DISSERTATION. Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

Transcription

1 Temporal Organization in the Masses of Johannes Ockeghem DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Andrew J. Farina, M.M. Graduate Program in Music The Ohio State University 2014 Dissertation Committee: David Clampitt, Advisor Graeme M. Boone Anna Gawboy

2 Copyright by Andrew J. Farina 2014

3 Abstract How was mensural music temporally organized and is the composed structure indicative of individual style? This dissertation aims to begin addressing this question by exploring the temporal organization of the masses by Johannes Ockeghem. A metrical analysis of mensural music poses difficulties on account of the divergent properties of meter and mensural structures. On the one hand, meter manifests in both the notational and phenomenal dimensions. It can be seen in notational practice with bar lines and time signatures; it can also be assessed aurally based on context. Mensuration, on the other hand, is a strictly notational construct. Cadence positions, voice entrances, and other musical events may indicate a mensuration but cannot alter it in the way that meter can be perceived to have changed. Thus, interpreting mensuration as congruent to meter creates false and anachronistic biases. I submit that while mensural music fails to be organized by meter, there are organizational characteristics inherent in the music that are observable and analyzable. These structures in turn can be reflective of compositional practice. This dissertation offers an analytical model as an alternative means of assessing this temporal organization in mensural music and applies the model to Ockeghem s masses. I demonstrate how the temporal organization is an active yet emergent attribute of music of this time period and suggest what implications this has for better understanding Ockeghem s style. The analytical model considers how musical events ii

4 interact with and are positioned within the mensural hierarchy. The results of the analysis may not be necessarily congruent with the governing mensural structure. Analysis begins with a temporal profile, which tallies the musical events as they occur at various mensural positions. This method is derived from a modified approach to Graeme Boone s pulse framework. Although Boone s original model focused on sounding pitches, this model considers all musical events, such as notes, rests, and rest groupings. These are tallied to find the total possible number of musical events in a given mensural position. Next, there is a graphical representation of the event-percentage, which is how often a musical event occurs at a given position. The temporal profiles reveal internal privileging or biasing toward certain mensural positions or organizational structures. Trends emerge toward more archetypical structures, indicating potential aspects of compositional practice. At the same time, each individual movement in Ockeghem s masses possesses a unique temporal profile and wide variations can exist within the same mass. I contend that both the commonalities and the differences lead to a better understanding of how Ockeghem conceived of temporal organization. The result is a challenge to the idea of sameness as a marker of style. iii

5 Acknowledgments It is with tremendous pleasure and gratitude that I thank God for the wonderful opportunities and people that have come into my life during my graduate studies. The initial sparks that set my intellect ablaze and ultimately led to this dissertation have their origins during my time at the University of Kansas, where Dr. Scott Murphy exposed me to the world of historical music theory in his seminars. I could have never known then that the names of Prosdocimus de Beldemandis, Johannes Tinctoris, Franchino Gaffurio, and John Hothby (among so many others) would become permanent fixtures in my mind. Although I did not begin a large-scale pursuit of Renaissance theory at that time, his instruction and insight has remained with me. I came to the Ohio State University with the intent and hope to stoke the burning desire to learn about music before The theory faculty encouraged my curiosity and many in the musicology department graciously accepted me as one of their own. From the very beginning, I had the privilege of sitting under Dr. Charles Atkinson for seminars and papers on Greco-Roman music, evolution of chant, liturgical music of the medieval period, and development of notation. I am grateful to him for his insight and backing. His comments and suggestions have always been held in high regard and were instrumental in shaping aspects of this dissertation. iv

6 I wish to thank the members of my dissertation committee, to whom I feel indebted. I could not have asked for a more gracious, intelligent, and willing set of individuals with whom to work. Dr. Anna Gawboy has been a remarkable mentor during my tenure at Ohio State. She has permanently shaped my passion for theory pedagogy and guided my research by offering timely and direct advice. She coached me through my first conference paper and stretched me in the areas of professional development. It is not an exaggeration to say that I would not be where I am today as an academic without her impartation of wisdom and willingness to explore outside-the-box thinking. Dr. Graeme Boone has been a driving force behind much of my Renaissance research. The topical origins of this document were spawned from a rhythmic study I undertook as part of his Renaissance Music seminar. The project continued to evolve and expand, and his continual barrage of inquiry was wholly resonant with my curiosity. The term paper evolved into a summer project, before transforming into a possible conference paper and eventually part of this dissertation. Dr. Boone always pushed me further and has been enthusiastic about where this project would lead. His previous writings on music of the fifteenth century have informed my analytical method and process the most. I owe unending thanks to my advisor, Dr. David Clampitt. He has encouraged me to grow as a theorist and scholar in ways that are immeasurable. Without his help, I would not have my current breadth of knowledge and understanding. The foundation he has laid will be a blessing and benefit for years to come. He openly encouraged me to continue working with medieval and Renaissance music while still providing me with the knowledge and tools of twentieth-century theory. He has willingly labored through my v

7 research, dedicating his time and energy to the process. Although Dr. Boone s research forms the launching point of my own work, Dr. Clampitt s fingerprints are everywhere. Beyond research, I am grateful for his guidance with regards to coursework, networking, and conference papers. He has been a tremendous support to all I have done academically and a passionate advocate on my behalf. I should like to thank others at Ohio State for their support and friendship throughout my time here. Dr. Gregory Proctor has been an incredible support behind-thescenes, encouraging me to go where no theorist dares to go. I cherish the times we spent in the hallways or his office simply bantering about music and life. Dr. Ann Stimson has been a great support to me in my growth as an aural skills pedagogue. The staff members of the Music and Dance Library are the unseen gems of this university. I am grateful to Dr. Alan Green (Library Head), Ms. Gretchen Atkinson, Mr. Sean Ferguson, Dr. Michael Murray, Mr. Jarod Ogier, and Mr. Nick Wilkinson for all they do that all too often goes overlooked. I wish to especially thank Mr. Ferguson, who has really been my point-person for everything research related in the library. He has been instrumental in tracking down manuscripts, facsimiles, scores, microfilms, and other research materials that have proven elusive. Mrs. Rebecca Chappell deserves praise for her assistance on the administrative side of the degree program and tolerating my obsessiveness about making sure all the paperwork is correct. There are so many others that I wish to thank for their love, kindness, and friendship over the years. Katherine Maskell has been a sounding board both personally and scholarly. More importantly, she is a true friend. Every music theorist should be so blessed to have a musicologist as this in their life. Given what we have done together vi

8 already, I am excited to see where our collaboration takes us in the future. I thank Mr. R. Scott Osborne for his friendship. I cherish our bi-weekly meals together and his understanding of matters academic and personal. My friends outside of academia have contributed to this work in more ways than could ever be expressed. The people of Bethel Christian Church in Michigan and Christian Assembly in Columbus have offered their unending love and prayer. So many of these people have given selflessly and graciously to help me through the past four years. Specifically, I should like to thank Mike Bellish, Daniel and Danielle Hodgson, Christina Martoni, and Mel and Judy Rutkoske for taking time out of their lives to travel from Detroit to spend time with me. The Climer, Lee, Lenn, Mattson, and Scribner families are forever part of my family. My aunt, Paulette Farina, has been an unwavering support in my endeavors at Ohio State. She opened her spare bedroom and kitchen to me for four years, demanding nothing in return. Her immeasurable kindness has allowed me to live in Ohio and focus on the educational process. I thank my brother, Stephen, and my grandfather for their love and support without condition or prerequisite. Lastly, but most particularly, I thank God for my parents, William and Roberta. Their undying belief that I could be anyone and accomplish anything has set my life on this incredible path. Without their love, care, and wisdom, I would not be who I am or where I am today. vii

