Speculative ‘Musica’ and the Medieval University of Paris Boethius’ De institutione musica

Speculative 'Musica' and the Medieval University of Paris Author(s): Joseph Dyer Source: Music & Letters , May, 2009, Vol. 90, No. 2 (May, 2009), pp. 177-204 Published by: Oxford University Press Stable URL: https://www.jstor.org/stable/20532895 JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to Music & Letters This content downloaded from 192.87.31.155 on Sun, 26 Nov 2023 10:13:25 +00:00 All use subject to https://about.jstor.org/terms

Music & Letters, Vol. 90 No. 2, © The Author (2009). Published by Oxford University Press. All rights reserved. doi:10.1093/ml/gcn089, available online at www.ml.oxfordjournals.org SPECULATIVE ‘MUSICA AND THE MEDIEVAL UNIVERSITY OF PARIS By JosePH DYER* QUESTIONS ABOUT THE PRESENCE or absence of musica speculativa in the curriculum of the early European university have elicited contradictory responses. Some scholars maintain that speculative musica, one of the seven liberal arts highly esteemed in Antiquity and the Middle Ages as the foundation of knowledge and preparation for the study of philosophy and theology, continued to enjoy an honoured place in the university curriculum. Others point to a lack of evidence that this was so. It is my intention to consider this question mainly from an institutional perspective by examining the curriculum of the University of Paris: what was taught, how it was taught, and the degree of interest in speculative musica that may have existed among thirteenth-century academics. Though Paris, the paradigm for other European institutions, will be the central focus of this essay, the place of musica in the teaching programmes of Oxford, Cambridge, and the universities of Central Europe will be the subject of comments later in this essay. At a conference held at the University of Notre Dame in 1987, a paper entitled “The Influence of Aristotle on French University Music Texts’ took as its subject music theory treatises. Their place in university studies was argued on the basis of the presence in these treatises of terminology drawn from logic, the dominant intellectual fashion of the time.’ That same year, at the meeting of the International Musicological Societyin Bologna a round table on music in the history of the university was introduced with the assertion that ‘the vast majority of treatises on music theory can be directly or indirectly linked to a university environment’, and further, ‘the challenge to the historianis to determine to what extent these treatises actually constituted part of the curriculum of the university? Thus framed, the question embodied dubious assumptions about the intellectual interests of thirteenth-century university masters and students.” In his classic study of the medieval universities (1895, revised 1936) Hastings Rashdall stated flatly that ‘at Paris we hear nothing of music’.* Similarly, Pearl Kibre, after reviewing indications that the study of arithmetic and geometry continued to be cultivated at Oxford, noted with regard to music that, at Paris ‘the *, Email: joseph.dyer@umb.edu. ! Jeremy Yudkin, ‘The Influence of Aristotle on French University Music Texts’, in André Barbera (ed), Music Theory and its Sources: Antiquity and the Middle Ages (Notre Dame, Ind., 1990), 173-89. ? Craig Wright, Introduction to the Round Table ‘La Musica nella storia delle università’, in Angelo Pompilio et al. (eds), Atti del XIV congresso della Società Internazionale di Musicologia: Trasmissione e recezione delle forme di cultura musicale, Bologna, 27 agosto—1 settembre 1987, Ferrara-Parma, 30 agosto 1987, 3 vols. (Turin, 1990), 1. 27. 3 Still less is there any evidence that ‘the study of practical music entered the university because of the need to understand cantus ecclesiasticus, the music of the divine service’ (ibid. 29) or that practical music was studied at all in the medieval university. * Hastings Rashdall, The Universities of Europe in the Middle Ages, 3 vols. (Oxford, 1895); new edn. by Frederick M. Powicke and Alfred Brotherston Emden (Oxford, 1936), 1. 450.

university statutes are mute’. She suggested, nevertheless, that ‘other evidence similarly attests the continuing concern with this subject as one of the mathematical arts in university circlesin the thirteenth century’? After summarizing the views of Robert Grosseteste and Roger Bacon on the moral, medical, and theological value of music, she alludes to the treatises of Boethius, Hélie Salomon, Marchetto, Engelbert of Admont, and Jerome of Moravia, but without explaining how any of them might have figured in the university milieu. The only comprehensive survey of music and the medieval university to date is Nan Cooke Carpenter’s Music in the Medieval and Renaissance Universities, now fifty years old. Most of the evidence cited by Carpenter concerns not the teaching of music but musical performances at university functions and the (hypothetical) links she sensed between music theorists and the universities. Though well informed, her study does not distinguish sufficiently between the cultivation of the liberal arts in twelfth-century Paris and the transformed curriculum of the university in the next century. She does not, moreover, draw distinctions between the different circumstances that prevailed outside Paris, nor does she take into account the considerable time span covered by her sources. She maintains, nevertheless, that ‘there is overwhelming evidence from many other sources for the study, cultivation, and practice of music as science and art at the great French university [Paris]’.° The nature of these ‘other sources’ remains unclear. Most recently, the subsection of The Cambridge History of Western Music Theory dedicated to ‘Musical study in the medieval university’ avoided discussing this problematical topic altogether. The author concluded, nevertheless, that ‘the earliest musical curriculum of the medieval universities drew heavily upon Boethius and his program of the seven liberal arts, in which music was included as one of the quadrivial sciences’.’ This is far from an accurate portrayal of the situation, as I hope to demonstrate. Michael Bernhard, who approached the topic mainly (but not exclusively) from the standpoint of music theory treatises, found little support for assuming the presence of musica in the instructional programme of the thirteenth-century university, even though many music theorists demonstrated some level of ‘Universitätsbildung” In a survey of thirteenth-century chant treatises I found that the presence of philosophical terminology and the occasional resort to logical methods of argumentation indicated no more than that these authors had attended university long enough to imbibe the logical terminology and methodology that pervaded all branches of knowledge.” Many music theory treatises commence with a flourish of erudition before settling down to the ° Pearl Kibre, ‘The Quadrivium in the Thirteenth-Century Universities (with Special Reference to Paris)’, in Arts libéraux et philosophie au moyen âge: Actes du quatrième congrès international de philosophie médiévale, Montréal, 27 aoüt-2 septembre 1967 (Montréal and Paris, 1969), 175-91 at 185. © Music in the Medieval and Renaissance Universities (Norman, Okla. 1958; repr. New York, 1972), 32-127 at 48. One of the few earlier studies devoted to this topic is André Pirro, ‘L'Enseignement de la musique aux universités françaises’, Mitteilungen der internationalen Gesellschaftfür Mustkwissenschaft, 1 (1930), 26-32, 45-56 (very rich in historical references but few relate to instruction in the early university); also Peter Wagner, ‘Zur Musikgeschichte der Universitat’, Archiv für Musikwissenschaft, 3 (1921), 1-16. Christopher Page noted the absence of any references to polyphony in university documents; The Owl and the Nightingale: Musical Life and Ideasin France, 1100-1300 (Berkeley, 1990), 137-43. ” Robert W. Wason, Musica practica: Music Theory as Pedagogy’, in Thomas Christensen (ed), The Cambridge History of Western Music Theory (Cambridge, 2001), 49-50. “Das musikalische Fachschrifttum im lateinischen Mittelalter‘, in Frieder Zaminer (ed), Rezeption des antiken Fachs im Mittelalter (Geschichte der Musiktheorie, 3; Darmstadt, 1990), 39-103 at 64 Emil Platen doubted the inclusion of musica as a‘Lehrfach’in the early university (‘Universität und Musik’, in MGG?, Sachteil 9, col. 1168). 9 Joseph Dyer, ‘Chant Theory and Philosophyin the Late Thirteenth Century’, in László Dobszay et al. (eds), Cantus Planus: Papers Read at the Fourth Meeting—Pecs, Hungary, 3-8 September 1990 (Budapest, 1992), 99-118.

practical aspects of music theory.” The theorist known only as Anonymous IV was a student in Paris during the second quarter of the thirteenth century, and Johannes de Grocheio is identified in one of the manuscripts of his treatise as ‘magister’.!! Frank Hentschel remarked that the quadrivial disciplines ‘were de facto still present in the faculty of arts in the thirteenth century” but he carefully refrained from assigning to them a specific place in the programme of instruction. If an intellectually curious student learnt something outside the confines of the curriculum, that should not be astonishing. Iréne Rosier has reminded us ‘not to mistake what people knew with what was taught at university”. It will be my contention in the present study that speculative musica (by default the De institutione musica of Boethius) had no place in the university curriculum, even though it attracted some interest outside that framework, something to be expected given the intellectual curiosity of scholars and the power of tradition embodied in the study of the artes liberales. Conflicting opinions about the place of speculative musica in the university curriculum are not unique to the modern scholarly literature. Jacques de Liège (c.1260—after 1329) reported that he heard lectures on the first two books of Boethius De ınstitutione musica at Paris, most likely in the 1270s, when he would have been a student there.“ This positive witness cannot be easily dismissed, especially since his statement refers specifically to the very books of Boethius’ Musica (1 and 2) identified as ‘de forma’ in documents associated with the University of Paris. (The implications of this phrase will be discussed below). Almost a generation later, Johannes de Muris (Jehan de Murs, c.1290/5-after 1344), a mathematician and distinguished astronomer as well as a music theorist, maintained exactly the reverse: that the mathematica were neglected at Paris, a state of affairs that he attributed in part to the difficulty of the subject: ‘these days the books of the older philosophers, not only those concerning music, but also those of the other mathematicals are not read; and this happens because [students] shrink from them as unintelligible or excessively difficult.” There must have been some interest in music at Paris, however sporadic or informal, for Muriss Musica speculativa was intended to rectify the neglect of Boethius by providing a summary of the first 10 The Commendacio omnium scientiarum et specialiter musice (late 13th c) borrows heavily from Hugh of St Victor's Didascalicon, Richard of St Victor’s Liber exceptionum, and the De ortu scientiarum of Robert Kilwardby, turning to John (of Afflighem) for examples of the various ‘effects’ of music. The Commendacio, nevertheless, is primarily an exposition of all the usual ‘regule de musica’: solmization, intervals, tones, and differentiae (incomplete) that one would expect to find in a work whose goal was practical instruction. See Wolfgang Hirschmann, ‘Wissenschaftstheorie im pragmatischen Kontext: Die “Commendacio omnium scientiarum et specialiter musice” im Heilsbronner Musiktraktat’, in Frank Hentschel (ed), Musik — und die Geschichte der Philosophie und Naturwissenschaften im Mittelalter: Fragen zur Wechselwirkung von ‘Musica’ und “Philosophia’ im Mittelalter (Studien und Texte zur Geistesgeschichte des Mittelalters, 62; Leiden, 1998), 229-67 (an edition of the prologue and the regule de musica is promised) Fritz Reckow, Der Musiktraktat des Anonymous IV, 2 vols. (Beihefte zum Archiv für Musikwissenschaft, 4-5; Wiesbaden, 1967), ii. 1-2. 12 der Sache nach an der Artistenfakultät des 13. Jh noch präsent waren’; Frank Hentschel, Sinnlichkeit und Vernunft in der mittelalterlichen Musiktheorie: Strategien der Konsonanzwertung und der Gegenstand der Musica sonora um 1300 (Beihefte zum Archiv für Musikwissenschaft, 47; Stuttgart, 2000), 260. 3 de ne pas confondre ce que les gens savaient avec ce que était enseigné à l’université’; Irene Rosier, as reported in Joel Biard, ‘Rapport de la Table ronde: Les disciplines du trivium’, in L'Enseignement des disciplines à la Faculté des arts, Paris et Oxford, XIIF- XIV” siècles (Turnhout, 1997), 177. # “Ut confidentius illa uti possem, qui de duobus primis libris [Boetii], quos Parisius audieram, aliqua extraxeram, plura coepi et de illis et de aliis excerpere’; Jacques de Liège, Speculum musicae, ed. Roger Bragard (Corpus Scriptorum de Musica, 3; Rome, 1961), 11. 136 (2.56.17). 5 ‘Verum, quia istis diebus libri antiquorum philosophorum nedum de musica, sed et de ceteris mathematicis non leguntur, et ob hoc accidit quod eos tamquam inintelligibiles aut nimis difficiles abhorrer?; Die Musica speculativa des ‚Johannes de Muris: Kommentar zur Überlieferung und kritische Edition, ed. Christoph Falkenroth (Beihefte zum Archiv für Musikwissenschaft, 34; Stuttgart, 1992), 74 (prologue of ‘version A).

