Thermodynamics and Harmony.

物理学是发现和理解自然规律的“艺术”；寻找联系，并利用它们看得更远。建立自然模式与音乐和谐模式之间的直接联系是一个诱人的研究途径。这个项目试图将热力学和统计力学的基础研究与音乐和作曲结合起来。这项研究建立在PI最近发表的一项研究的基础上，该研究是关于和声如何在数学物理的指导下，在这两方面产生新的见解。最终目标是推导出一种由自然本身驱动的通用音乐理论，而不是18世纪欧洲作曲家的和声风格。PI所在机构的学生将有机会在物理背景下运用他们的艺术专长，帮助开发创新的教学工具，展示音乐是如何表达数学的。该项目将以三种不同的方式研究物理和音乐之间的协同作用：1)在音乐中，和声研究如何将一个八度（频率范围从f到2f）按时间划分并排列成音高模式。这些音高模式与二维物理系统相变过程中出现的顺序模式相关联，通过最小化作为音高函数的“音乐自由能”来获得。将这项工作扩展到3-D将允许建立和谐的模式，以深入了解早期宇宙的宇宙学。2)研究在符号动态尺度上的扩展，如从Thue-Morse序列得到的扩展，到其他符号动态序列，如Fibonacci， Feigenbaum等。PI将构建一个3-D版本的欧拉Tonnetz来解释它们和谐的几何形状，从而将和谐与这些动力系统联系起来。3)对节奏泛音在和声中的作用进行详细的研究，并通过开发第一个动态合唱和声器，以创新的技术方式使用它们。这是一种新的电子效果，有可能影响现场和录制音乐的声音景观。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Physics is the "art" of discovering and understanding the patterns of nature; seeking connections and using them to look further. Establishing direct connection between the patterns of nature and those of harmony in music is a tantalizing avenue of research. This project seeks to unify basic research in thermodynamics and statistical mechanics with music and composition. The research builds upon the PI’s recently published work on how harmony, informed by mathematical physics, can generate new insights in both. The ultimate goal is to derive a general music theory driven by nature itself, instead of the harmonic style of 18th century European composers. Students at the PI’s institution will get opportunities to use their artistic expertise, in the context of physics, to help develop innovative pedagogical tools that show how music is the voice of mathematics.The project will study the synergy between physics and music in three different ways: 1) In music, harmony studies ways in which an octave (frequencies ranging from f to 2f) can be divided and ordered into patterns of pitch in time. These patterns in pitch are connected to the patterns of order that emerge during phase transitions in 2-D physical systems, obtained by minimizing a “musical free energy” as a function of pitch. Extending this work to 3-D will allow established patterns in harmony to give insight into cosmology of the early universe. 2) Investigate extensions on symbolic dynamic scales like those obtained from the Thue-Morse sequence, to other symbolic dynamic sequences such as Fibonacci, Feigenbaum, etc. The PI will construct a 3-D version of the Euler Tonnetz to interpret the geometry of their harmony, and thereby link harmony to these dynamical systems. 3) Perform a detailed investigation of the role of beat overtones in harmony, and to use them in an innovative technological way by developing the first dynamic, chorus harmonizer. This is a new electronic effect that has the potential to impact the sonic landscape of live and recorded music.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.