9 Vita B.M. Performance, University of Kansas M.M. Theory, University of Kansas 2011 to present... Graduate Teaching Associate, School of Music, The Ohio State University Major Field: Music Fields of Study viii

10 Table of Contents Abstract... ii Acknowledgments... iv Vita... viii List of Tables... x List of Charts... xv List of Figures... xvi List of Abbreviations and Symbols... xvii Introduction... 1 Chapter 1: On Meter and Mensuration Chapter 2: Analytical Model and Method Chapter 3: Mass Sections in O and o Chapter 4: Mass Sections in C and c Chapter 5: Other Elements of Temporal Profiles Conclusion References Appendix: Temporal Profiles by Mass Movement ix

11 List of Tables Table 1.1: Two dimensions of meter and mensuration Table 2.1: Diachronic plot of musical event-initia derived from the hypothetical setting in Figure Table 2.2: Tally of event-initia by tempus position from the setting in Figure Table 2.3: Musical-event tally per mensural class by semiminim from Ockeghem, Missa Caput, Gloria Table 2.4: Event-initia and spanning percentages from Ockeghem, Missa Caput, Gloria Table 2.5: Masses of Ockeghem included in this study Table 2.6: Mensurations by movement in the eleven analyzed masses Table 3.1: Average of EIP tallies in O by movement Table 3.2: The first group of mass sections in O Table 3.3: Event-initia tallies for the super Ma maistresse, Gloria Table 3.4: Event-initia tallies for the super Ma maistresse, Gloria Table 3.5: The second group of mass sections in O Table 3.6: Event-initia tallies for the Missa Ecce ancilla domini, Kyrie Table 3.7: The third group of mass sections in O Table 3.8: Event-initia tallies for the Missa Cuiusvis toni, Kyrie x

12 Table 3.9: The fourth group of mass sections in O Table 3.10: Event-initia tallies for the Missa Cuiusvis toni, Gloria Table 3.11: Event-initia tallies for the Missa Primi toni, Kyrie Table 3.12: Event-initia tallies for the Missa Primi toni, Gloria Table 3.13: Comparison of (t1) EIPs from the Missa Primi toni Table 3.14: Event-initia tallies for the Missa Mi-mi, Kyrie Table 3.15: Tree of potential rhythmic idioms for the Missa Mi-mi, Kyrie Table 4.1: Average of (t2) initia tallies as a percentage of (t1) by movement and mensuration Table 4.2: Average of (p2) EIPs and their percentage of the (t1) values by movement and mensuration Table 4.3: Tempus-level tallies for the Kyrie sections in C Table 4.4: Prolatio-level tallies for the Kyrie sections in C Table 4.5: Semiminim-level tallies for the Kyrie sections in C Table 4.6: Tempus-level tallies for the Gloria sections in C Table 4.7: Prolatio-level tallies for the Gloria sections in C Table 4.8: Prolatio-level tallies for the Kyrie sections in c Table 4.9: Tempus-level tallies for the Kyrie sections in c Table 4.10: Tempus-level tallies for the Gloria sections in c Table 4.11: Prolatio-level tallies for the Gloria sections in c Table 4.12: Tree of potential rhythmic idioms for sections in tempus imperfectum Table 5.1: EIP tallies for the sections in O from the Missa Caput xi

13 Table 5.2: EIP tallies for the opening Kyrie and Gloria passages from the Missa Ecce ancilla domini Table 5.3: EIP tallies for the second Kyrie and Gloria passages from the Missa Ecce ancilla domini Table 5.4: Total number of fusas by mass and movement Table 5.5: Fusa tallies in O by mensural position Table 5.6: Fusa tallies in C by mensural position Table 5.7: Fusa tallies in c by mensural position Table 5.8: List of (f2) event-initium tallies greater Table 5.9: Modus-level EIP tallies of select Gloria passages with a two-modus periodicity Table A.1: Event-initia tallies for the Missa Au travail suis, Kyrie Table A.2: Event-initia tallies for the Missa Au travail suis, Kyrie Table A.3: Event-initia tallies for the Missa Au travail suis, Kyrie Table A.4: Event-initia tallies for the Missa Au travail suis, Gloria Table A.5: Event-initia tallies for the Missa Au travail suis, Gloria Table A.6: Event-initia tallies for the Missa Caput, Kyrie Table A.7: Event-initia tallies for the Missa Caput, Kyrie Table A.8: Event-initia tallies for the Missa Caput, Kyrie Table A.9: Event-initia tallies for the Missa Caput, Gloria Table A.10: Event-initia tallies for the Missa Caput, Gloria Table A.11: Event-initia tallies for the Missa Cuiusvis toni, Kyrie Table A.12: Event-initia tallies for the Missa Cuiusvis toni, Kyrie xii

14 Table A.13: Event-initia tallies for the Missa Cuiusvis toni, Kyrie Table A.14: Event-initia tallies for the Missa Cuiusvis toni, Gloria Table A.15: Event-initia tallies for the Missa Cuiusvis toni, Gloria Table A.16: Event-initia tallies for the Missa De plus en plus, Kyrie Table A.17: Event-initia tallies for the Missa De plus en plus, Kyrie Table A.18: Event-initia tallies for the Missa De plus en plus, Kyrie Table A.19: Event-initia tallies for the Missa De plus en plus, Gloria Table A.20: Event-initia tallies for the Missa De plus en plus, Gloria Table A.21: Event-initia tallies for the Missa De plus en plus, Gloria Table A.22: Event-initia tallies for the Missa Ecce ancilla domini, Kyrie Table A.23: Event-initia tallies for the Missa Ecce ancilla domini, Kyrie Table A.24: Event-initia tallies for the Missa Ecce ancilla domini, Kyrie Table A.25: Event-initia tallies for the Missa Ecce ancilla domini, Gloria Table A.26: Event-initia tallies for the Missa Ecce ancilla domini, Gloria Table A.27: Event-initia tallies for the Missa Mi-mi, Kyrie Table A.28: Event-initia tallies for the Missa Mi-mi, Kyrie Table A.29: Event-initia tallies for the Missa Mi-mi, Kyrie Table A.30: Event-initia tallies for the Missa Mi-mi, Gloria Table A.31: Event-initia tallies for the Missa Mi-mi, Gloria Table A.32: Event-initia tallies for the Missa Primi toni, Kyrie Table A.33: Event-initia tallies for the Missa Primi toni, Kyrie Table A.34: Event-initia tallies for the Missa Primi toni, Kyrie Table A.35: Event-initia tallies for the Missa Primi toni, Gloria xiii

15 Table A.36: Event-initia tallies for the Missa Primi toni, Gloria Table A.37: Event-initia tallies for the Missa Primi toni, Gloria Table A.38: Event-initia tallies for the Missa Quinti toni, Kyrie Table A.39: Event-initia tallies for the Missa Quinti toni, Kyrie Table A.40: Event-initia tallies for the Missa Quinti toni, Kyrie Table A.41: Event-initia tallies for the Missa Quinti toni, Gloria Table A.42: Event-initia tallies for the Missa Quinti toni, Gloria Table A.43: Event-initia tallies for the setting super Fors seullement, Kyrie Table A.44: Event-initia tallies for the setting super Fors seullement, Kyrie Table A.45: Event-initia tallies for the setting super Fors seullement, Kyrie Table A.46: Event-initia tallies for the setting super Fors seullement, Gloria Table A.47: Event-initia tallies for the setting super Fors seullement, Gloria Table A.48: Event-initia tallies for the setting super Ma maistresse, Kyrie Table A.49: Event-initia tallies for the setting super Ma maistresse, Kyrie Table A.50: Event-initia tallies for the setting super Ma maistresse, Kyrie Table A.51: Event-initia tallies for the setting super Ma maistresse, Gloria Table A.52: Event-initia tallies for the setting super Ma maistresse, Gloria Table A.53: Event-initia tallies for the setting super Ma maistresse, Gloria Table A.54: Event-initia tallies for the mass setting sine nomine, Kyrie Table A.55: Event-initia tallies for the mass setting sine nomine, Gloria xiv

