Abstract

This article considers music that stages the decline of the tonal system through “entropy”—the process conceived in the domain of thermodynamics by which energy is wasted through randomized dispersal or decrease in organization. Tonal organization faced challenges at the turn of the twentieth century, much of the music possessing a sense of tonal drive but with an increased array of outlets for this drive’s tension to be released. This article regards the dominant-seventh complex and its variant configurations as paradigms of this tonal drive and attempts to understand their new ambiguities and the increased richness of possibility they enjoy. In order to achieve this, the study engages in probability theory to create a unique profile for each tonal drive in a given piece, effectively measuring its strength. The fluctuating strengths can be mapped and the process of entropy tracked through a single piece, potentially even across repertoires. Using a new method of visually laying out the patterns of these dominant drives, combined with concepts from information theory that allow us to measure and compare levels of entropy mathematically, I attempt to combine qualitative and quantitative data to model the entropic processes that inhere in early twentieth-century music.

中文翻译：

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扩展色调中的熵之谜

摘要

本文认为音乐是通过“熵”逐步改变音调系统的衰落的，熵是热力学领域中设想的过程，通过随机分散或组织的减少，能量被浪费掉了。在20世纪初，音调的组织面临挑战，许多音乐具有音调的驱动力，但是释放这种驱动力的张力的出口却增加了。本文将占主导地位的第七复合体及其变体配置视为这种音调驱动的范例，并试图理解它们的新模糊性以及它们所享受的可能性的日益丰富。为了实现这一目标，该研究采用概率论为给定乐曲中的每个音调驱动创建一个唯一的轮廓，从而有效地测量其强度。可以绘制起伏的强度并通过单个片段（甚至可能跨曲目）跟踪熵的过程。我使用一种可视化地布局这些主导驱动器模式的新方法，并结合了信息理论的概念，这些概念使我们能够数学地测量和比较熵的水平，我尝试结合定性和定量数据来对早期的熵过程进行建模。二十世纪的音乐。