论文标题
计算口述音乐传统中的旋律模板
Computing Melodic Templates in Oral Music Traditions
论文作者
论文摘要
术语旋律模板或骨骼是指在音乐表演过程中会发生变化的基本旋律。在许多口头音乐传统中，这些模板在整个世代都隐含地传递，而从未被形成得分。在这项工作中，我们引入了一个新的几何优化问题，即跨度管问题，以近似旋律模板，以适用于一组标记的性能转录，该模板与口腔音乐传统中的特定样式相对应。给定一组$ n $分段线性函数，我们解决了找到连续函数的问题，$ f^*$和最低价值，$ \ varepsilon^*$，这样，将长度$ 2 \ varepsilon^*$的垂直部分置于$（x，x，f^*（x）$ p $ p $ p p p p p p p p p p p p pe）。此处探索的方法还提供了一种新颖的工具，用于定量评估跨性能的旋律变化量。
The term melodic template or skeleton refers to a basic melody which is subject to variation during a music performance. In many oral music tradition, these templates are implicitly passed throughout generations without ever being formalized in a score. In this work, we introduce a new geometric optimization problem, the spanning tube problem, to approximate a melodic template for a set of labeled performance transcriptions corresponding to an specific style in oral music traditions. Given a set of $n$ piecewise linear functions, we solve the problem of finding a continuous function, $f^*$, and a minimum value, $\varepsilon^*$, such that, the vertical segment of length $2\varepsilon^*$ centered at $(x,f^*(x))$ intersects at least $p$ functions ($p\leq n$). The method explored here also provide a novel tool for quantitatively assess the amount of melodic variation which occurs across performances.