16 List of Charts Chart 2.1: Visual plot of the EIP tallies from the Missa Caput, Gloria Chart 3.1: Hypothetical temporal profile in O Chart 3.2: Chart of average EIP tallies in O by movement Chart 3.3: EIP tallies for the Missa Cuiusvis toni, Kyrie Chart 3.4: EIP tallies for the Missa Cuiusvis toni, Kyrie Chart 3.5: EIP tallies for the Kyrie sine nomine Chart 3.6: Differentiation of (t2) over (t3) for mass sections in O Chart 3.7: Length of mass sections in O by grouping Chart 4.1: Hypothetical temporal profile in C Chart 4.2: EIP tallies for the Missa Quinti toni, Kyrie Chart 4.3: EIP tallies for the setting super Fors seullement, Kyrie Chart 4.4: Chart of (t2) EIP tallies by Gloria section in c from longest to shortest in modus-span length xv

17 List of Figures Figure 1.1: Excerpt from Ockeghem, Missa Au travail suis, Kyrie (first 9 semibreves) as transcribed by Jaap van Benthem Figure 1.2: Reproduction from the Chigi Codex of the Contratenor from the beginning of Ockeghem, Missa Mi-mi, Gloria Figure 2.1: Hypothetical setting demonstrating binary semibreve rest copulates Figure 2.2: Excerpt from Ockeghem, Missa Caput, Gloria, <m90:m94> Figure 3.1: Excerpt from Ockeghem, Gloria super Ma maistresse, <m5:m9> Figure 3.2: Excerpt from Ockeghem, Kyrie sine nomine, <m3:m5> Figure 3.3: Excerpt from Ockeghem, Missa Mi-mi, Kyrie, <m1:m3> Figure 4.1: Excerpt from Ockeghem, Missa Au travail suis, Gloria, <m1:m5> Figure 4.2: Excerpt from Ockeghem, Missa Ecce ancilla domini, Gloria, <m163:m171> Figure 4.3: Excerpt from Ockeghem, Missa Au travail suis, Gloria, <m18:m23> Figure 4.4: Excerpt from Ockeghem, Missa Au travail suis, Gloria, <m105:m120> xvi

18 List of Abbreviations and Symbols I have limited the use of abbreviations throughout the dissertation to charts and figures so the reader will not need to turn to this page often. Abbreviations are employed where full mass, movement, or voice names would be too cumbersome. Mensural symbols are freely used after being introduced, however. They are also included here as a reference. Mass names MATS... Missa Au travail suis MC... Missa Caput MCT... Missa Cuiusvis toni MDPP... Missa De plus en plus MEAD... Missa Ecce ancilla domini MMM... Missa Mi-mi MPT... mass setting sine nomine in three voices, Missa Primi toni MQT... Missa Quinti toni sfs... partially-extant mass setting super Fors seullement smm... partially-extant mass setting super Ma maistresse sn... mass setting sine nomine in five voices xvii

19 Movement names G... Gloria movement, followed by section number K... Kyrie movement, followed by section number Voices B... Contratenor Bassus C... Contratenor or Contratenor Altus D... Discantus S... Tenor secundus T... Tenor Mensuration symbols O... tempus perfectum cum prolatione minore o... tempus perfectum cum prolatione minore diminutio C... tempus imperfectum cum prolatione minore c... tempus imperfectum cum prolatione minore diminutio G... tempus imperfectum cum prolatione maiore xviii

20 Introduction How were musical events temporally organized in mensural music? This very basic question truly has no easy answer. The period of mensural music, which lasted more than three hundred years, was one of constant change and development. Each composer, theorist, and musician had their own philosophies and ideas that they brought to their work. This prompts the question as to whether temporal structure can be a marker of individual style as much as a representation of local custom or then-current trend within the mensural epoch. No one set of analyses or methods will ever be able to provide a complete view of temporal organization in mensural music. This dissertation, however, aims to offer a model for representing large-scale temporal organization and reflect on what this indicates for the style of Johannes Ockeghem. One of the biggest challenges is to attempt to view mensural music on its own terms and not superimpose modern conceptions onto it. This is especially pertinent in the realm of temporal modeling. The modern research done on the evolution and practices of notation has been thorough and detailed. Yet, notation only provides an indirect view of Renaissance conceptions of musical time. On a purely basic level, in notation we see a system of fractions and ratios that harkens back to the Greco-Roman influences of music and mathematics. Systems of perfection, imperfection, and alteration may seem 1

21 unnecessarily complicated and convoluted next to our modern symbols with fixed values. The discrepancies between notation and performance shed light onto a system of thought a conceptual understanding of how music exists in time. Even so, the host of antiquated ideas can seem distant and undefined to the modern individual. One analytical approach to mensural music is to view the notation strictly at face value. This conceptualization is wholly understandable and appropriate to music of the period. After all, Renaissance discourse on rhythmic elements is almost entirely confined to notation and mensuration. Following the extant writings of the period, all notes of the same species are viewed as the same regardless of their mensural position. Perfection, imperfection, and alteration have no bearing at this fundamental level. A second and more nuanced methodology takes a notational understanding deeper and has proliferated through modern scholarship. It remains bound to the notation but is willing to acknowledge the dissimilitude among notes of the same species within the context of a mensural framework. Notation endures as the primary focus but varying degrees of concern are shown to how rhythmic durations might relate to one another. This reflects the Renaissance theoretical discourse of how mensural rules affect notation in performance. Although a notational study, the foundation for the first forays into temporality and rhythmic motion was laid in part by Charles Hamm and his exploration into the music of Guillaume Dufay. 1 Hamm discussed Dufay s style and how it changed and evolved throughout his life by tabulating the cumulative number of notes by species. As 1 Charles E. Hamm, A Chronology of the Works of Guillaume Dufay Based on a Study of Mensural Practice (Princeton: Princeton University Press, 1964). 2

22 Hamm noted, they also served to distinguish the works of Dufay from those of other contemporaneous composers. 2 Arthur Mendel replaced Hamm s species-tabulation system with an average of note values. 3 Under this system, duration is translated into an integer for each notated value. Semibreves, for example, would be given a relative value of 1; proportional values are then given to other species based on their relationship to the recta, or unaltered, semibreve under the governing mensuration. Robert Wegman used this technique to discuss an anonymous mass from the manuscript San Pietro B 80 and its relationship to the oeuvre of Johannes Ockeghem. 4 Mendel s system is one that measures the generalized pacing of a mass movement and was instrumental in Wegman s later research on tempo and relative speed. 5 The works of Hamm, Mendel, and Wegman began a process of shifting the focus away from a purely notational perspective to one that considered temporality and the effects it might have on a work. I believe that while these notationally-based approaches are firmly and rightly couched in contemporaneous theories, they offer only a partial view that takes limited risk in the discussion of mensural music. Neither system provides insight into how rhythm is organized within the mensural framework. Sean Gallagher took another step toward rhythmic organization when he reflected on individual rhythmic 2 Hamm, Chronology, A comparison was made between the masses of Dufay and two other works approximately contemporaneous with the latter part of Dufay s career: Ockeghem s Missa Quinti toni and Josquin s Missa L homme armé. 3 Arthur Mendel, Towards Objective Criteria for Establishing Chronology and Authenticity: What Help Can the Computer Give? in Josquin des Prez: Proceedings of the International Josquin Festival- Conference, ed. Edward E. Lowinsky (London: Oxford University Press, 1976), Robert C. Wegman, An Anonymous Twin of Johannes Ockeghem's "Missa Quinti Toni" in San Pietro B 80, Tijdschrift van de Vereniging voor Nederlandse Muziekgeschiedenis 37 (1987). 5 Robert C. Wegman, Concerning Tempo in the English Polyphonic Mass, c , Acta Musicologica 61/1 (1989):

