Primes
Prime numbers play a crucial role in music theory, and in particular in the theory of tuning. In this chapter, we prove uniqueness of prime decomposition for the integers and polynomial rings.
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Guerino Mazzola Maria Mannone Yan Pang
Cool Math for Hot Music A First Introduction to Mathematics for Music Theorists
Computational Music Science
Series Editors Guerino Mazzola Moreno Andreatta
More information about this series at http://www.springer.com/series/8349
Guerino Mazzola • Maria Mannone • Yan Pang
Cool Math for Hot Music A First Introduction to Mathematics for Music Theorists
Guerino Mazzola School of Music University of Minnesota Minneapolis, Minnesota, USA
Maria Mannone School of Music University of Minnesota Minneapolis, Minnesota, USA
Yan Pang School of Music University of Minnesota Minneapolis, Minnesota, USA
ISSN 1868-0305 ISSN 1868-0313 (electronic) Computational Music Science ISBN 978-3-319-42935-9 ISBN 978-3-319-42937-3 (eBook) DOI 10.1007/978-3-319-42937-3 Library of Congress Control Number: 2016956578 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Cover illustration: Cover image designed by Maria Mannone Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
All enjoyment is musical, consequently mathematical. (Novalis)
Preface
Fig. -1.1. Maria Mannone, Guerino Mazzola, and Yan Pang. Photo and © 2015 by A.J. Wattamaniuk.
The idea for this book came from Yan Pang, a PhD student taking the course “Mathematics for Music Theorists” at the School of Music of the University of Minnesota. She was not in love with mathematics at all—bad experiences, bad teachers, the usual story. Fortunately, Maria Mannone, another PhD student taking that course who had studied theoretical physics, helped Yan get acquainted with mathematical rigor and beauty. Soon, Guerino Mazzola, the teacher, learned how to teach math using thorough musical motivation
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Preface
and avoiding abstract nonsense in favor of concrete conceptual deve
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