为语料库编码相关作品。这将在OMR（“光学音乐识别”）的帮助下进行，或手动完成。虽然这很费时，但作者有这种编码的经验，并相信在给定的时间框架内这是可行的。那些版权过期的作品（到项目结束时，勋伯格，贝格和韦伯恩的所有作品）将在网上发表，让其他学者从编码中受益。同样，为该项目编写和使用的任何代码都将以开放源代码的方式在网上公布。这不仅允许进行建设性的讨论和改进，而且允许其他音乐学家在自己的工作中使用这些工具，为更广泛的音乐学做出积极的社会贡献。由于这些工具中的许多都与广泛的曲目相关，它们将附有明确的说明，使没有数字经验的音乐学家和专家能够使用它们。在数据收集过程之后，将根据不同的作曲家和时间顺序介绍和讨论结果。事实上，这种比较方法是最初研究问题的最重要的扩展之一：这些作曲家之间的和声句法有多相似，他们各自的和声语言有多一致，以及他们如何随着时间的推移而变化？

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?