Using Fundamental Groups and Groupoids of Chord Spaces to Model Voice Leading

机译：使用和弦空间的基本群和类群来建模语音引导

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We model voice leading using tools from algebraic topology, principally the fundamental group, the orbifold fundamental group, and related groupoids. Doing so is a natural extension of modeling voice leading by continuous paths in chord spaces. The resulting algebraic precision in the representation of voice leadings and their concatenations allows for new distinctions between voice crossing cases, and enhanced connections with other approaches to voice leading.

机译：我们使用代数拓扑中的工具建模语音引导，主要是基本组，球面基本组以及相关的类群。这样做是对通过和弦空间中的连续路径引导的声音进行建模的自然扩展。语音引导及其连接的表示形式所产生的代数精度允许在语音穿越情况之间进行新的区分，并增强了与其他语音引导方法的连接。

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《International conference on mathematics and computation in music》|2015年|267-278|共12页
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James R. Hughes;
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Chord spaces; Orbifolds; Fundamental group; Fundamental groupoid; Gestures; Voice leading; Homotopy; Groups; Groupoids;

机译：和弦空间; Orbifolds;基本组;基本群像;手势;语音引导;同伦;团体;类群动物;

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专利

1. A new higher homotopy groupoid: the fundamental globular $ω$-groupoid of a filtered space [J] . Ronald Brown Homology, Homotopy and Applications . 2008,第1期

机译：一个新的更高同伦类群：已过滤空间的基本球状$ω$ -groupoid
2. Higher fundamental groupoids for spaces [J] . Marco Grandis Topology and its applications . 2003,第3期

机译：空间的更高基本组别
3. Groupoid Models for the C*-Algebra of Labelled Spaces [J] . Boava Giuliano, de Castro Gilles G., Mortari Fernando de L. Bulletin of the Brazilian Mathematical Society . 2020,第3期

机译：标有空格的C * -algebra的Glasoid模型
4. Using Fundamental Groups and Groupoids of Chord Spaces to Model Voice Leading [C] . James R. Hughes International Conference on Mathematics and Computation in Music . 2015

机译：利用基本组和弦空间的Galoids模型语音领导
5. An exploration of some non-tonal pitch-class spaces with implications for a theory of voice leading. [D] . Berry, Michael F. 2007

机译：探索一些非音调音调类空间，这对语音引导理论具有启示意义。
6. BMP-binding modules in chordin: a model for signalling regulation in the extracellular space [O] . Juan Larraín, Daniel Bachiller, Bin Lu, -1

机译：chordin中的BMP结合模块：一种信号传导调控细胞外空间的模型
7. A new higher homotopy groupoid: the fundamental globular ω-groupoid of a filtered space [O] . Ronald Brown 2008

机译：一个新的更高的同伦群：过滤空间的基本球状ω-群
8. Free-spinning-tunnel investigation to determine the effect on spins and recoveries of wing leading-edge chord-extensions and drooped leading-edge flaps on scale models of two sweptback-wing fighter airplanes [R] . Wilson, Jack H, Klinar, Walter J 1953

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Using Fundamental Groups and Groupoids of Chord Spaces to Model Voice Leading

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