Representing Melodic Patterns as Networks of Elaborations
Representing Melodic Patterns as Networks of Elaborations
复制标题
将旋律模式表示为阐述网络
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Marsden
中科院分区：
文献类型：
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作者：
A. Marsden
先前关于音乐定式的讨论强调了寻找音高序列、音程序列或其他局部和原子特征的定式的困难。本文描述了一种通过阐述的层次结构来表示旋律的方式，这种方式源于音乐理论中常见的概念（特别是Schenker和Lerdahl & Jackendoff的作品中发现的还原概念）。它的基本结构是一个平面的有向无环图，每个节点代表一个音符（不一定像它在实际旋律中那样存在）和一个在两个双亲的基础上产生那个音符的精加工。这些图形结构可以通过两种方式转换为树，以帮助处理和比较。首先，任何图都可以转换成一组二叉树，其中每个节点表示两个音符之间的间隔和该间隔的细化。其次，在平面图中，节点与其父节点之间的链接通常没有提供有用的信息，可以忽略不计，导致图的减少倾向于一组树。由此产生了一种解决旋律分割问题的新方法。以这种方式表示的旋律片段的例子表明，这种表示方式如何使片段之间产生明确的相似性，而这种相似性是通过接近特征序列无法发现的。
Previous discussions of musical pattern haveunderlined difficulties in seeking pattern as asequence of pitches, or of intervals or of other localand atomic features. This paper describes a manner ofrepresenting melodies through a hierarchical structureof elaboration, derived from concepts common in musictheory (in particular, the concept of reduction foundin the work of Schenker and of Lerdahl & Jackendoff).The fundamental structure is a planar directed acyclicgraph, each node of which represents a musical note(not necessarily as it is present in the actualmelody) and an elaboration which generates that noteon the basis of two parents. These graph structurescan be converted to trees, aiding processing andcomparison, in two ways. Firstly, any graph can betransformed into a set of binary trees in which eachnode represents an interval between two notes and anelaboration of that interval. Secondly, in the planargraph, the link of a node to one of its parents oftenprovides no useful information and can be disregarded,resulting in a reduction of the graph tending towardsa set of trees. From this arises a new approach to thequestion of melodic segmentation. Examples of melodicfragments represented in this manner demonstrate howthe representation makes explicit similarities betweenfragments which would not be found by an approachusing sequences of features.