THE CRITICAL NEXUS AMS Studies in Music Mary Hunter, General Editor Editor for this volume Lawrence F.Bernstein Editorial Board Graeme M.Boone Bruce Alan Brown Scott Burnham Richard Crawford Suzanne Cusick Louise Litterick Elaine Sisman Ruth A.Solie Judith Tick Gretchen Wheelock Conceptualizing Music: Cognitive Structure,Theory,and Analysis Lawrence M.Zbikowski Inventing the Business of Opera: The Impresario and His World in Seventeenth-Century Venice Beth L.Glixon and Jonathan E.Glixon Lateness and Brahms: Music and Culture in the Twilight ofViennese Liberalism Margaret Notley The Critical Nexus: Tone-System,Mode,and Notation in Early Medieval Music Charles M.Atkinson The Critical Nexus Tone-System,Mode,and Notation in Early Medieval Music Charles M.Atkinson 1 2009 1 Oxford University Press,Inc.,publishes works that further Oxford University’s objective of excellence in research,scholarship,and education. 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Library of Congress Cataloging-in-Publication Data Atkinson,Charles M.(Charles Mercer),1941– The critical nexus:tone-system,mode,and notation in early medieval music / Charles M.Atkinson p. cm.— (AMS studies in music) Includes bibliographical references and index. ISBN978-0-19-514888-6 1.Music theory—History—500–1400. 2.Music theory—To 500—Influence. I.Title. ML174.A852008 781.2’63—dc22 2007011368 2 4 6 8 9 7 5 3 1 Printed in the United States of America on acid-free paper In memoriam Fritz Reckow The original impetus for this study came from my friend Fritz Reckow (1940– 1998),who invited me to participate in a symposium in Kiel in 1985.Held under the co-sponsorship of the Universität Kiel and the Schleswig-Holsteinische Lan- desbibliothek,the symposium dealt with the creation of a European musical culture in the Middle Ages (“Die Formung einer europäischen musikalischen Kultur im Mittelalter”).My presentation at the symposium was originally titled “On the For- mation of a Medieval Theory of Mode.”As I continued to work on the topic,with a view toward publishing the essay in the conference report,I realized that the sub- stance of my study encompassed far more than the original title conveyed.That re- alization notwithstanding,and given the restrictions of page limits and deadlines, the version I submitted for publication was essentially the paper I had presented at the symposium.Unfortunately,the proceedings of the original symposium had not been published at the time of Fritz’s untimely death on August 30,1998,and the plan for publishing the proceedings had to be abandoned.I hope that publishing this essay in its expanded form may serve to complete one small part of Fritz Reckow’s legacy to the fields of musicology and medieval studies. This page intentionally left blank acknowledgments As its title intends to suggest,this is a book with a broad scope but a narrow focus. It is simultaneously both an attempt to provide a satisfactory answer to a spe- cific question and a compendium of much of my work during the past three de- cades.Although its immediate impetus was the invitation from Fritz Reckow to participate in the 1985Kiel symposium mentioned in the dedication,its roots ulti- mately extend back to a paper I wrote on the parapteresfor a seminar on medieval theory with Calvin Bower at the University of North Carolina.As one might ex- pect of a work with such a long gestation period,this one owes much to many.I cannot possibly name all the people and institutions that have played a role in its re- alization,but I should like to name at least a few. The person who was present at the inception of this work,and who continues to be a source of information and inspiration to me,is Calvin Bower.His insights inform this study in ways too numerous to catalogue,but they are especially impor- tant to the sections on Boethius in chapter 1and on the Alia musicain chapter 5. I owe a debt of a special kind to Leo Treitler.His work on the advent of musi- cal notation in the West has been of seminal importance for me,as it has for many others.Beyond that,though,his interest in the subject of this book and his reading and commenting on parts of the manuscript itself have made it a far better work than it would otherwise have been. This study has profited additionally from intensive discussions with colleagues in the United States and Europe,who have afforded me the opportunity to present my work on this topic in seminars and colloquia at various stages of its development. The present study took its