23 patterns as they appear in the tempus perfectum selections by Johannes Ockeghem. 6 He discussed the proliferation and placement of certain patterns and suggested that their usage pointed toward a syntax indicative of the composer s style. Gallagher noted that certain configurations, and others proportionally or closely related, frequent Ockeghem s compositions. As far as mensural organization, however, he only notes that many of these patterns are often deployed to specific locations within the mensuration. Gallagher attested that although many of these rhythms are syntactic to the period, their usage offers a glimpse into Ockeghem s personal practice. 7 Such an assertion affirms the possibility that how rhythm interacts with mensuration might be a hallmark of style, but it also fails to explore beyond the localized level of isolated patterns. I propose to work within an approach that shifts the perspective toward rhythm on the larger scale as it is realized and projected into temporal space. At the risk of going too far afield, I want to emphasize that notation remains an important consideration for anyone working with mensural music. Temporal organization of this music, however, has been far less explored and analyzed. It is my hope that the research and analysis contained in this dissertation will begin to unveil elements of temporal structure as they might have been understood in the Renaissance by specifically exploring portions of the masses by Johannes Ockeghem. Attributes of notation can then be judged alongside temporal manifestations. 6 Sean Gallagher, Syntax and Style: Rhythmic Patterns in the Music of Ockeghem and His Contemporaries, in Johannes Ockeghem: Actes du XLè Colloque international d études humanistes. Tours, 3 8 février 1997, ed. Philippe Vendrix (Paris: Klincksieck, 1998), Gallagher, Syntax and Style,

24 As the notation is translated or rendered into temporal space via performance, questions of terminology emerge. Hamm used the term beat to discuss where a metrical pulse appeared to fall based on the orientation of his species tallies. Beat is an anachronism referent to Dufay, as it and derivative terminology (as we currently understand them) developed in the sixteenth century. 8 Edward Houghton is among those who have taken the view that the temporal arrangement found in mensural music is akin to a type of meter that is a participant in the rhythmic structure. 9 While elements of meter may have been emergent even long before the Renaissance, the imposition of meter onto mensural music is nothing short of anachronistic. It goes without saying that mensuration is not a primitive form of meter. At the same time, this does not preclude elements of metrical structures that are in place. The problem at hand, however, is that application of meter imposes a modern temporal sense onto music crafted within a different philosophical setting. As mentioned above, Renaissance-period inquiries into rhythmic elements were primarily notational affairs. There is no word for rhythm in the Renaissance that is akin to our modern understanding. In some ways, there exists a striking disconnect between music that is a direct ancestor yet so foreign to our own. Modern musicians are inheritors of a Cartesian point of view that orients us as to how time elapses in music performance. The beat-based system has further become imbued with a sense of accentuation and weightedness. Thus, overlaying meter and metrical terminology onto mensural music brings biases of 8 Graeme Boone explored the development of the term tactus and oft-equated terminology such as beat and ictus in Marking Mensural Time. See Graeme M. Boone, Marking Mensural Time, Music Theory Spectrum 22/1 (2000): Edward Houghton, Rhythm and Meter in 15th-Century Polyphony, Journal of Music Theory 18/1 (1974):

25 perspective and expectation. A view espousing where the beat lies in mensural music might unwittingly lead one to a series of false assumptions about how musical events are organized. Perfections and other groupings are not simply confining entities akin to modern notions of measures, although there may be parallel attributes. Regularity of event-placement should not be expected to align with a strong beat weak beat structure, even if it occurs at times. As I desire to show in the forthcoming analyses, the temporal organization of mensural music does often exhibit traits similar to its modern counterpart; at the same time, the differences that are present strongly defy modern conceptual understanding. I begin the first chapter with an exploration of meter from a modern understanding and show how it unsatisfactorily relates to mensural music. This includes a brief discussion about accentuation and weightedness, which reveals that meter possesses both notational and aural-perceptual elements. I lay out how it is simply not possible to overlay a twofold construct onto mensuration and expect them to be wholly congruent when the latter is strictly notational. After delimiting the boundaries of metrical applicability, I turn back toward mensuration. This includes a discussion on revealing an aural-perceptual layer derived from mensural music in temporal space that is independent of the notated schemas. Mensural hierarchy has no implicit bearing on this second-order organization in its own right. How musical events are organized in time may or may not reflect the mensuration in its structure. Every analysis hereafter is negotiated via this construct: only the music itself can define a broader meaning for the placement of musical events. Any discussion of how mensural music may be organized must tread carefully to avoid accidentally imposing meter. As a means of circumventing it and metrical biases, I 6

26 propose the use of terminology put forth by Graeme Boone in his book Patterns in Play and further extrapolated in Marking Mensural Time. 10 The first chapter of this dissertation begins to address these terms, specifically initium. It also includes a brief overview of tactus and how this relates to a more sound understanding of Renaissance musical conception. In the second chapter, I explain the analytical model and method applied to the Ockeghem masses. The analytical model is derivative of the procedures first put forth by Boone in his aforementioned writings and is also indebted to his use of the terms pulse framework and mensural class. I address Boone s model and outline the alterations made and the reasons behind the changes. Next, I set forth the parameters of the analysis, including how the model is deployed, the terminology that accompanies the analyses, and the repertoire. I believe the model has applicability to much music that falls outside the traditional confines of meter. Its goal is to assess how musical events interact with the mensural structure. That stated: a look at temporal organization across the breadth of mensural music is impractical for this dissertation. The focus hereafter will therefore be necessarily confined to one element of this organization and the works of one composer. I will discuss how the Kyrie and Gloria mass movements of Johannes Ockeghem relate to the mensural structures that are set forth by the composer. Because the aim of this dissertation is to address the music in the temporal dimension, the analyses that follow are necessarily oriented toward the phenomenal instead of the notational. The model used for these analyses has been developed to assess 10 Graeme M. Boone, Patterns in Play: A Model for Text Setting in the Early French Songs of Guillaume Dufay (Lincoln: University of Nebraska Press, 1999), 21 44; Boone, Marking Mensural Time,

27 this temporal organization systemically on a movement- or section-wide level, aiming to elucidate larger organizational structures and stylistic trends within Ockeghem s masses. Because of this broad and systematic orientation, the analytical model does not address perceived local deviations in pulse or rhythmic patterning. While such deviations may at certain points have their own significance, the establishment of broad and systematic temporal profiles has been a complex task in its own right and provides a baseline against which localized patterning can be evaluated in later research. The remaining chapters directly apply the analytical model to the masses of Ockeghem. The third chapter explores the mass sections in tempus perfectum. The sections are grouped based upon similar temporal attributes and comparisons are made. Chapter 4 addresses the mass sections in the forms of tempus imperfectum. The analysis reveals divisions on the grounds of mensuration and movement type that was not found to the same extent in the tempus perfectum sections. Both of these chapters conclude by addressing how the temporal organization may be manifest rhythmically. The fifth chapter brings all the sections together and sets up a dialogue with other attributes of temporal organization in the Ockeghem masses. Further considerations and alternate groupings are also outlined in this section. The valiant work that has been done on Ockeghem s oeuvre has generally been confined to notational, transmissional, and contrapuntal considerations. His use of mensural symbols has been exhaustively discussed by Margaret Bent, Bonnie J. Blackburn, Anna Maria Busse Berger and many others. 11 The transmission of the masses 11 Margaret Bent, The Use of Cut Signatures in Sacred Music by Ockeghem and His Contemporaries, in Johannes Ockeghem: Actes du XLe Colloque international d études humanistes. Tours, 3 8 février 1997, 8

