Journal of Mathematics and Music ( IF 0.5 ) Pub Date : 2019-06-20 , DOI: 10.1080/17459737.2019.1623336 Michael D. Fowler 1
This article analyses the 1958 graphic score, Variations I, by John Cage (1912–1992). I firstly trace the resistance that the work has established towards traditional analysis, given its meta-score qualities, and the “distance metric problem,” which arises from the necessity to generate musical parameter data from the measurement of perpendiculars between points and lines printed on six transparent sheets. I propose that an extension to Cage's instructions allows the symmetry of the transparencies to be described as the dihedral group of order 8 (). I also report on the size of the k-combinations (with and without repetition) of the transparencies and account for the sound densities and sound classes of the work. This analysis then allows for the development of two opposing realization frameworks that are determinate and indeterminate in nature.
中文翻译:
将John Cage的变体I中的k组合和Dih 4映射为确定的和不确定的实现策略的实用程序
本文分析了约翰·凯奇(John Cage,1912–1992年)在1958年创作的图形评分《变体I》。首先,鉴于其元得分质量和“距离度量问题”,我首先追溯了该作品对传统分析的抵制,这是由于有必要通过测量点和线之间的垂直线来生成音乐参数数据六张透明纸。我建议对Cage指令进行扩展,以将透明胶片的对称性描述为8阶二面体组()。我还报告了透明胶片的k个组合的大小(有无重复),并说明了作品的声音密度和声音等级。然后,该分析允许开发两个在本质上是确定的和不确定的相对的实现框架。