initial shape in a seminar I presented at Harvard Univer- sity in 1984,at the invitation of David Hughes.I was able to present more fully de- veloped versions in seminars at the University of North Carolina,where I had the honor of being a guest professor in the spring of 1987,and at the Graduate Center of the City University of New York in 1994,upon the invitation of Raymond Erickson.The work took something close to its present form in Paris in 2001, thanks to Marie-Noël Colette’s having arranged for me to present it as a course at the École Pratique des Hautes Études of the Sorbonne.Her searching questions and viii acknowledgments observations as we translated the text into French were of great help in clarifying a number of issues,especially those concerning notation.The seminars and collo- quia I was subsequently asked to present by Susan Patrick (University of New Mexico),Wulf Arlt (Universität Basel),and Andreas Haug (Universität Erlangen- Nürnberg) likewise contributed substantially to giving the work its present shape and substance.My profound thanks go to these friends and colleagues and to their students. Of course,the people who have been most immediately involved in this work are my colleagues and students in musicology at Ohio State University.Arved Ashby,Daniel Avorgbedor,Graeme Boone,Burdette Green,Herbert Livingston (deceased),Martha Maas,Margarita Mazo,Lois Rosow,and Udo Will have been constant sources of inspiration and encouragement.I have been fortunate to have had a number of fine students in the various courses and seminars I offered on top- ics related to this study.Two of them,Cynthia Cyrus and Jane Warburton,con- tributed directly to this work by writing excellent papers on the Alia musica and on species theory,respectively.I take special pleasure in acknowledging their con- tributions here. The following institutions provided support for this work in different ways,for which I am extremely grateful:The Ohio State University and its libraries;Bam- berg,Staatsbibliothek;Bern,Burgerbibliothek;Besançon,Bibliothèque Municipale; Brussels, Bibliothèque Royale; Düsseldorf, Universitäts- und Landesbibliothek; Erlangen, Universitätsbibliothek; Karlsruhe, Badische Landesbibliothek; Leiden, Universiteitsbibliotheek;London,The British Library;Munich,Bayerische Staats- bibliothek;Orléans,Bibliothèque Municipale;Oxford,Bodleian Library;Paris,Bib- liothèque nationale de France;Reims,Bibliothèque Municipale;Rochester,Sibley Music Library,Eastman School of Music of the University of Rochester;and St. Gall,Stiftsbibliothek.I should especially like to acknowledge the Österreichische Nationalbibliothek in Vienna for its permission to reproduce on the cover of this book the picture of Guido d’Arezzo and Bishop Theodaldus that appears on folio 35v of the manuscript cpv 51in their collection. The excursus on Aurelian and the Paleofrankish script in Chapter 3 is drawn from my article,“De accentibus toni,”which appeared in Essays on Medieval Music in Honor of David G.Hughes.I wish to thank the Department of Music of Harvard University,publisher of the volume,and its editor,Graeme Boone,for their permis- sion to republish that material here. A special acknowledgment is due the National Endowment for the Humanities, whose fellowship for the academic year 2003/04enabled me to complete this book and prepare the final manuscript. I cannot close this section of acknowledgments without expressing my deep gratitude to the members of the Publications Committee of the American Musico- logical Society,who serve as the editorial board for the AMS Studies in Music.I am especially grateful to the two readers who reviewed the final manuscript for the Publications Committee.They raised questions about various parts of the study and made a number of valuable comments and suggestions.I have tried to respond to their questions and incorporate their suggestions in every case,but,should mistakes or shortcomings still remain,I accept full responsibility for them. acknowledgments ix I should especially like to thank the series editor for this volume, Lawrence Bernstein,not only for his wonderful editorial work but also for his unflagging sup- port in seeing the book through to publication. Finally,I must express my profound gratitude to my family,Gretchen,Karen,and David,for their constant encouragement despite the fact that they so often had to compete with a manuscript,a book,or an article for my attention.This project would not have been possible without their support.