Sixty undergraduate students who had completed at least one semester of jazz improvisation were assigned to either: (a) physical practice (PP); (b) mental practice (MP); (c) combined 66 percent PP and 33 percent MP (66%PP:33%MP); and (d) combined 33 percent PP and 66 percent MP (33%PP:66%MP) groups. Subjects were to perform a 3-1-7-5 tonal pattern…

Mathematics can be used to analyze musical rhythms, to study the sound waves that produce musical notes, to explain why instruments are tuned, and to compose music. This book explores the relationship between mathematics and music through proportions, patterns, Fibonacci numbers or the Golden Ratio, geometric transformations, trigonometric…

This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and…