two books of De institutione musica for the benefit of those lacking advanced mathematical skills. THE SCHOOLS OF PARIS IN THE TWELFTH CENTURY In Paris as in other French cities (Chartres, Orleans, Reims, Laon, and Tours), independent schools flourished during the twelfth century, their reputations and ability to attract students dependent on the charisma of gifted teachers who acted as intellectual and spiritual fathers to their students. At times, the teacher himself was de facto the ‘school’, since no licensing requirement was imposed by civic, ecclesiastical, or royal authority. The curriculum, the seven liberal arts, recovered centuries earlier by the Carolingian renascence, carried on the traditions of the monastic and cathedral schools. Since the schools were open to all comers who possessed a basic command of Latin, ambitious and intellectually curious students gladly travelled from place to place so that they might sit at the feet of celebrated teachers. From a Christian perspective the liberal arts were not an end in themselves. Rather, they predisposed the mind and the heart to a more profound understanding of the Scriptures and sacred theology, just as in Antiquity they were deemed the indispensable preparation for the study of philosophy. They did not lack eloquent proponents: Adelard of Bath (De eodem et diverso), Bernard and Thierry of Chartres_(Heptateuchon), ” John of Salisbury (Metalogicon),” and Hugh of St Victor (Didascalicon).” Given the propaedeutic aspect of the liberal arts, it is understandable that more emphasis was placed on the trivium than on the quadrivium. The development of grammatical skills received the most attention. The mathematical disciplines were not ignored; not only did they have numerous practical applications, but familiarity with arithmetic was essential to the allegorical interpretation of the numbers found in the Old and New Testaments. The Didascalicon de studio legend: of Hugh of St Victor (c.1096-1141) describes a comprehensive educational programme that neglects none of the branches of human knowledge, not even the scientie (artes) mechanice, either excluded or merely mentioned in passing by later authors. The value of the trivium and quadrivium for the acquisition of wisdom was obvious to Hugh from their very names: ‘from this the trivium and the quadrivium take their names, inasmuch as by so many paths the alert mind arrives at the secrets of wisdonY.* Hugh’s allegorical De vanitate mundi, a dialogue between an omniscient teacher-guide and a curious questioner, depicts an idealized classroom, in which groups of eager students of all ages labour simultaneously at mastering one or another of the liberal arts. ‘Those applying themselves to the study of music sit in one '© Stephen C. Jaeger, The Envy of Angels: Cathedral Schools and Social Ideals in Medieval Europe, 950-1200 (Philadelphia, 1994). A readable survey is Pierre Riché and Jacques Verger, Des nains sur des épaules de géants: Maîtres et élèves au Moyen Age (Paris, 2006), 172-308. See also Stephen C. Ferruolo, The Origins of the University: The Schools of Paris and their Critics, 1100-1215 (Stanford, Calif., 1985), 11-44. 7 Des Adelard von Bath: Traktat De eodem et diverso, ed. Hans Willner (Beiträge zur Geschichte der Philosophie des Mittlealters, Texte und Untersuchungen, 4/1; Münsterin Westf., 1903). 8 Gillian R. Evans, ‘The Uncompleted Heptateuchon of Thierry of Chartres’, History of Universities, 3 (1983), 1-13; Peter Dronke, “Thierry of Chartres’, in id. (ed), A History of Twelfth-Century Western Philosophy (Cambridge, 1988), 358-85. 19 Metalogicon, ed. J. B. Hall (Corpus Christianorum Continuatio Medievalis, 98; Turnhout, 1991). 20 Hugh of St Victor, Didascalicon de studio legendi, ed. Charles Henry Buttimer (The Catholic University of America Studiesin Medieval and Renaissance Latin, 10; Washington, DC, 1939). ‘Hinc trivium et quadrivium nomen accepit, eo quod his, quasi quibusdam viis, vivax animus ad secreta sophiae introeat’; ibid. 53 (3.7); Daniel F. Blackwell, “The Artes liberales as Remedies: Their Order of Study in Hugh of St Victor’s Didascalicon, Theologische Zeitschrift, 45 (1989), 115-24.

