The study of jazz harmony treats the configuration and concatenation of chords within a phrase, performance, tune, style, or genre. Harmonic analysts typically seek to segment musical surfaces into collections of notes sounded (nearly) simultaneously, and these chords receive labels imbricated in a representation system capturing (and partially defining) their structural properties and functional uses. Since at least the 1970s, music theorists have drawn on paradigms from linguistics to describe patterns and norms in the deployment of the resulting chord objects. If jazz (and music generally) is language-like, then the normative or allowable orderings of chords in time might bear some structural resemblance to the syntax of well-formed sentences. This dissertation questions and reframes the concept of harmonic syntax, drawing on a corpus of jazz piano performances and elementary machine learning to construct data-driven chord categories which generalize across traditional notions of harmonic progression and function.;In Chapter 1, I argue that traditional, roman-numeral type data representations cannot provide a ground for assessing extant theories of syntax, linguistic or otherwise. An examination of the labeling and parsing procedures employed by a range of jazz theorists suggests that content-based chord labeling, which implicitly or explicitly identifies chord similarity based on the pitch content of individual verticalities, both cuts across and pre-supposes assumptions regarding the contextual behavior of the resulting chord categories. After placing these latent syntactic theories in dialog with Chomskyan linguistics and recent computational work, I suggest that comparatively content-free chord labeling agnostic about the structure and deployment of the chords represented can underpin statistical claims regarding a surface-oriented local harmonic syntax.;Chapter 2 pursues such chord labeling in the context of voicings and locally transposed scale-degree sets observed in the Yale Jazz MIDI Piano corpus (YJaMP). Relaxing chord labeling assumptions regarding rooted, tertian-stack, diatonic chord structures extends chord labels to a wide array of harmonic objects. I frame the process of turning musical surfaces into harmonic objects with semiotic terms taken from Paul Kockelman, and I claim that algorithmic parsing of MIDI performance data can produce chord labels uniquely suited to the contextual chord categorization of Chapters 3 and 4. Algorithmic processes here and elsewhere in the dissertation do not explain how humans perceive or conceptualize jazz piano syntax; rather, they provide a minimally-circular way to specify a meaning for chord labeling claims that is temporally sensitive and syntactically productive.;Chapter 3 provides a framework for investigating the temporal behavior of the generalized chord objects identified in Chapter 2. Taking the traditional ii chord as a case study, I challenge traditional notions of "progressions" as bigram adjacencies. Attending to the probabilistic statistics for chords following ii at time delays of up to five seconds, I suggest that the contextual behavior of voice-leading neighbors (like other ii chords) and syntactic progression destinations (like V chords) can provide temporal probability templates against which other chord behaviors may be measured. Drawing on time series analytical approaches common in machine learning, I show that principal component analysis (PCA) allows the automated extraction of these templates from the statistics for ii or any other chord. The resulting principal components provide a computational translation of analytical intuitions regarding phonetic-scale and syntactic-scale harmonic progressions.;Chapter 4 generalizes the PCA-reduced temporal statistics for ii to the full set of YJaMP scale-degree sets, introducing a quantitative basis for comparing the behavior of arbitrary chord structures across multiple time scales. With time series statistics embedded in the chord representation, simple metrics and machine learning methods then permit surprisingly sensitive chord categorization schemes. I show that agglomerative hierarchical clustering reproduces human analytical expectations regarding syntactic category formation, and naive supervised classifiers like k-nearest neighbors can place new or lower-probability chords into the resulting framework with low computational overhead.;Chapter 5 places the categorization of Chapters 2-4 back in the context of formalist music theories, drawing on critiques from Richard Wollheim and Paul Kockelman to indicate that the data analytical pipeline in these pages avoids many common kinds of circularity while also limiting its human interpretability. I mean the representation and classification scheme advocated here to serve as a starting point, not an ending, and I suggest several modes of algorithmic-human semiotic communication which might yield productive observations regarding jazz syntax. In a way, I situate syntactic descriptions of temporal progressions as emerging from the relations between agents suited to different tasks -- and I hope to spur harmonic claims more accountable to the means of their own production than to the assumed properties of pre-existing harmonic objects.