28 and some of their stylistic traits has been a subject painstakingly examined by Fabrice Fitch. 12 Others, including Alejandro Planchart, Edward Houghton, and Robert Wegman have considered these elements as well. 13 My aim in this dissertation is to address the music in the temporal dimension. I will explore how Ockeghem creates temporal structures that exhibit different levels of conformity to the mensural hierarchy. I also suggest how trends in his use of temporal organization may be an element of style heretofore unexplored. It is my hope that the following exploration into the works of Ockeghem provides another step into uncovering his compositional practice by offering a perspective that is different from what has henceforth been considered. I believe it will further serve as another piece in addressing the fundamental question posed at the outset of this dissertation. ed. Philippe Vendrix (Paris: Klincksieck, 1998), ; Bonnie J. Blackburn, Did Ockeghem Listen to Tinctoris? in Johannes Ockeghem: Actes du XLè Colloque international d études humanistes. Tours, 3 8 février 1997, ed. Philippe Vendrix (Paris: Klincksieck, 1998), ; Anna Maria Busse Berger, Mensuration and Proportion Signs: Origins and Evolution (Oxford: Clarendon Press, 1993). 12 Fabrice Fitch, Johannes Ockeghem: Masses and Models (Paris: Honoré Champion, 1997). 13 Alejandro Planchart, Fifteenth-Century Masses: Notes on Performance and Chronology, Studi Musicali 10/1 (1981): 3 29 passim; Edward Houghton, Rhythmic Structure in the Masses and Motets of Johannes Ockeghem (PhD diss., University of California, Berkeley, 1971); Wegman, Anonymous twin,

29 Chapter 1: On Meter and Mensuration Discussion of temporal organization in the music of Johannes Ockeghem requires careful use of terminology due to the now distant nature of mensural music. In some modern efforts to understand and study the music of the past, terminology is anachronistically applied in an attempt to convey a conception of what the previous generations understood. The words rhythm and meter, as they are known and used today, have no equivalent terms in the Renaissance. Descriptions of the passage of time, such as the terms rhythmus, mensura, and tactus, may bear some similarities with but are otherwise incongruent to modern ideas of rhythm, measure, and beat. Rhythmus, for example, may have actually served as the progenitor for the notions of mensuration and meter. 14 Modern ideas of rhythm first developed as it became a factor in notational schemes. Rhythm, however, is far less contentious than meter. At present, the application of metrical terminology and concepts to mensural music has been met with disagreement and even confusion. This is amazing given the extensive work done in the scholarship and performance of mensural music and mensural theory. Part of the difficulty lies in the sheer historical breadth of mensural music. Concepts ranging from notation to tempo form numerous layers, which underwent changes from the inception of mensuration 14 Richard Crocker, Musica Rhythmica and Musica Metrica in Antique and Medieval Theory, Journal of Music Theory 2 (1958):

30 toward the end of the thirteenth century through its acquiescence to metrical practice over three centuries later. During the intervening time, countless innovations were made, concepts were given new terms, existing terminology was often conflated or repurposed, and concurrent schools of thought emerged. 15 Meter, Accent, and Applicability to Mensural Music Application of the word meter to music written prior to 1600 is highly problematic. Of course, to apply the word meter in the first place, one must define what one means by it. Although definitions vary, meter generally includes both a notational and an aural perceptual element. Justin London suggests as much in his definition of meter: (1) A synonym for time signature (2) [T]he temporal hierarchy of subdivisions, beats and bars that is maintained by performers and inferred by listeners which functions as a dynamic temporal framework for the production and comprehension of musical durations. 16 Although London might be read to be simply offering two meanings of the word, he is highlighting two distinct yet bound attributes of the same phenomenon. The notational element of the time signature is an organizational legend of how beats are grouped on the 15 The variation found in the mensuration symbols and concepts directly related to them have been explored thoroughly in Busse Berger, Mensuration and Proportion Signs. Since then, scholarship has further explored the discrepancies and peculiarities in the mensural system as interpreted and put forth by various theorists. The nature and relationship of cut symbols has been a particular touchstone. What the stroke actually means, the nature of diminution, and the implications with regard to transcription and performance tempo are discussed at length in Anna Maria Busse Berger, Cut Signs in Fifteenth-Century Musical Practice, in Music in Renaissance Cities and Courts: Studies in Honor of Lewis Lockwood, ed. Jessie Ann Owens and Anthony M. Cummings (Warren, Michigan: Harmonie Park Press, 1997), ; Blackburn, Did Ockeghem Listen, ; Bent, The Use of Cut Signatures in Sacred Music by Ockeghem, ; Bent, The Use of Cut Signatures in Sacred Music by Binchois, in Binchois Studies, ed. Andrew Kirkman and Dennis Slavin (Oxford: Oxford University Press, 2000), ; Bent, The Early Use of the Sign c, Early Music 24 (1996): London, Metre, in Grove Music Online, accessed 14 March 2013, Oxford Music Online. 11

31 score. The notational element of meter also impinges upon how time in music is organized by serving as an indicator of normative beat hierarchies within each measure. Thus, the time signature is indicative of the temporal hierarchy attested in the second part of the definition. The temporal organization and hierarchy is expressly stated in the aural perceptual aspect of meter, whereby the performer and listener dictate metric organization through creation and interpretation of sound. London s definition of meter is fluid and general by his own admission. 17 Nevertheless, it highlights the dichotomous nature of the phenomenon, and it serves as a centrist, foundational perspective on modern meter. It can be said, therefore, that a modern view of meter is both conceptual and experiential. The fundamental issue remains that meter is determined by or executed through a temporal framework that features accentuation and non-accentuation that can be aurally perceived. Alison Latham echoes London s bipartite definition of meter, more directly connecting notational and phenomenal aspects. Her synopsis, found in the Oxford Companion to Music, highlights the organization of pulses and their arrangement within the temporal confines of a bar: 18 The pattern of regular pulses (and the arrangement of their constituent parts) by which a piece of music is organized. One complete pattern is called a bar. The prevailing metre is identified at the beginning of a piece (and during it whenever it changes) by a time signature, which is usually in the form of a fraction. Latham keenly notes that the time signature is simply a prevailing meter rather than a rigid rule. Perception of any meter is conditional on recognition of the downbeat, which 17 London, Metre. 18 Alison Latham, Metre, in The Oxford Companion to Music, accessed 14 March 2013, Oxford Music Online. 12

32 Latham cites as the strongest in the musical context. 19 Because one of the primary conceptions of meter is found in the idea of pulse and accent, metric perception is influenced by pulse placement and accentuation regardless of the notational scheme employed by the composer. The musical notation is merely a static representation of the actual music that defines temporal organization within the confines of a time signature. Accents and weightings implicit from the time signature and explicit from compositional markings color the interpretation of a work by the performer and the hearing of the listener. Contrasts between strong and weak, as a manner of weightedness, developed in part from poetic meter and syllabic organization. Composers have traditionally attempted to respect the text s accentuation by matching accented syllables to accented beats in the music, thus highlighting both rhythm and sense, often to the benefit of both words and music. 20 Yet, as Latham noted, with a few exceptions, composers setting poetry to music have not felt obliged to follow the poet s metrical scheme in detail and have not restricted themselves to one note per syllable. 21 In this scheme, accentuation is contingent on text setting and placement and not on rhythmic or temporal organization. This is echoed in the application of classical metrics to craft theories of poetic and musical rhythmics, as was done by Francisco Salinas in the seventh book of his De musica Latham, Metre. 20 Latham, Metre. 21 Latham, Metre. 22 See Matthew Royal, Tradition and Innovation in Sixteenth-Century Rhythmic Theory: Francisco Salinas s De Musica Libri Septem, Music Theory Spectrum 34/2 (2012):

