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Parsimonious graphs for the most common trichords and tetrachords
Journal of Mathematics and Music ( IF 1.1 ) Pub Date : 2021-06-06 , DOI: 10.1080/17459737.2021.1923844
Luis Nuño 1
Affiliation  

Parsimonious transformations are common patterns in different musical styles and eras. In some cases, they can be represented on the Tonnetz, Cube Dance, Power Towers, or the central region of an orbifold, mainly when they only include the most even trichords and tetrachords. In this paper, two novel graphs, called Cyclopes, are presented, which include more than double the number of chord types in previously published graphs, thus allowing to represent a larger musical repertoire in a practical way. Apart from parsimonious transformations, they are also especially suitable for representing trichords a major third apart, tetrachords a minor third apart, and the cadences V7–I(m) and IIØ–V7–I(m) with major or minor tonic chords. Therefore, they allow to clearly visualize the relationship among the corresponding chords and better understand those patterns, as well as being efficient mnemonic resources, all of which make them useful tools both for music analysis and composition.



中文翻译:

最常见的三和弦和四和弦的简约图

简约变换是不同音乐风格和时代的常见模式。在某些情况下,它们可以出现在 Tonnez、Cube Dance、Power Towers 或轨道的中心区域,主要是当它们只包含最均匀的三和弦和四和弦时。在本文中,提出了两个称为 Cyclopes 的新颖图表,其中和弦类型的数量是先前发布的图表中的两倍多,从而能够以实用的方式表示更大的音乐曲目。除了简约变换之外,它们还特别适用于表示大三度相隔的三和弦、小三度相隔的四和弦以及节奏 V7–I(m) 和 IIØ–V7–I(m) 带有大调或小调和弦。因此,它们允许清楚地可视化相应和弦之间的关系并更好地理解这些模式,并且是有效的助记符资源,所有这些都使它们成为音乐分析和作曲的有用工具。

更新日期:2021-06-06
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