{"title":"PROPORTION AND SYMMETRY AS MUTUAL ANTAGONISTS IN TUNING: SOME QUARTER-TONE RESOURCES","authors":"Joe Bates","doi":"10.1017/s004029822400007x","DOIUrl":null,"url":null,"abstract":"Quarter-tones have the dubious honour of being the microtonal default in Western art music, yet they have been of little recent interest to those most involved with extended intonation. Other microtonal equal divisions have appealed as pragmatic approximations of consonant just-intonation intervals, something that quarter-tones do not offer. This article proposes that quarter-tones can be valued in a different way, for their ability to generate symmetrical harmonic resources that divide the fourth and fifth as the tritone does the octave. These resources are offered as examples of a broader aesthetic of symmetry, which is contrasted with an aesthetic of proportion. These antagonistic principles are explored through the case of the ever problematic tritone, illustrating how proportion and symmetry are best understood using the symbolic resources of just intonation and equal temperament respectively. Drawing on the work of Robert Hasegawa, Georg Friedrich Haas and Ivan Wyschnegradsky, the article argues for a hybrid approach that embraces both just intonation and equal temperament.","PeriodicalId":22355,"journal":{"name":"Tempo","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tempo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s004029822400007x","RegionNum":4,"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
Abstract
Quarter-tones have the dubious honour of being the microtonal default in Western art music, yet they have been of little recent interest to those most involved with extended intonation. Other microtonal equal divisions have appealed as pragmatic approximations of consonant just-intonation intervals, something that quarter-tones do not offer. This article proposes that quarter-tones can be valued in a different way, for their ability to generate symmetrical harmonic resources that divide the fourth and fifth as the tritone does the octave. These resources are offered as examples of a broader aesthetic of symmetry, which is contrasted with an aesthetic of proportion. These antagonistic principles are explored through the case of the ever problematic tritone, illustrating how proportion and symmetry are best understood using the symbolic resources of just intonation and equal temperament respectively. Drawing on the work of Robert Hasegawa, Georg Friedrich Haas and Ivan Wyschnegradsky, the article argues for a hybrid approach that embraces both just intonation and equal temperament.
在西方艺术音乐中，四分音有着微调默认音程的殊荣，然而对于那些最热衷于扩展音调的人来说，四分音近期却鲜有人问津。其他微调的等分法是对辅音刚音音程的实用近似，而四分音却不具备这种优势。本文认为，四分音可以以另一种方式得到重视，因为它们能够产生对称的和声资源，像三度音划分八度音那样划分四度和五度。这些资源是更广泛的对称美学的范例，与比例美学形成鲜明对比。我们通过一直存在问题的三度音来探讨这些对立的原则，说明如何分别利用公正音调和平均律的象征性资源来最好地理解比例和对称。文章借鉴了罗伯特-长谷川（Robert Hasegawa）、格奥尔格-弗里德里希-哈斯（Georg Friedrich Haas）和伊万-维施内格拉德斯基（Ivan Wyschnegradsky）的研究成果，主张采用一种混合方法，同时包含公正音调和平均律。
期刊介绍：
Tempo is the premier English-language journal devoted to twentieth-century and contemporary concert music. Literate and scholarly articles, often illustrated with music examples, explore many aspects of the work of composers throughout the world. Written in an accessible style, approaches range from the narrative to the strictly analytical. Tempo frequently ventures outside the acknowledged canon to reflect the diversity of the modern music scene. Issues feature interviews with leading composers, a tabulated news section, and lively and wide-ranging reviews of recent recordings, books and first performances around the world. Selected issues also contain specially-commissioned music supplements.
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