33 The connotations of weighted and unweighted emphasis with time units began no later than the early Baroque and gradually became more and more refined. 23 It was as late as 1636 when Charles Butler put forth a discussion in his Principles on weighting of notes due to their temporal placement. 24 In the generations that followed, metrical accentuation became embedded in the broader discourse on rhythm. 25 Accentuation, to varying degrees, also became an indispensable part of the metrical studies through the Classical and Romantic eras. 26 At the same time as this evolution, composers were also experimenting with metric perception. Music was composed with rhythmic patterns designed to imply metric organizations that were dissonant to the notated scheme. Meter, accentuation, and rhythm became inexorably linked through these successive and often parallel developments. With the deep-rooted connections between rhythm and meter in historical musical understanding, it is unsurprising that modern definitions would be co-contingent. In this way, rhythm defines meter in the musical experience, but the experience of the meter colors the interpretation of the rhythm. Therefore, the aural perception of meter is, at the lowest levels, implicitly affected by pulse placement regardless of the notational scheme employed by the composer. Similarly, the notational symbols and their associated 23 Leo Treitler has argued in favor of accentuation as early as eighth-century musica plana. His contention is that types of accent existed in the artful performances of the day but became lost as time progressed. Furthermore, any existing accentuation implicit in the music became subverted in mensural music, only to be reawakened in the transition to the Baroque. See Treitler, Regarding Meter and Rhythm in the 'Ars Antiqua', The Musical Quarterly 65/4 (1979): William E. Caplin, Theories of musical rhythm in the eighteenth and nineteenth centuries, in Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge: Cambridge University Press, 2001), Among the theories that promulgated was rhythmopoeia, which was articulated by Johann Mattheson and Wolfgang Caspar Printz. Cf. George Houle, Meter in Music, , (Bloomington, Indiana: Indiana University Press, 1987), 62 77; Caplin, Theories of musical rhythm, Philipp Kirnberger led the innovations that evolved into Akzenttheorie, which strongly encased the discussion of accentuation into metrical understanding. Caplin, Theories of musical rhythm,

34 divisions of time can color the interpretation of a work in performance through the placement of accents or weighting. For music in the fifteenth century, these interrelationships among meter, rhythm, and accentuation verge on being anachronistic, if not ahistorical, concepts. Foremost, developments that tied accentuation and metrical organization together occurred more than a century later. Is this to say that mensural music is not influenced by agogic accents, classical metrics, or an aural-temporal delineation of pulse? No, there is nothing that explicitly precludes such accentuation and it would be unwise to immediately limit our understanding otherwise. Leo Treitler suggested that accentuation in the ars antiqua receded in the period of mensural notation, inferring that structures of weightedness may lurk in the background or underlie various elements of Renaissance music. 27 Phenomenal accents, as defined by Lerdahl and Jackendoff, can be created by the attack points of pitch-events. 28 If the mensural structure influenced a composer to emphasize temporal positions by placing musical events there, it seems more prudent to ask whether or not this is a residual, innate form of accentuation that Treitler suggests. Edward Houghton, in his appeal to view fifteenth-century polyphony as metrical, stated that Tinctoris s prohibition of dissonance at certain mensural locations would be useless outside a metrical construction. 29 It could be perceived that Tinctoris s regulation of dissonance in the temporal framework is an implicit form of structural emphasis; however, such a view glosses over the instances in mensural music of dissonances that occur at Tinctoris s 27 Treitler, Regarding Meter, Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, Mass.: MIT Press, 1983), Houghton, Rhythm and Meter,

35 prohibited positions. 30 Houghton adds the caveat that the metrical nature of mensural music should be distinguished from the varying metrical functions of other styles. 31 Meter here is a functional subheading under rhythm of pulse-groupings that does not necessarily imply regular dynamic accents. 32 Based on these observations and postulates alone, one might perceive it possible to imply some type of metrical accent existing in mensural music. 33 Such a view stands in opposition to other twentieth-century scholarship on the matter. 34 A point of confusion may rest on the word tactus as put forward by Adam von Fulda in 1490 and by other contemporary theorists. 35 Graeme Boone explains that Adam described tactus as a dynamic span of time that has an inherent, unbroken motion. All tactus spans are contiguous to one another as they progress through temporal space. 36 It is important to emphasize that for Adam tactus refers to the motion within the span of time that occurs from its impetus until the ultimate, terminal ending of the span. Boone notes that although the term is translated as beat, Schlag, and stroke, Adam never defines the tactus through a pulse-centric perspective, which varies from a post-1600 definition of 30 Types of dissonances and their locations within the temporal structure of mensuration are explored further in Anne-Emmanuelle Ceulemans, Les dissonances dans la polyphonie des XVe et XVIe siècles: Quelques indications envue d'une analyse assistée par ordinateur, Musurgia 3/2, Avatars de la modalité, du XVe au XVIIe siècle (1996): Ceulemans makes a distinction, as well, between dissonances accentuées and dissonances non accentuées with regard to the composer s placement of the dissonance. 31 Houghton, Rhythm and Meter, Houghton, Rhythm and Meter, Boone notes that he and others hear strong weak relationships in mensural music. It is unclear and will likely never be known if this is a predisposed bias toward metrical accents on account of modern performance practice (both in performance and reception) or due to the actual nature of the music proper. See Boone, Marking Mensural Time, Cf. Edward E. Lowinsky, Early Scores in Manuscript, Journal of the American Musicological Society 13/1 (1960): Boone delves deeply into the discussion of tactus and its implications for our modern understanding of mensural music. He contrasts the scholarly writing on the matter with his own detailed dissection of Adam s statements. See Boone, Marking Mensural Time, Boone, Marking Mensural Time,

36 the term. 37 Opposition to interpreting beat or the modern German Takt in reference to fifteenth-century music as a type of accentuating pulse is promulgated to varying degrees by Charles Hamm, Russell Harris, Antonio Tirabassi, Curt Sachs, and others. 38 In the absence of a true understanding of the nature of accentuation, the focus hereafter will be primarily on temporal divisions of time without regard to any potential application of stress or weightedness. The concept of tactus must be addressed in brief, however, as it is pertinent to an understanding of how the relationship between mensuration and rhythm is analyzed. The continuation of time is a constant in music, as the art exists in the temporal realm. Mensural theory engaged the Aristotelian framework of time as a continuously elapsing entity. Thus, measuring off and assessing spans of time, what Johannes Tinctoris termed mensura and others termed tactus, became the foundation of the Renaissance theoretical understanding. 39 Alexander Blachly, in his research into alleged metrical aspects of late mensural music, sought to distinguish between mensura and tactus by approaching the latter as almost exclusively a beat-based or pulse-based entity. 40 Boone illustrates how this is incorrect based on Adam von Fulda. Tactus does have an inherent, defined beginning that is pulse-related, but it also has a subsequent duration that lasts until the 37 Boone, Marking Mensural Time, 28, Boone provides a detailed discussion of this opposing view in Marking Mensural Time, 26. Cf. J.A. Bank, Tactus, tempo and notation in mensural music from the 13th to the 17th century (Amsterdam: Annie Bank, 1972), ; Russell Harris, An Analysis of the Design of the Caput Masses by Dufay and Okeghem in Their Metric and Rhythmic Aspects in Hamline Studies in Musicology 1 (1946): 2 46; Antonio Tirabassi, La Mesure dans la notation proportionelle et sa transcription moderne (Brussels: Delvigne, 1927), 62; Curt Sachs, Rhythm and Tempo (New York: Norton, 1953), See Eunice Mary Schroeder, Mensura according to Tinctoris: in the context of musical writings of the fifteenth and early sixteenth centuries (PhD. diss,, Stanford University, 1985); Busse Berger, Mensuration and Proportion Signs, 78 86, Alexander Blachly, Mensura versus Tactus, in Quellen und Studien zur Musiktheorie des Mittelalters, ed. Michael Bernhard (Munich: C.H. Beck, 2001),

