Sound, Shape, and Harmony: A Mathematician's Perspective

The historical development of the geometric understanding of harmony is the subject of this lecture. The analysis of stringed instruments lies at the root of the Western theory of music, while in Chinese music stone chimes have played a special role. A vibrating string is essentially one-dimensional, while stone chimes depends on their two-dimensional geometries, whose analysis requires more sophisticated mathematics. More recently, the vibration of three- and even higher-dimensional objects have even been investigated.