Tonal Preliminaries
The usual diatonic system is “dyadic,” for it privileges two intervals, the perfect octave and fifth; the usual harmonic system is “triadic,” for it privileges, in addition, the major and minor thirds (Sect. 9.1). The dyadic and triadic privileged interva
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Eytan Agmon
The Languages of Western Tonality
Computational Music Science
Series Editors Guerino Mazzola Moreno Andreatta
For further volumes: http://www.springer.com/series/8349
ThiS is a FM Blank Page
Eytan Agmon
The Languages of Western Tonality
Eytan Agmon Department of Music Bar-Ilan University Ramat-Gan Israel
ISSN 1868-0305 ISSN 1868-0313 (electronic) Computational Music Science ISBN 978-3-642-39586-4 ISBN 978-3-642-39587-1 (eBook) DOI 10.1007/978-3-642-39587-1 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013951826 © Springer-Verlag Berlin Heidelberg 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
. . . Each of these four notes governs, as its subjects, a pair of tropes. . .. Thus every melody. . . is necessarily led back to one of these same four [notes]. Therefore they are called “finals,” because anything that is sung finds its ending ( finem) in [one of] them. —Hucbald of Saint-Amand, late Ninth Century1
As an object of inquiry, “tonal music” is far from homogenous. The music of the ninth century with which Hucbald was familiar was very different, we may assume, from (say) the music of the seventeenth century. Nonetheless, there are striking points of contact. Most notably, a “background
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