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焦点：从音调级集合理论到绘制连续行的操作图表，它在文献中得到了广泛的讨论。然而，随着数字工具的出现，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，从而使分析在某种程度上是“客观的”。事实上，通过这样做，可以使用统计分析和数字数据收集来审问文体实践，并发展对作曲家所做的事情的准确感觉，而不是只关注个别段落或作品，并由此推断。本项目审查的曲目是第二维也纳学派的非调性作品，重点是考虑这些作曲家所使用的和声语言。主要的研究问题是和弦：是否有某些和弦类型和和弦序列比其他类型出现得更频繁？在这些和弦的背景下，随后的问题探索了和声的其他方面：特定的和弦类型是否与特定的音高或音域相关联，以及它们是否倾向于以类似的方式发声。这些调查产生的首要问题是，特定作曲家的作品中是否存在时间趋势，以及这些和声实体在音乐表面被曝光的程度。数据的汇编方法主要是数字的，并将采取多种形式，具体取决于调查中的和声元素。尽管如此，作者已经为他们的M.Phil开发了代码。研究，用Music21(一个基于Python的计算音乐学工具库)编写，这肯定是中肯的。这个代码找到了在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。这个数字过程收集了关于给定曲目的大量数据，引起了人们对特别感兴趣的和弦类型和和弦序列的注意。虽然上面的例子只涉及和弦类型和和弦序列，但在博士课程期间，很可能会开发出更多的数字工具来收集更广泛范围的谐波元素的数据。当然，目前很少有相关作品被编码为计算机可读文件并公开访问，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。虽然这很耗时，但作者在这种编码方面有经验，并相信在给定的时间框架内是可行的。那些版权过期的作品(到项目结束时，勋伯格、伯格和韦伯恩的所有作品)将在网上发布，允许其他学者从这种编码中受益。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线发布。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者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，它们将伴随着明确的说明，使缺乏数字经验的音乐学者以及专业人士能够使用它们。在数据收集过程之后，将按照不同的作曲家和时间顺序展示和讨论结果。事实上，这种比较方法是最初研究问题最重要的扩展之一：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，它们是如何随着时间的推移而变化的？

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?