37 next tactus begins. 41 This creates a group of contiguous timespans. Each unit itself features unbroken, continuous motion. Terminology that describes time-points exists as early as Johannes de Muris, and a pulse-oriented understanding of time cannot be fully dismissed. 42 Terms such as pulsus and ictus, according to Boone, are not solely demarcations of time-points, per our conception of meter, but rather terms used as vehicles for properly describing spans of time. 43 Even so, pulsus and ictus may imply a weighting or stress. To strip any potential anachronistic element from the discussion, Boone purposes the word initium to indicate the beginning point of any given duration. 44 If the initia were to be accented, this would constitute a phenomenon that Boone defines as ictus. 45 Instead, initia are merely points within temporal space that exist at the beginning of each tactus-as-duration. 46 The tactus spans form a cyclical, continuous structure with regular periodicities imposed on it by the governing mensuration. For example, tempus spans are divisions of a modus that repeat with the passing of each modus span. There will always be a second tempus-span within a unique modus, leading to a level of periodicity. This cycling exists at all levels as modus is divided into tempus, which in turn is parsed into prolatio divisions and onward. These periodicities allow for spans of mensural music to be compared directly regardless of their placement within the piece ultimately, and it is an important element of the temporal analyses explored in this document. 41 Boone, Marking Mensural Time, Cf. Example 1 on Boone, Marking Mensural Time, Boone, Marking Mensural Time, Boone, Marking Mensural Time, Boone, Marking Mensural Time, 7, Boone, Marking Mensural Time, Boone, Marking Mensural Time,

38 Contrasting Meter and Mensuration: A Case Study The relationship between meter and rhythm is symbiotic. This stands in contrast to how mensuration and rhythm interact. Mensural rules, indicated in symbols, were abstract divisions of time that governed the interpretation of notated patterns. While figures and figuration schemes in the notated passages (rests or dots of perfection) may reveal a mensural rule, rhythmic patterns can neither change nor alter it. This is because mensuration is notational convention that possesses no explicit implication of accentuation or aurally-perceivable organization. Any change of mensuration must be notated regardless of how the music in performed or heard in real time. In essence, mensuration is a temporal construct that elapses concurrently with the music but is not influenced by it. This contrasts meter, which can be perceived, at least implicitly, as being something other than what is notated on the score. Of course, mensuration itself is a raw measuring-out of time spans that transcends the rhythmic complexion of a work. Graeme Boone has explained that mensural music differs from our modern practice in how time is divided. 47 Modern temporal understanding divides time into a series of points, which themselves have no temporal value. 48 Points are separated equidistantly and become grouped into a structural hierarchy by distinct, perceptible weightedness or accentuation. 49 Mensural music, however, is a hierarchy of delimited tactus spans, whose measuring-out is regulated by the governing mensural rule and not influenced by the notated rhythm. 50 The hierarchy is formed by 47 Boone, Marking Mensural Time, Boone, Marking Mensural Time, Lerdahl and Jackendoff, A Generative Theory, Boone, Marking Mensural Time, 7. 19

39 either grouping smaller tactus units into larger entities or further subdividing larger spans into smaller durations with no regard to its aural saliency. Thus, rhythm and mensuration only interact directly in the realization process from notation into performance. Once rhythm has been projected into the temporal plane, it interacts indirectly with mensuration by occurring within the delimitation of time as set out by the mensural rule. In spite of some very limited congruency between meter and mensuration, deductions about the mensural nature of a passage must not be driven by a metrical understanding of fifteenth-century music. Jaap van Benthem s 1998 transcription of Ockeghem s Missa Au travail suis exhibits this dichotomy. Ockeghem derived some of the contrapuntal content from the rondeau-quatrain Au travail suis, which was composed in three-voices. 51 The original rondeau was written in tempus perfectum (O) but the mass movements are transmitted in the source documents in tempus imperfectum (C) and tempus imperfectum diminutio (c). 52 Although the manuscripts that preserve the Kyrie and Sanctus movements present them in C, van Benthem editorially alters the arrangement in his transcription to reflect O. He addresses the change in the transcription s front matter, citing the temporal alignment of various musical elements. 53 Firstly, van Benthem notes that the opening four-note passage of each movement, derived from the rondeau, is found in imitation offset by three semibreves, creating a perceived 51 The question of authorship has been raised given that one of the sources indicates that this Missa Au travail suis was composed by Barbinguant. Attribution to Ockeghem has remained the prevailing opinion, and the mass is included in this study accordingly. See Jaap van Benthem, ed., Missa Au travail suis, in Johannes Ockeghem: Masses and Mass Sections (Utrecht: Koninklijke voor Nederlandse Muziekgeschiedenis, ), II/3:xvii. 52 See van Benthem, Missa Au travail suis, II/3:xvi xvii. 53 While it is unlikely, it must be acknowledged that the transmission of the mass in all four manuscripts may be faulty or corrupted. A hypothetical reading of the Kyrie as if it were in O on account of the limited number of breves found in the movement amounts to no change in the rhythmic transcription; the remaining breves would likely be imperfected by attached semibreves throughout given the absence of dots of perfection. In other movements, however, the counterpoint may be skewed by such a reading. 20

40 disjunction. The imitative structure of the rondeau s opening seems to be at odds with the opening of the first four Mass movements, of which the transmitted readings do not always fit comfortably with a tempus imperfectum layout. 54 The Kyrie and Sanctus movements are adjusted to have the imitation align with the beginning of a modus boundary, but the other movements have their mensuration retained. Figure 1.2 shows van Benthem s transcription of the opening passage from the Kyrie as measured out in a tripartite semibreve-division akin to O. He notes that any barring in a manner influenced by a reading in C obscures the elegant layout of the cantus prius factus motive. 55 Such sophistication is not accommodated in the Gloria, Credo, or Agnus dei movements, however. Figure 1.1: Excerpt from Ockeghem, Missa Au travail suis, Kyrie (first 9 semibreves) as transcribed by Jaap van Benthem. Van Benthem also addresses the position of cadences in the Credo and Agnus dei by remarking that some fail to resolve on the start of a mensuration implicitly the 54 van Benthem, Missa Au travail suis, II/3:xvii. 55 van Benthem, Missa Au travail suis, II/3:xvii. 21

41 modus boundary. 56 This aspect alone is not sufficient enough for van Benthem to warrant a transcription under another mensural rule, although Edward Houghton s research indicated that such alignment is normative. 57 Likewise, he asserts that the notation of the final cadences in the Kyrie movement imply a perfect tempus mensuration. The end result is a shift of the cadences off the mensural modus boundary, whereas the first Kyrie and Christe sections would have arrived accordingly. The third Kyrie closes with a semibreve displacement if the movement is read separately. Since the Christe ends at a semibreve with fermata, a continuous reading of the two final Kyrie sections accommodates the third Kyrie ending, which van Benthem acknowledges. 58 The intent of this exploration into the transmission and transcription of the Missa Au travail suis is not to critique carefully considered editorial practices. Rather, it prompts a difficult question about whether metrical understandings influence a view of mensuration. While it is true that modern bar lines in the Missa Au travail suis obscure the nature of the imitative cantus prius factus figure at the beginning of the movements when read in C, it must be considered that this is a notational convention that is foreign to the music of the period and thus essentially irrelevant. 59 There are other movements where material derived from the cantus prius factus sources crosses bar-line barriers. These instances do not preclude their placement in a manner disjunctive to a metrical reading elsewhere in van Benthem s transcriptions. Furthermore, cadences are not prescribed to arrive at the beginning of a modus span even if they typically resolve at 56 van Benthem, Missa Au travail suis, II/3:xvii. 57 Houghton, Rhythm and Meter, van Benthem, Missa Au travail suis, II/3:xvii. 59 Cf. Lowinsky, Early Scores,

