Mathematics of music and art

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Includes bibliographical references and index.Preliminaries -- The pigeonhole principle -- Continued fractions -- Pythagoras and music -- Temperaments of the scale -- Patterns in music -- Analysis and synthesis of music -- Beats, resonance, and tuning -- Digital music and information -- Last thoughts."This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a general audience as opposed to delving into very technical details. The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each others advancement. The presentation as well as the collection of topics covered throughout is unique and serves to encourage exploration and also, very concretely, illustrates the cross- and multidisciplinary nature of knowledge. Inspired by an introductory, multidisciplinary course, the author explores the relationships between the arts, sciences, and mathematics in the realm of music. The book has no prerequisites; rather it aims to give a broad overview and achieve the integration of thethree presented themes. Mathematical tools are introduced and used to explain various aspects of music theory, and the author illustrates how, without mathematics, music could not have been developed. In addition, this book: Discuses the relationships between the arts, sciences, and mathematics in the realm of music Explores the language of music as deciphered through the language of mathematics Shows readers how apparently unrelated areas of knowledge complement each other and propel each others advancement." --