corner of the room with a monochord. Significantly, they are picking out intervals and melodies, not studying proportion, as one might expect of diligent quadrivial students.” Quadrivial music was a speculative discipline, not a method of elementary instructionin singing intervals. One of the voices raised in defence of the traditional educational corpus was that of Alexander Nequam (also Neckam, 1157-1217), who lamented the obsession of contemporary schoolmen with dialectic to the neglect of the broader educational values embodied in the liberal arts. He claimed that although Italy had already ‘sold out’ to the study of civil law, ‘the heavenly scriptures and the liberal arts persuade the city of Paris that they are to be preferred to other things’, or such was his optimistic hope. In Sacerdos ad altare Nequam listed the books that should be studied by‘a scholar to be educatedin the liberal arts’ (presumably at Paris, where he taught the artes)2* Included are not only the essential texts on grammar (Donatus, Priscian), but also literary works of pagan authors: Ovid, Sallust, Livy, Seneca, Cicero, etc. Boethius’ Arıthmetica and Musica (followed by ‘axiomata musice’) are naturally among the required texts. Alas, Nequam’s statement about Parisian commitment to the liberal arts was no more than wishful thinking. By the end of the twelfth century the liberal arts were already far along in surrendering their central place in higher studies. The trivium and the quadrivium were included in classifications of knowledge (divisio scientiarum), documents of varied scope and comprehensiveness produced from the middle of the twelfth until the end of the thirteenth century. These systematizations of all branches of human knowledge were not necessarily prescriptive of the programme of university study.” Musica had to be includedin the classifications because it formed part of the quadrivium, reinterpreted as the second of the three degrees of abstraction: (1) bodies that cannot be separated from matter and motion either in the intellect or in reality (natural philosophy); (2) forms that can be abstracted from matter but are not entirely separate from it (mathematics); and (3) beings entirely separate from matter and motion (metaphysics, theology) Its secure placein the classifications did not translate into a regular place in the university classroom. The schools of Paris embarked on a new direction in the first half of the twelfth century, thanks in part to the brilliant Pierre Abelard (1079-1142). After studying at Tours under the tutelage of Rocelin (c.1050-1122), Abelard went to Paris and entered 22 ‘Magna est multitudo; diversas ibi aetates hominum conspico: pueros, adolescentes, juvenes, senes; diversa quoque studia.... Alii tensum in ligno nervum percutientes diversorum sonorum melodias proferunt’; De vanitate mundi et rerum transeuntium usu, in Patrologiae cursus completus: Series latina, ed. J.-P. Migne, 176:709. For this reference I am indebted to Urban T. Holmes, Jr., “Transitions in European Education’, in Marshall Clagett et al. (eds), TwelfthCentury Europe and the Foundations of Modern Society: Proceedings of a Symposium . . . November 12-14, 1957 (Madison Wis., 1966), 15-38 at 22. 23 “Civilis juris peritiam vendicat sibi Italia; sed caelestis scriptura et liberales artes civitatem Parisiensem caeteris [studiis] praeferendam esse convincunt’; Alexandri Neckam De naturis rerum libri duo with the Poem of the Same Author, De laudibus divinae sapientiae, ed. Thomas Wright (Rerum Brittanicarum Medii Aevi Scriptores, 34; London, 1863), 311; the artes are treated in De natura rerum and its verse paraphrase, Laus sapientie divine 10.37-166. See Richard W. Hunt, in Margaret T. Gibson (ed), The Schools and the Cloister: The Life and Writings of Alexander Nequam (1157-1217) (Oxford, 1984), 28-30, 33-5. Nequam did not oppose the study of dialectic: he recommended all the texts of the ‘old logic’. 24 «colaris liberalibus educandus artibus’. The ‘bibliography’ section of Sacerdos ad altare is edited in Charles Homer Haskins, Studies in the History of Mediaeval Science (Cambridge, Mass., 1924), 356—76, esp. 372-6. 2° Gordon Leff, Paris and Oxford Universities in the Thirteenth and Fourteenth Centuries (New York, 1968), 116-60, 181-4; Jacques Verger, ‘The First French Universities and the Institutionalization of Learning: Faculties, Curricula, Degrees’, in „john Van Engen (ed.), Learning Institutionalized: Teaching in the Medieval University (Notre Dame, Ind., 2000), 5-19. ° Joseph Dyer, ‘The Place of Musica in Medieval Classifications of Knowledge’, Journal of Musicology, 24 (2007),

the class of William of Champeaux, scholasticus of the cathedral school and a famous dialectician. William was unwilling to countenance his disciple as a rival, so Abelard was forced to teach outside the city, first at Melun, then at Corbeil. Abelard returned in 1108, by which time William had established a foundation of canons regular at St-Victor, where he continued his teaching activities. Abelard founded his own school on Mont Ste-Geneviève, safely outside episcopal jurisdiction.” His teaching stressed logical argument and the weighing (though not necessarily resolution) of contrarieties, a point made in the title of his celebrated Sic et non.°* He established the study of logic as the academic discipline par excellence at Paris—a step that, along with the acquisition of the complete Aristotelian corpus beginning in the latter half of the twelfth century, was to have a momentous impact on the instructional programme of the University of Paris and other universities founded on its model. This road led inevitably to the marginalization of the liberal arts at the University of Paris. THE UNIVERSITY OF PARIS AND ITS CURRICULUM Some details about the curriculum at the thirteenth-century University of Paris can be extracted from university statutes that regulated the customary academic exercises: lecture, dispute, and examination.” Unlike the Parisian schools of the previous century, the new university strove to standardize its curriculum, regulate examinations, and dictate conditions for the award of degrees. By the middle of the thirteenth century (and probably before) the curriculum had taken on a set of emphases radically different from the traditional programme of studies based on the liberal arts. The standard quadrivial texts were overwhelmed by a renewed interest in and a more sophisticated appreciation for the logica vetus (Aristotle’s Categories and Perihermeneias, Porphyry’s /sagoge—itself an introduction to the Categories—Cicero’s Topics, and Boethius’ original works on logic, his translations of Aristotle, and commentaries on Aristotelian