This article develops, for the Parisian modernist repertoire, a model of additive harmony in which voicing plays a foundational role. In comparison with the conventional extendedtriad model of additive harmony, the voicing-based model be&er describes the range of novel verticalities used in tonal progressions in this repertoire, and the features that allow those verticalities to serve as stand-ins for common-practice chords. This study also enriches our understanding of the important developments in Western tonal language that took place in the late nineteenth and early twentieth centuries. Most research on these stylistic developments details how innovation within certain horizontal-domain pitch constraints allowed for the incorporation of new harmonic successions into tonal contexts; this paper demonstrates that a similar process can be read in the vertical domain, wherein adherence to certain vertical-domain pitch constraints allowed for the incorporation of new chords into tonal contexts. Volume 23, Number 3, September 2017 Copyright © 2017 Society for Music Theory [1] The music of composers working in Paris around the turn of the twentieth century is shot through with harmonic moments like that in Example 1, the final cadence of Ravel’s one-act opera L’enfant et les sortilèges (1925). These are moments where the Roman-numeral sense of a chord progression is clear, but the chords used in that progression are unconventional by commonpractice standards. In the Ravel example, the first of the two bracketed chords is neither a triad nor a seventh chord (and in pitch-class terms is actually the scalar subset [B, C, D, E]; the pitches of the chorus evaporate upon the strings’ entrance), while the final G-major triad is accompanied by an F . Yet the progression retains the character of an authentic cadence. The chords are voiced in such a way as to suggest D–G falling-fifth root motion while accommodating the opera’s falling-fourth “maman” motive in the upper voice, and serve to complete the tonic–subdominant–dominant– tonic progression that begins at R153. [2] This phenomenon is known as additive harmony, defined as the vertical enrichment of

中文翻译：

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一种基于声音的加和声模型

本文为巴黎现代主义曲目开发了一种附加和声模型，其中发声起着基础性作用。与传统的加性和声扩展三和弦模型相比，基于声部的模型 be&er 描述了该曲目中用于音调进行的新垂直度的范围，以及允许这些垂直度作为常用和弦的替代品的特征。这项研究还丰富了我们对 19 世纪末和 20 世纪初西方声调语言的重要发展的理解。大多数关于这些风格发展的研究都详细说明了某些水平域音高限制内的创新如何允许将新的和声连续融入音调环境中；本文证明了在垂直域中可以读取类似的过程，其中遵守某些垂直域音高限制允许将新和弦合并到音调上下文中。第 23 卷，第 3 期，2017 年 9 月 版权所有 © 2017 Society for Music Theory [1] 二十世纪之交在巴黎工作的作曲家的音乐在与示例 1 中的和谐时刻一样，拉威尔的最后节奏-act 歌剧 L'enfant et les sortilèges (1925)。在这些时刻，和弦进行的罗马数字意义是明确的，但是按照惯例标准，该进行中使用的和弦是非常规的。在拉威尔的例子中，两个带括号的和弦中的第一个既不是三和弦也不是七和弦（并且在音级术语中实际上是标量子集 [B、C、D、E]；合唱的音高在弦的入口处消失），而最后的 G 大调三和弦伴随着 F 。然而，进展保留了真实节奏的特征。和弦以这样的方式发声，即暗示 D-G 降五根音运动，同时在高音中适应歌剧的降四“maman”动机，并用于完成开始的主音 - 次主音 - 主音 - 主音进行在 R153。[2] 这种现象被称为加性和谐，定义为垂直富集 和弦以这样的方式发声，即暗示 D-G 降五根音运动，同时在高音中适应歌剧的降四“maman”动机，并用于完成开始的主音 - 次主音 - 主音 - 主音进行在 R153。[2] 这种现象被称为加性和谐，定义为垂直富集 和弦以这样的方式发声，即暗示 D-G 降五根音运动，同时在高音中适应歌剧的降四“maman”动机，并用于完成开始的主音 - 次主音 - 主音 - 主音进行在 R153。[2] 这种现象被称为加性和谐，定义为垂直富集