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机译：爵士和声的研究处理乐句，演奏，曲调，风格或风格中和弦的配置和串联。谐音分析人员通常试图将音乐表面分割成同时（几乎）发声的音符集合，这些和弦会接收到代表系统中的颤音标签，以捕捉（并部分定义）它们的结构特性和功能用途。至少从1970年代开始，音乐理论家就借鉴了语言学的范式来描述所产生的和弦对象的部署方式和规范。如果爵士乐（通常是音乐）类似于语言，那么按时间顺序排列或允许的和弦顺序可能与结构良好的句子在结构上相似。本文以爵士钢琴演奏和基础机器学习为基础，提出并重新定义了和声语法的概念，以构造数据驱动的和弦类别，并概括了传统的和声进行和功能概念。 ，罗马数字类型的数据表示形式不能提供评估现有语法，语言学或其他理论的基础。对一系列爵士理论家所采用的标记和解析程序的研究表明，基于内容的和弦标记可以基于各个垂直音高的音调内容来隐式或显式地识别和弦相似性，这既贯穿了上下文假设，也为涉及上下文的假设作了预设产生的和弦类别的行为。在将这些潜在句法理论与Chomskyan语言学和最新的计算工作进行对话之后，我建议相对于内容无关的和弦标签，与所表示的和弦的结构和部署不可知，可以支持有关面向表面的局部和声语法的统计主张。 2在Yale Jazz MIDI钢琴语料库（YJaMP）中观察到的声音和局部移调的比例度设置的背景下，进行了这种和弦标记。关于有根，三叠系，全音阶和弦结构的松弛和弦标签假设，将和弦标签扩展到各种谐波对象。我将使用Paul Kockelman的符号学术语将音乐表面变成谐和对象的过程进行构架，并声称对MIDI演奏数据的算法解析可以产生和弦标签，该和弦标签独特地适合于第3章和第4章的上下文和弦分类。论文的其他部分没有解释人类如何感知或概念化爵士钢琴的语法；相反，它们提供了一种最小限度的循环方式来指定和弦标记要求的含义，该含义在时间上是敏感的并且在语法上是富有成效的。；第3章提供了一个框架，用于研究在第2章中确定的广义和弦对象的时间行为。和弦作为案例研究，我将传统的“进步”概念作为二元组邻接来挑战。考虑到ii后最多五秒的延迟后和弦的概率统计，我建议语音主导邻居（如其他ii和弦）和句法进展目的地（如V和弦）的上下文行为可以提供针对可以测量哪些其他和弦行为。利用机器学习中常见的时间序列分析方法，我证明了主成分分析（PCA）可以从ii或任何其他和弦的统计信息中自动提取这些模板。由此产生的主成分为语音级和句法级和声级数的解析直觉提供了计算上的转换。;第4章将ii的PCA简化的时态统计概括为整个YJaMP规模度集，从而为比较跨多个时间尺度的任意和弦结构的行为。通过将时间序列统计信息嵌入和弦表示中，简单的度量和机器学习方法即可实现令人惊讶的敏感和弦分类方案。我证明了聚集式分层聚类重现了人类对句法类别形成的分析期望，并且像k-最近邻居这样的幼稚监督分类器可以以较低的计算开销将新的或概率较低的和弦放入生成的框架中;第5章将第2章的分类-4在形式主义音乐理论的背景下，借鉴了Richard Wollheim和Paul Kockelman的评论，指出这些页面中的数据分析管道避免了许多常见的循环性，同时也限制了其人类可解释性。我的意思是这里提倡的表示形式和分类方案只是一个起点，而不是终点，我提出了几种算法-人类符号通信的模式，这些模式可能会产生有关爵士语法的有益观察。从某种意义上讲，我将时间进展的句法描述定位为适合于不同任务的主体之间的关系-我希望促使对谐波的主张对自己的生产方式负责，而不是对预先存在的谐波的假定性质负责对象。
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