全音阶的转换

IF 1.6 1区艺术学 0 MUSIC

MUSIC THEORY SPECTRUM Pub Date : 2023-11-06 DOI:10.1093/mts/mtad017

Leah Frederick

{"title":"全音阶的转换","authors":"Leah Frederick","doi":"10.1093/mts/mtad017","DOIUrl":null,"url":null,"abstract":"Abstract This article draws on the mathematical approaches of Tymoczko (2011) and Hook (2008) to construct a transformational space of closed-position diatonic triads. The group acts on a set of twenty-one objects: the seven diatonic triads differentiated by the three closed-position inversions. After constructing the transformation group as an abstract voice-leading space, I interpret the system as an instrumental space (De Souza 2017) that captures the chord shapes required to play triadic progressions on a keyboard. This emphasis on the space’s ability to capture such chord shapes leads to generalizations of the system that explore interactions between voice leading and chord spacing using geometric and diatonic theory.","PeriodicalId":44994,"journal":{"name":"MUSIC THEORY SPECTRUM","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diatonic Voice-Leading Transformations\",\"authors\":\"Leah Frederick\",\"doi\":\"10.1093/mts/mtad017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract This article draws on the mathematical approaches of Tymoczko (2011) and Hook (2008) to construct a transformational space of closed-position diatonic triads. The group acts on a set of twenty-one objects: the seven diatonic triads differentiated by the three closed-position inversions. After constructing the transformation group as an abstract voice-leading space, I interpret the system as an instrumental space (De Souza 2017) that captures the chord shapes required to play triadic progressions on a keyboard. This emphasis on the space’s ability to capture such chord shapes leads to generalizations of the system that explore interactions between voice leading and chord spacing using geometric and diatonic theory.\",\"PeriodicalId\":44994,\"journal\":{\"name\":\"MUSIC THEORY SPECTRUM\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2023-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"MUSIC THEORY SPECTRUM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/mts/mtad017\",\"RegionNum\":1,\"RegionCategory\":\"艺术学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"0\",\"JCRName\":\"MUSIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"MUSIC THEORY SPECTRUM","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/mts/mtad017","RegionNum":1,"RegionCategory":"艺术学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"MUSIC","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文借鉴Tymoczko(2011)和Hook(2008)的数学方法构造了一个闭合位置全音阶三和弦的变换空间。这个团体作用于一组21个对象:由三个闭合位置反转区分的七个全音阶三和弦。在将转换组构建为抽象的语音引导空间之后，我将该系统解释为一个乐器空间(De Souza 2017)，该空间捕获了在键盘上演奏三和弦进行所需的和弦形状。这种强调空间捕捉这种和弦形状的能力导致了系统的一般化，即利用几何和全音阶理论探索声导和和弦间距之间的相互作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Diatonic Voice-Leading Transformations

Abstract This article draws on the mathematical approaches of Tymoczko (2011) and Hook (2008) to construct a transformational space of closed-position diatonic triads. The group acts on a set of twenty-one objects: the seven diatonic triads differentiated by the three closed-position inversions. After constructing the transformation group as an abstract voice-leading space, I interpret the system as an instrumental space (De Souza 2017) that captures the chord shapes required to play triadic progressions on a keyboard. This emphasis on the space’s ability to capture such chord shapes leads to generalizations of the system that explore interactions between voice leading and chord spacing using geometric and diatonic theory.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

MUSIC THEORY SPECTRUM MUSIC-

CiteScore

2.30

自引率

20.00%

发文量

期刊介绍： A leading journal in the field and an official publication of the Society for Music Theory, Music Theory Spectrum features articles on a wide range of topics in music theory and analysis, including aesthetics, critical theory and hermeneutics, history of theory, post-tonal theory, linear analysis, rhythm, music cognition, and the analysis of popular musics. The journal welcomes interdisciplinary articles revealing intersections with topics in other fields such as ethnomusicology, mathematics, musicology, philosophy, psychology, and performance. For further information about Music Theory Spectrum, please visit the Society for Music Theory homepage.