【“第三届全国音乐分析学学术研讨会”专栏】论不变子集、交集与差集的分析模式与应用-武汉音乐学院
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【“第三届全国音乐分析学学术研讨会”专栏】论不变子集、交集与差集的分析模式与应用
2016-03-08  来源:  点击数:

杨和平

摘要:文章分两部分,第一部分围绕不变子集展开论述,主要讨论了同一集合转换、同基数集合相缀、不同基数集合相缀等产生不变子集以及不变子集的线性控制等相关问题。第二部分是子集讨论的延伸,即集合群之交集与差集的相关论述。大规模集合群分析是音乐理论研究者的困扰之一,如何在方法论上进行较为理性、有效的分析呢?本文以集合复合型与集合类属理论为基础,通过它们的交集分析来探讨集合群之间的关联性,通过它们的差集分析来探讨集合群之间的对比性。其中,交集也可以成为不同复合型或类属的转换基础。

关键词:不变子集;交集;差集;复合型转换;类属转换;筛选过滤

On the Analysis Model of Invariant Subset, Intersection and Difference Set with its Application

YANG He-ping

Abstract: This article consisted of two parts, the first one discussing the invariant subset, focused on the conversion of same set, linking the sets of the same cardinality, the invariant subset made by linking the sets of the different cardinality, and the linear control of invariant subset and other relation issues. The second part was an extending discussion of subset, namely the related exposition on the intersection and difference set of set-group. The large-scale set-groupanalysis was one bothering for the researcher of music theory, how on the methodology to analysis with more rational and effective? Based on the theory of set compound and set generic, this paper explored the relevance among the set-groups through analysis of their intersection, and explored the comparative among the set-groups through analysis of their difference set. Among them, the intersection can also become the basis of difference compound conversion or generic conversion.

Key Words: invariant subset, intersection, difference set, compound conversion, generic conversion, screening

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