Computational geometric aspects of rhythm, melody, and voice-leading
Computational geometric aspects of rhythm, melody, and voice-leading
复制标题
节奏、旋律和声音引导的计算几何方面
DOI：
10.1016/j.comgeo.2007.01.003
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
G. Toussaint
中科院分区：
文献类型：
--
作者：
G. Toussaint
许多与节奏、旋律和声音引导的理论和技术有关的问题本质上是几何性质的。因此，计算几何领域能够对这些问题做出巨大贡献也就不足为奇了。计算几何和音乐之间的相互作用为节奏、旋律和声音引导理论带来了新的见解，并为从数学和计算机科学到音乐理论、音乐感知和音乐学等多个领域的研究提出了新的问题。回顾了在节奏、旋律和声音引导的几何和计算方面的最新结果，指出了与计算机科学、数学、统计学、计算生物学和结晶学的现有领域的联系，并提出了新的开放问题。
Many problems concerning the theory and technology of rhythm, melody, and voice-leading are fundamentally geometric in nature. It is therefore not surprising that the field of computational geometry can contribute greatly to these problems. The interaction between computational geometry and music yields new insights into the theories of rhythm, melody, and voice-leading, as well as new problems for research in several areas, ranging from mathematics and computer science to music theory, music perception, and musicology. Recent results on the geometric and computational aspects of rhythm, melody, and voice-leading are reviewed, connections to established areas of computer science, mathematics, statistics, computational biology, and crystallography are pointed out, and new open problems are proposed.