Behind the Mirror Revealing the Contexts of Jacobus’s Speculum musicae by Karen Desmond A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Music New York University May, 2009 ___________________________ Edward H. Roesner © Karen Desmond All Rights Reserved, 2009 DEDICATION For my family iv ACKNOWLEDGMENTS I would like to thank my advisor, Edward Roesner, for his unfaltering support throughout this process, for his thoughtful suggestions regarding lines of inquiry, and his encyclopedic knowledge of the field. I would like to thank Stanley Boorman and Gabriela Iltnichi for their friendship and expertise, and their critical eye in their careful reading of many drafts of my work. For their assistance during my research trip to Belgium, I must mention Monsieur Abbé Deblon and Christian Dury at the Archives de l’Evêché, Liège, Paul Bertrand at the Archives de l’Etat, Liège, Philippe Vendrix for his kind hospitality, and to Barbara Haggh-Huglo for her tips and advice in advance of my trip, and for also reading a final draft of this dissertation. I would also like to thank Margaret Bent and Ruth Steiner for help during the early stages of my doctoral research, and Suzanne Cusick for her reading of the final draft. Finally, heartfelt thanks are due to my husband, Insup; my two sons, Ethan and Owen; and my parents, John and Chris, who have been steadfast in their encouragement of this endeavor. v ABSTRACT This study addresses the general question of how medieval music theory participated in the discourse of the related disciplines of philosophy, natural science and theology. I focus on a specific instance of scientific inquiry: the fourteenth-century music treatise Speculum musicae , written by an author known to us as Jacobus. A detailed analysis of Speculum musicae reveals an aesthetic system whose elements are assigned meaning and value through the anagogical relationships that the author posits (either explicitly or implicitly) with systems articulated in philosophical and theological treatises at the turn of the fourteenth century. My central concerns are uncovering the impetus behind the production of this treatise, determining where Jacobus’s philosophies fit within particular schools of medieval thought, as revealed through his vocabulary choices, supporting sources, and methods of reasoning, and then extrapolating from these philosophies which rationale ( ratio ) most informs his positions on particular issues, such as his classification of music, or his defense of the ancient art of singing against the modern art. I hope to present a fresh perspective on one of the most important yet one of the most mysterious ages in the history of music. The turn of the fourteenth century was a fascinating time for music: we find musical systems in a pronounced state of flux with various vi theoretical solutions proposed in response to the problems of notating this increasingly complex music. Analyzing the background of these theoretical formulations, and assessing the various judgments of “good” practice, and the kinds of arguments used to bolster these judgments, will uncover reasons for the overturning of musical systems and go some way toward explaining the nature of musical change. vii TABLE OF CONTENTS DEDICATION ..................................................................................................... iv ACKNOWLEDGMENTS .................................................................................... v ABSTRACT ........................................................................................................ vi LIST OF FIGURES .............................................................................................. x LIST OF TABLES ............................................................................................... xi LIST OF APPENDICES.................................................................................... xii ABBREVIATIONS .......................................................................................... xiii CHAPTER 1: INTRODUCTION ............................................................................... 1 CHAPTER 2: LITURGICAL CONTEXTS ................................................................ 23 Brussels, Bibliothèque royale, Ms. 10162/66 ................................................. 29 Late-Medieval Liturgical Sources from Liège ............................................... 43 Tonaries in Late-Medieval Theoretical Works ............................................... 54 CHAPTER 3: MATHEMATICS ............................................................................. 68 Mathematics in the Later Middle Ages .......................................................... 72 Book 3 of Speculum musicae .......................................................................... 75 Compounding Ratios ...................................................................................... 99 CHAPTER 4: MATTERS OF DISPUTE ................................................................ 106 Longs ............................................................................................................ 121 Breves ........................................................................................................... 140 viii Semibreves/Minims/Semiminims ................................................................. 144 CHAPTER 5: TIME AND MOTION ..................................................................... 167 Motion........................................................................................................... 169 Time .............................................................................................................. 186 CHAPTER 6: FROM TREES TO DEGREES FORM , MATTER , AND MENSURAL THEORY ........................................................ 210 The Unity of Form ........................................................................................ 212 Quantifying Qualities and the Latitude of Form ........................................... 215 Jacobus on the Unity of Form ....................................................................... 224 Mensural Theory and the Unity of Form ...................................................... 244 The Context of Mensural Theory ................................................................. 265 CHAPTER 7: MUSICA CAELESTIS AND THE BEATIFIC VISION ............................ 279 The Divisions of musica ............................................................................... 281 The Music of the Celestial Movers ............................................................... 285 The Incessant Praise of God ......................................................................... 292 Music and the Beatific Vision ...................................................................... 299 CONCLUSION................................................................................................. 313 APPENDICES……………………………………………………………….331 BIBLIOGRAPHY……………………………………………………………426 ix LIST OF FIGURES Figure 1 Musical examples of the duplex long in CS 3, Anon. 4 ( F-Pn lat. 15128, f.129r) ........................................................................................... 124 Figure 2 Larga perfecta and larga imperfecta in Vitry anon. 1964d (GB-Lbl Add. 21455), f. 5r .................................................................................... 132 Figure 3 Caudae through the maxima long in Sweeney anon.; De musica mensurabili (I-Rvat 307, f. 24v) ............................................................... 133 Figure 4 Johannes de Muris’s chart of figures in his Libellus (I-Vnm 85, f.11v) .................................................................................................................. 263 Figure 5 Arbor of Johannes de Burgundia ...…………………………………263 Figure 6 The correspondence of musica to each of the speculative sciences, Jacobus, Speculum musicae ...................................................................... 283 x LIST OF TABLES Table 1 Comparision of B-Br 10162/66 and Jacobus Book 6 ......................... 38 Table 2 Liège late-medieval liturgical manuscripts containing tonaries .......... 45 Table 3 Late-medieval theoretical treatises containing tonaries ....................... 55 Table 4 Antiphon differentiae comparison ....................................................... 59 Table 5 Book 3 structure ................................................................................... 77 Table 6 Semitone discussion in Speculum musicae .......................................... 95 Table 7 Transitional anonymous treatises on the ars nova ............................. 112 Table 8 Speculum musicae Book 7 content summary .................................... 117 Table 9 Speculum musicae Book 4 content summary .................................... 236 Table 10 Descriptions of musica caelestis in music theory .............................. 294 xi LIST OF APPENDICES Appendix 1 Account books and charters, St. Paul ............................................ 331 Appendix 2 Structure of tonary in Book 6 ........................................................ 342 Appendix 3a Codicological examination of B-Br 10162/66 ............................ 352 Appendix 3b Watermarks in B-Br 10162/66 …….……………………………361 Appendix 3c Gathering Structure in B-Br 10162-66…….……………………362 Appendix 4 Comparison of D-Ds 1988 and B-Br 10162/66 ............................ 366 Appendix 5 Transcriptions