42 these points. Houghton said, Cadential resolutions [in Ockeghem s masses] were observed to coincide regularly with mensural divisions. 60 The point of resolution could be described in modern terms [as] the downbeat of the measure. 61 Houghton s observations in the Ockeghem masses are correct in that the majority of cadences do conform to this temporal alignment, but one need look no further than the closing cadence of the first Kyrie from the Missa Mi-mi for a counterexample. 62 The contention here is that a metrical reading need not be obliged. This neither negates the retransmission theories that van Benthem proposes nor the changes in mensuration on account of a corruption in the mensural rule. 63 Instead, it suggests that there may be instances where a modern metrical reading may not be congruent to the temporal structures built music regardless of the mensural divisions. Perhaps it even suggests that the mensuration is unimportant insofar as it concerns realization of broad-scale temporal organization. Constructing a Second-Order Organization for Mensural Music The quandary of Johannes Ockeghem s Missa Au travail suis highlights an important matter in analysis of mensural music: conceptual organization of the music may not align with or conform to the mensural hierarchy. It is certainly plausible that Ockeghem may have composed the Missa Au travail suis with the cantus prius factus in mind, retaining a 60 Houghton, Rhythm and Meter, Houghton, Rhythm and Meter, The first Kyrie from the Missa Mi-mi, which is in tempus perfectum, resolves to the closing consonance on the third semibreve of the final perfection. See Jaap van Benthem, Missa My my, in Johannes Ockeghem: Masses and Mass Sections (Utrecht: Koninklijke voor Nederlandse Muziekgeschiedenis, ), III/2:1. 63 van Benthem, Missa Au travail suis, II/3:xviii xix. 23

43 conceptual three-semibreve grouping that permeates much of the mass. At the same time, there is nothing that requires each of these three-semibreve divisions to align with the beginning of a modus division. It goes without saying that groups of rhythmic patterns and consecutive perfections do not themselves create a construct of meter in mensural music. Imposing arbitrary or irregular meter onto mensural music fails to advance objective transcription. 64 As mentioned above, meter possesses two dimensions whereas mensuration is confined to notation. Table 1.1 illustrates this dichotomy. Notational Temporal Phenomenal Metrical music Notated meter (Time signature and barring) Perceived meter (Accent or rhythm-influenced organization) Mensural music Mensuration (Mensural symbols and dots of perfection) Table 1.1: Two dimensions of meter and mensuration. Van Benthem uses dashed barring as a means of communicating the beginning of a modus division with the assumption that there is no bias toward accentuation. His effort appears to be an attempt to communicate where the mensuration intersects with the music while not portraying it as a metrical rule. The modern score is a visual representation of how the music aligns temporally among all voices and within the mensural hierarchy. This tactic is a step toward a second-order of organization in mensural music and addressing the how the music projects into the temporal dimension. 64 Cf. Lowinsky, Early Scores,

44 Since no single term exists in Renaissance discourse that discusses how mensural music exists in the temporal dimension, it is tempting and seemingly expedient to anachronistically employ the term meter. I contend that given the definitions of meter presented above, the term is unsatisfactory for the description of mensural music. The concept is too laden with modern notions of time-points and accentuation to be appropriately applied to music of the fifteenth century without challenge. However, it is important to consider how music is temporally organized while turning away from strong weak relationships as a grouping mechanism. In place of meter, I propose an analytical model that assesses the interaction between mensuration and the placement of musical events. Mensuration and the delimited spans of time within it form an abstract framing mechanism that serves as a temporal scaffolding within which musical events are placed. Rhythm and rhythmic patterns in turn interact with time that is measured off into these recurrent, cyclical spans within a temporal hierarchy of subdivisions. This results in the periodicity and patterning of said spans. The framework of this model is guided within a work by the predetermined arrangement of time-spans given by mensuration; yet, the results are also an emergent property of the music, as they are defined by how the temporal-rhythmic elements of the music occupy the mensural divisions. One purpose of this model, as opposed to meter, is to focus on the contiguous spans of time that make up the mensural hierarchy to see how they are occupied by rhythmic elements apart from other elements that may or may not be in one s working definition of meter. Another goal is to strip time-measurement down into cycles of periodicities that form a temporal scaffolding in which musical events are placed. Doing this allows an exploration of any potential congruency with the mensural rules and other 25

45 notational practices, such as line-wrapping, rest delimitation, and so forth. It also permits a consideration of what rhythmic arrangements might be revealed on a larger scale to be structurally important. Rhythm: Duration, Perfection, and Notation Whereas mensural music may not contain accentuation, it does feature distinct rhythm and rhythmic patterns that may be considered allusive of meter from a modern context. At the same time, complications arise in the application of the term rhythm to mensural music. In a highly generalized sense, rhythm can be defined as the organization of musical events in time. 65 Considering this as a baseline definition, there is no word for rhythm in the Renaissance. 66 Composers and theorists who wrote about rhythmic value did so in the context of notation or mensuration. This is an important correlation, as duration is measured out based on the notational scheme, unlike our modern metrical system wherein each symbol has an inherent and expected value regardless of context. Thus, when theorists wrote on as many as eight primary species of notes maxima, longa, breve, semibreve, minim, semiminim, fusa, and semifusa the mensural structure and surrounding context dictates the actual durational value of most species. 67 Although 65 Arnold Whittall, Rhythm, in The Oxford Companion to Music, accessed 07 October 2013, Oxford Music Online. 66 Margaret Bent, What is Isorhythm? in Quomodo cantabimus canticum? Studies in Honor of Edward H. Roesner, ed. David Butler Cannata, et al. (Middleton, Wis.: American Institute of Musicology, 2008), Not every theorist explored the possibilities of each note species. Johannes Tinctoris famously denied the plausibility of any note smaller than a minim in his Tractatus de notis et pausis. Other notational values and schemes were also possible. Ramis cited theorists that proposed cursaea and minarea notes to denote other divisions of time. Even so, these eight became the primary species and the basis for the evolution into modern notation. See Johannes Tinctoris, Opera theoretica, ed. Albert Seay, Corpus Scriptorum de Musica 22 (Colorado Springs: American Institute of Musicology, ), 1: ; Bartolomeo Ramis de Pareia, Musica Practica, trans. Clement A. Miller, Musicological Studies and Documents 44 (Neuhausen- Stuttgart: American Institute of Musicology, 1993),

46 naming conventions varied among theorists and composers alike, only the durational values below a minim were fixed to a scheme of binary divisions not contingent on the governing mensural rules. This contrasts our modern system, where a symbol signifies a specific place within the hierarchy of binary divisions and an absolute and relative length. The modern whole note is equivalent to two half notes in all cases, and its absolute value is defined by having a duration of the equivalent value thereof. A breve in mensural notation, however, could be divided into either two or three equal semibreves or two unequal semibreves dependent on the mensural rule and the musical context. This creates a disjunction between the notated patterns and the rendering of the rhythm in temporal space. Figure 1.2, an excerpt from Ockeghem s Missa Mi-mi as seen in the Chigi Codex, highlights this disjunction. Figure 1.2: Reproduction from the Chigi Codex of the Contratenor from the beginning of Ockeghem, Missa Mi-mi, Gloria. (Vatican City, Biblioteca apostolica vaticana, MS Chigi C VIII 234, folio 5r) In this excerpt from the Gloria of Ockeghem s Missa Mi mi, the notated pattern can be listed simply as B Sb Sb Sb B (Sb) B Sb Sb L. The dots of division (punctum divisionis) that interrupt both groups of semibreves are vital to realizing the rhythm as durational values. The first two notes must fit within the space of a single perfection on 27