texts). To this corpus was soon added the challenging logica nova—newly translated or hitherto underappreciated works of Aristotle—the Posterior Analytics, Topics, and Sophistical Refutations, together with the Liber sex principiorum of Gilbert de la Porrée (then attributed to Aristotle). Eventually the entire corpus of Aristotle’s works on natural science began to be read and taught at the University of Paris. There was simply no time to pursue the old-fashioned liberal arts, reduced mainly to a propaedeutic role on a level lower than heretofore.” Whereas the artes had earlier been ordained to the study of the sacra pagina and theology, they now prepared academically *” For an excellent survey of the intellectual dynamism of 12th-c. Paris see Helmut G. Walther, ‘St. Victor und die Schulen in Paris vor der Entstehung der Universitat’, in Martin Kintzinger et al. (eds), Schule und Schüler im Mittelalter: Beiträge zur europäischen Bildungsgeschichte des 9. bis 15. Jahrhunderts (Beiheft zum Archiv für Kulturgeschichte, 42; Cologne, Weimar, and Vienna, 1996), 53-74. 28 Sic et non, ed. Blanche B. Boyer and Richard McKeon (Chicago, 1976-7). “2 See Rashdall, The Universities of Europe in the Middle Ages, i. 439-71; Charles Homer Haskins, The Rise of the Universities (Providence, RI, 1923; repr. 1957); Stephan d’Irsay, Histoire des universités françaises et étrangères des origines à nos jours, 2 vols. (Paris, 1933-5); Alan B. Cobban, The Medieval Universities: Their Development and Organization (London, 1975), 75-95; Hilde de Ridder-Symoens (ed), A History of the University in Europe, 1: Universities in the Middle Ages (Cambridge, 1992); Lowrie J. Daly, The Medieval University, 1200-1400 (New York, 1961); Olaf Pedersen, The First Universities: Studium generale and the Origins of University Education in Europe, trans. Richard North (Cambridge, 1997), esp. 271-301; Pearl Kibre and Nancy G. Sirasi, “The Institutional Setting: The Universities’, in David C. Lindberg (ed), Science in the Middle Ages (Chicago, 1978), 120-44. 3% For lists of the texts with commentary see Palémon Glorieux, La Faculté des arts et ses maîtres au XIII siècle (Etudes de philosophie médiévale, 59: Paris, 1971), 13-58, and Philippe Delhaye, ‘La Place des arts libéraux dans les programmes scolaires du XII” siècle’, in Arts libéraux et philosophie au moyen áge, 161—73.

talented students for philosophia, a course of studies based primarily on the works of Aristotle. The earliest reference to the content and organization of the university curriculum at Paris occurs in a famous letter of the papal legate Cardinal Robert de Courçon addressed in 1215 to ‘universis magistris et scholaribus Parisiensibus’.” In obedience to a papal mandate, the cardinal enunciated a series of administrative and curricular guidelines—more of the former than the latter. Since the situation prevailing at the new university when the letter was written is unknown, the curricular provisions are not easy to interpret. Probably whatever did not receive specific attention simply maintained its status.” Courcon’s letter is thought to represent not an unwelcome intervention but a consensus between the masters and the cardinal, who had been one of their number before Pope Innocent III elevated him to the cardinalate three years earlier. The letter prescribes that the logical works of Aristotle—both the old and the new logic, as well as the grammar of Priscian, or at least the last two books (Priscianus minor)” are to be the subject of ‘ordinary’ lectures by the masters. With respect to academic activity on dies festivi, when no ordinary lectures or disputations were held, the cardinal decreed that ‘[The masters] shall not lecture on feast days, except on philosophers and rhetoric and the quadrivium [quadruvialia] and Barbarismus and ethics (if desired), and the fourth book of the Topics + No common thread seems to bind these dies festivi books together. They range from ‘philosophers’ (assumed to be Boethius’ Consolation of Philosophy and Plato's Timaeus) to rhetoric and grammar (the third book of Donatus’ Ars maior, known as ‘Barbarismus’ from its opening word), ethics (the first three books of the Nicomachean Ethics, the complete text of which did not become available until translated by Robert Grosseteste, c.1246/7), and Boethius’ De differentiis topicis. At least for the moment, quadruvialia continued to occupy a limited place in the curriculum, but this general reference does not prove that speculative musica was taught. The cardinal’s decree does not entirely clarify the distinction between the curriculum of ferial days and that of dies festivi. Did he mean to identify a category of topics (e.g. rhetoric, the quadrivium) on which lectures were not given on ordinary days but only on feast days, when lectures on the principal texts of the curriculum were suspended? If the works mentioned formed part of the normal curriculum, were they privileged, allowing them to be taught on dies festivi, when other lectures were suspended? Vague though the allusion to the quadrivium in the cardinal’s letter might be, it is the unique thirteenth-century reference to instruction in the quadrivium (or parts thereof) in the 31 On this much discussed statute see Stephen C. Ferruolo, ‘The Paris Statutes of 1215 Reconsidered’, History of Universities, 5 (1985), 1-14; id., The Origins of the University, 279-315. It may be noted in passing that the cardinal has achieved some musical notoriety for his strictures on magistri organici. He was willing to tolerate their music in church, provided that they avoided annoying ‘scurriles notule’ (minstrelish little notes), a comment made primarily as a churchman not as a scholar. I am indebted for this reference (and the translation of the phrase) to Christopher Page, The Owl and the Nightingale, 145-6. The phrasing ‘duos Priscianos vel alterum ad minus’ implies that Priscianus minor, books 17 and 18 of the grammar, would suffice. Books 1-16 on grammatical forms (morphology) were considered a unit and known as Priscianus mator. ‘Non legant [magistri] in festivis diebus nisi philosophos et rhetoricas et quadruvialia et barbarismum et ethicam, si placet, et quartum topichorum’; Chartularium Universitatis Parisiensis (hereafter CUP), ed. Heinrich Denifle and Emile Chatelain, 4 vols. (Paris, 1889-97), i. 78-9 (no. 20). Key documents from the CUP are translated in Lynn Thorndike, University Records and Life in the Middle Ages (New York, 1944). The books on rhetoric were Cicero's De inventione and the pseudo-Ciceronian Rhetorica ad Herennium. The ‘topics’ refers to Boethius De differentus topicis, a rhetorical work, not the Topics of Aristotle, part of the ‘logica nova’.

