Includes bibliographical references (pages 307-308) and index.

Pitch, frequency, musical scales -- Basic musical notation -- Some music theory -- Spectrograms and musical tones -- Spectrograms and music -- Analyzing pitch and rhythm -- A geometry of harmony -- Audio synthesis in music -- Exercise solutions -- Music software -- Amplitude and frequency results.

At first glance, mathematics and music seem to be from separate worlds--one from science, one from art. But in fact, the connections between the two go back thousands of years, such as Pythagoras's ideas about how to quantify changes of pitch for musical tones (musical intervals). Mathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students' understanding of music through mathematics. In an accessible way, the text teaches the basics of reading music and explains how various patterns in music can be described with mathematics. The authors extensively use the powerful time-frequency method of spectrograms to analyze the sounds created in musical performance. Numerous examples of music notation assist students in understanding basic musical scores. The text also provides mathematical explanations for musical scales, harmony, and rhythm and includes a concise introduction to digital audio synthesis. Along with helping students master some fundamental mathematics, this book gives them a deeper appreciation of music by showing how music is informed by both its mathematical and aesthetic structures [Publisher description].

College of Arts and Sciences