Description

Gain new perspective on two of the greatest achievements of human culture—music and math—and the fascinating connections that will help you morefully appreciate the intricacies of both.Great minds have long sought to understand the relationship between music and mathematics. On the surface, they seem very different. Music delights the senses and can express the most profound emotions, while mathematics appeals to the intellect and is the model of pure reasoning.Yet music and mathematics are connected in fundamental ways. Both involve patterns, structures, and relationships. Both generate ideas of great beauty and elegance. Music is a fertile testing ground for mathematical principles, while mathematics explains the sounds instruments make and how composers put those sounds together. Moreover, the practitioners of both share many qualities, including abstract thinking, creativity, and intense focus.Understanding the connections between music and mathematics helps you appreciate both, even if you have no special ability in either field—from knowing the mathematics behind tuning an instrument to understanding the features that define your favorite pieces. By exploring the mathematics of music, you also learn why non-Western music sounds so different, gain insight into the technology of modern sound reproduction, and start to hear the world around you in exciting new ways.Among the insights offered by the study of music and mathematics together are these:   Harmonic series: The very concept of musical harmony comes from mathematics, dating to antiquity and the discovery that notes sounded together on a stringed instrument are most pleasing when the string lengths are simple ratios of each other. Harmonic series show up in many areas of applied mathematics.   “Air on the G String”: One of Bach’s most-loved pieces was transposed to a single string of the violin—the G string—to give it a more pensive quality. The mathematics of overtones explains why this simple change makes a big difference, even though the intervals between notes remain unchanged.   Auditory illusions: All voices on cell phones should sound female because of the frequency limits of the tiny speakers. But the human brain analyzes the overtone patterns to reconstruct missing information, enabling us to hear frequencies that aren’t there. Such auditory illusions are exploited by composers and instrument makers.   Atonal music: Modern concert music is often atonal, deliberately written without a tonal center or key. The composer Arnold Schoenberg used the mathematics of group theory to set up what he called a “pan-tonal” system. Understanding his compositional rules adds a new dimension to the appreciation of this revolutionary music.http://www.thegreatcourses.com/tgc/courses/course_detail.asp…