TABLE 1. Statute (1252) of the English Nation of the University of Paris on lecture requirements for the award of the baccalaureate degree Work Ordinaria Cursoria Aristotle: Predicamenta, 2 times l time 1 time 1 time l time ‘or at least cursorie’ Aristotle: Topica, Sophistici elenchi 2 times l time at least (or 3 times Aristotle: Prior Analytics l time l time (‘vel sit in audiendo”) Aristotle: Posterior Analytics l time (‘complete’) — Priscian: Ars minor 2 times l time (‘at least’) Perihermenias Gilbert de la Porrée: Liber sex principiorum Boethius: De topicis differentis (books 1-3) and De divisionibus ordinarie) Donatus: Barbarismus | Priscian: Ars mator — l time Aristotle: De anima l time? (‘vel sit — in audiendo’) Source: Chartularium universitatis Parisiensis, i. 227-30; trans. Thorndike, University Records, 53-4. official documentation of the University of Paris. Apparently, at this early stage in the University’s history the traditional programme of instruction in the artes liberales had not yet been marginalized. A detailed regulation from 1245 on the permissible times of day and periods of the year for lectures says nothing about the topics of those lectures.” It hints, nevertheless, that the primary distinction was no longer between ferial days and feasts, but on the modality of the lecture—ordinary or cursive. (The distinction between ‘ordinary’ and ‘cursive’ lectures will be discussed below) The same distinction appears in a statute of 1252 applicable to students of the ‘English nation’ of the University of Paris that lists the grammatical and logical books required of candidates presenting themselves for the award of the baccalaureate and the licentia determinandi (see Table 1). Two of the 1215 ‘dies festivi books—Donatus’ Barbarismus and the fourth book of Boethius Topics—had apparently migrated to ordinary days and were no longer confined to feast days, as they might have been in 1215. Now, the prescribed texts are allocated a certain number of weeks determined according to dates of the temporal and sanctoral cycles of the ecclesiastical calendar. Neither the ‘philosophers’, nor rhetoric, nor the quadrivium is mentioned, a fact that cannot be surprising in a regulation that concerns principally the grammar and logic curricula. A student spent four or five years (‘per quinque annos vel quatuor ad minus’) attending lectures on the required texts, but the number of ‘times’ a text had to be heard seems to bear no relationship to its level of difficulty. It is inconceivable, for example, that one ‘time’ would have been sufficient to master the intricacies of the Posterior Analytics. The meaning of ‘time’ might be interpreted in the light of a statute of the Faculty of Arts published three years later. In 1255, in order to correct masters who were neglecting their duties by ‘hurrying to finish their lectures sooner than the length 35 CUP i. 178-9 (no. 137).

and difficulty of the text permits’, very precise guidelines were established, not only about the content of the curriculum but also about the period of time that had to be devoted to each of the obligatory texts.” The same statute confirms, incidentally, that the entire Aristotelian corpus of natural science had been incorporated into the teaching programme of the University. In addition to the works cited in Table 1 this now includes the Physics of Aristotle, Metaphysics, and De animalibus;...De celo et mundo, the first book of Meteorology with the fourth; ... De anima; ... De generatione; De causis in seven weeks; De sensu et sensato in six weeks; De sompno et vigilia in five weeks; De plantis* in five weeks; De memoria et reminiscentia in two weeks; De differentia spiritus et animae”” in two weeks; De morte et vita in one week.” Music and the other quadrivial disciplines are conspicuous by their absence from this exceptionally detailed description of the programme of instruction in force at the University of Paris in the middle of the thirteenth century. The breadth of Aristotelian natural science had overwhelmed the quadrivium, a cluster of disciplines based on number, not on the observation of phenomena characteristic of Aristotelian natural science. No more is heard of mathematics in official statutes of the University until the year 1366, 150 years after the letter of Robert de Courçon. Two cardinals resident at Avignon (in consultation with the chancellor and several masters of the University) decreed that scholars at Paris were obligated to attend lectures on ‘some mathematical books’ (‘aliquos libros mathematicos audiverit’)* This vague reference to a mathematics requirement occurs almost as an afterthought at the end of a long list of important works of Aristotle on logic and natural science that had been the foundation of the university curriculum for more than a century. The 1366 statute does not say, by any means, that all (or which) of the quadrivial disciplines were obligatory; much less does it give any hint as to the intensity of study required. A slightly earlier statute from Ste-Genevieve (c.1350) required students of that college to hear ‘at least a hundred lectures on mathematics’ (‘centum lectiones de mathematicas ad minus’), but a gloss in one of the % ‘Noverint universi quod nos omnes et singuli magistri artium de communi assensu nostro nullo contradicente propter novum et inestimabile periculum quod in facultate nostra imminebat, magistris aliquibus lectiones suas terminare festinantibus, antequam librorum quantitas et difficultas requireret’; CUP i. 277-8 (no. 246); trans. Thorndike, University Records, 64. Lectures on the ‘old logic” began on 1 Oct. and finished on the feast of the Annunciation (25 Mar). The same length of time was allotted to Priscian (maior and minor), and Aristotle’s Topics, Sophistici Elenchi, and Posterior Analytics. | 37 Adriaan Pattin, Le ‘Liber de causis’: Édition établie à l'aide de 90 manuscrits avec introduction et notes (Leuven, 1966); see also Jill Kraye et al. (eds), Pseudo-Aristotle in the Middle Ages: The Theology and Other Texts (London, 1986). Thomas Aquinas seems to have been the first to recognize De causis as dependent on the Elementatio theologica of Proclus (c.410-85), as transmitted through a work in Arabic by the Jewish scholar David (Ibn Daoud/Avendauth). By the Augustan-age author Nicholas of Damascus; see Nicolaus Damascenus De plantis: Five Translations, ed. Hendrik J. Drossaart Lulofs and Emilie L. J. Poortman (Aristoteles Semitico-Latinus, Verhandelingen der Koninklijke Nederlandse Akademie van Wetenschappen afd. Letterkunde, nieuwe reeks, deel 139; Amsterdam, Oxford, and New York, 1989), 75-95 (Latin translation). 39 Attributed to Costa ben Luca; for the Latin text see De differentia animae et spiritus liber translatus a Johanne Hispalensi, ed. Carl Sigmund Barach (Bibliotheca Philosophorum Mediae Aetatis 2; Innsbruck, 1878), 120-39. # CUP i. 278 (no. 246); Thorndike, University Records, 53-4. # CUP iii. 145 (no. 1319), Thorndike, University Records, 246; this provision was repeated in the 1452 reform statute of Cardinal Guillaume d’Estouteville (CUP iv. 729 (no. 2690)). For the probable list of works see Jacob H. J. Schneider, ‘Wissenschaftseinteilung und institutionelle Folgen‘, in Maarten Hoenen et al. (eds.), Philosophy and Learning: Universities in the Middle Ages (Education and Society in the Middle Ages and Renaissance, 6; Leiden 1995), 63-121 at 104.

manuscripts noted that this could be interpreted to mean that a single subject would suffice.*” Musica was probably not the ‘mathematical of choice. Economic considerations played an important (perhaps decisive) part in what masters were inclined to teach. Since students at the University of Paris paid the master directly for their instruction, his income depended on the number of students he could attract. Masters, typically young men in their early twenties without comfortable benefices to support them, might not have considered lecturing on De institutione musica a preferable option, when a higher income could be earned by giving courses on the vast array of required Aristotelian texts, whose difficulty required more than a single traversal. Many students attended university in the hope that a few years of advanced education would improve their career prospects. Individual intellectual curiosity aside, how many would have considered subtle command of the proportions of musica speculativa a step towards their career goals? It is difficult to imagine that the conventional medieval music treatises would have ever been deemed suitable to the goals of the thirteenth-century university. Almost all of them, whether they treat chant or polyphonic music, are oriented to practical ends in a manner that was foreign to the speculative orientation of the university curriculum (ethics alone excepted), the goal of which was knowledge or wisdom.” It has been suggested that the collection of music theory treatises assembled by Jerome of Moravia (Moray?) may have been a collection of ‘university texts’, a conclusion based mainly on the fact that the sole manuscript source (Paris, Bibliotheque nationale de France, lat. 16663; dated 1272-4) is divided into pecie.'* The term pecia was applied to a segment (two to six bifolios) of a complete work that was rented out to students by university stationers for copying.’ There is, however, no reason to assume that all pecia manuscripts were exclusively or necessarily texts related directly to university teaching. A study of two stationer’s lists (1274/5 and after 1304) by Olga Weijers led her to conclude that ‘among the manuscripts produced as pecie, very few come from the Faculty of Arts’. Impecunious pre-baccalaureate students were not the only clientele served by the stationers. Titles in the fields of theology and law predominate in these *2 “Istud per facultatem sic est interpretatum quod sufficit audivisse unum librum totalem mathematice, sicut tractatum De Spera, et alium librum actu audire cum spe audiendi usque ad finem sine fraude’; CUP ii. 678-9 (App. 14). This was given classic expression by Albert the Great: ‘finis autem omnis speculationis est scire et veritas, et praxis omnis finis est opus’; Metaphysicorum Libri XIII, in B. Alberti Magni Ratisbonensis episcopi, ordinis Praedicatorum, Opera omnia, ed. Auguste Borgnet, 38 vols. (Paris, 1890-95), vi. 31. Hieronymus de Moravia, O.P : Tractatus de Musica, ed. Simon Cserba (Freiburger Studien zur Musikwissenschaft 2; Regensburg, 1935), p. lxxxii. The collection is attributed to Jerome (‘Musica fratris Jeronimi’) in the sole manuscript and in the l4th-c. catalogue of the library of the Sorbonne. According to G. Vuillemin-Diem the manuscript consists “ausnahmlos aus Binionen (24 Lagen)‘, as one would expect of a university exemplar; see Hentschel, Sinnlichkeit und Vernunft, 276-9 (where this opinion is quoted). Identifying markers include the number of the pecia in the upper margin and the presence of ‘corrigitur’ in the lower margin. On the pecia, see Jean Destrez, La Pecia dans les manuscrits universitaires du XIIT et du XIV” siècle (Paris, 1935); G. Fink-Errera, ‘Une institution du monde médiéval: La “pecia”” Revue philosophique de Louvain, 60 (1962), 184-243; Graham Pollard, “The Pecia System in the Medieval Universities’, in Malcolm B. Parkes and Andrew G. Watson (eds), Medieval Scribes, Manuscripts, and Libraries: Essays Presented to N. R. Ker (London, 1978), 145-61. For a list of exemplaria, see Marie-Dominique Chenu, ‘Exemplaria universitaires des xm° et x1v° siècles’, Scriptorium, 7 (1953), 68-80. A fundamental study in an important collection of essays on this subject is Richard H. and Mary A. Rouse, “The Book Trade at the University of Paris, ca. 1250-ca. 1350’, in Louis J. Bataillon, Bertrand G. Guyot, and Richard H. Rouse (eds), La Production du livre universitaire au Moyen Age (Paris, 1988), 41-114. ‘parmi les manuscrits produits par pecte, très peu émanent de la Faculté des Arts’; Olga Weijers, T'Oral et l’écrit dans les universités médiévales’, in ead., Le Maniement du savoir: Pratiques intellectuelles à l’époque des premières universités (XTIT-XIV" siècles) (Studia Artistarum Subsidia, 3; Turnhout, 1996), 145-55, esp. Ill. 10 (Vatican City, Bibl. Apost. Vat., Reg. lat. 406, fo. 64”). Similar rental schemes for university textbooks have recently made a comeback in the United States.

lists, an indication that stationers offered a varied selection of texts aimed at nonstudent professionals who could afford to have the desired texts copied. As it happens, the earliest university stationers to have plied the manuscript rental trade at Paris carried on their business next door to the Dominican convent of St-Jacques. where Jerome resided.*’ They may have made his compendium of music treatises available at their shop for all interested parties, not just the student trade. Under the title ‘Musica fratris Jeronimr, the manuscript became one of the catenati in the library of the Collége de Sorbonne, where it arrivedin 1306, and a recent examination has led to the conclusion that it was indeed consulted.*® In sum, the fact that Jerome’s collection of music treatises is divided into pecie is not relevant to the question of the teaching of music at the University of Paris. If music had been regularly taught at the University of Parisin the thirteenth century, one might expect (assuming a normal survival rate) at least a modest rise in the number of surviving manuscripts of De inshtutione musica, the canonical quadrivial text on the subject. The needs of students to have copies of the authorized texts, however crudely copied, caused a multiplication of manuscript copies of the logical and scientific works of Aristotle. Most of these ad hoc student copies have perished, but the number of surviving manuscripts of the required texts confirms their unique position in the curriculum. In the case of music the reverse situation prevails. A chart published by Michel Huglo indicates that the number of manuscript copies of Boethius, not to mention Macrobius and Calcidius, falls off considerably in 1 the thirteenth century. The number of extant sources of De instituttone musica declines from thirty-sevenin the twelfth century to only twenty-one in the thirteenth. The decrease in the number of surviving manuscripts is quite consistent with the absence of music in the thirteenthcentury university curriculum. Both Michael Bernhard and Max Haas drew attention to the diminution in the number of Boethius manuscripts, glossed or not, beginning in the later twelfth and continuing into the thirteenth century, the very time that saw the establishment of the universities. Bernhard observed that ‘it seems almost as if the glossing tradition disappears with the rise of the universities “—not quite what one would expect, were Boethius an official (and hence frequently copied and studied) university text. THE ORDINARY AND THE CURSORY LECTURE The principal mode of medieval university teaching was the lecture on an authoritative text established by custom and confirmed by official statute. ‘The lecture took two principal forms: the lectio ordinaria, which belonged by right to the master, and the lectio cursoria, usually assigned to a bachelor but occasionally delivered by a master. A few sources also mention a third type, the ‘extraordinary’ lecture, a term whose *7 Richard and Mary Rouse, “The Book Trade’, 56-64, 84-5. *8 Hentschel, Sinnlichkeit und Vernunft, 278-9 (reporting the new evaluation of the manuscript by Gudrun Vuillemin Diem). # Michel Huglo, ‘The Study of Ancient Sources of Music Theory in the Medieval University’, in Barbera (ed), Music Theory and its Sources, 150-72 at 167. °° Michael Bernhard, ‘Boethiusim mittelalterlichen Schulunterricht’, in Martin Kintzinger et al. (eds), Schule und Schülerim Mittelalter: Beiträge zur europäischen Bildungsgeschichte des 9. bis 15. Jahrhunderts (Cologne, 1996), 11-27 at 19; see also Max Haas, ‘Studien zur mittelalterlichen Musiklehre I: Eine Ubersicht tiber die Musiklehre im Kontext der Philosophie des 13. und frühen 14. Jahrhunderts’, in Hans Oesch and Wulf Arlt (eds), Aktuelle Fragen der musikbezogenen Mittelalterforschung (Forum Musicologicum, 3; Winterthur, 1982), 323-456 at 352.

several meanings will be examined below.” Each type had its own characteristics and function, based on the time of day when it was delivered, the academic status of the lecturer, or the method of delivery. The ordinary lecture was the venue for the master’s exposition of an authoritative text.” Following a basic explanation, the master raised difficulties and introduced objections that might be made against his interpretation: ‘dubitatur de hoc quod’ or ‘queritur postea’. His response, introduced by phrases like ‘sed dicendum quod’ or ‘sed intellige quod’, reaffirmed his interpretation. A cursory lecture covered exactly the same texts as the ordinary lecture, but without the latter’s interpretative elements. ‘The lecturer, normally a bachelor, paused only for brief definitions or explanations of difficult or obscure points. The desirable balance between ordinary and cursory lectures was the subject of the 1252 statute of the English nation discussed earlier (see above, Table 1), which specified not only the required texts but also the number of times each had to be ‘heard’ according to the two different lecture formats. To lecture cursorie could also signify a rapid reading of the text (cf. the English cognate ‘cursory’). An Oxford statute dated before 1380 entitled ‘De diebus festivis in quibus magistri festine legent’ identifies days on which cursory lectures were given by the abbreviation ‘le. fe.’ (‘legibiles festinanter”)4 A third type of lecture mentioned in the university statutes of Paris, Oxford, and Cambridge, the lecho extraordinaria, has given rise to a number of interpretations, understandably so, given the various ways in which the term was employed.”* Did ‘extraordinary’ signify a lecture on a text (e.g. Boethius’ Musica) that stood outside the standard university curriculum, and thus ‘a mechanism whereby new works or older texts that had never been included in the official syllabus could be brought to the attention of students?” Such a possibility cannot be excluded, but neither is it confirmed by any of the university documents that employ this term. Malcolm Hackett, in his definitive study of the Cambridge statutes, concluded that ‘in the final analysis, it was the mode of lecturing that really distinguished an extraordinary from an ordinary lecture”. This ‘mode’ depended either on the academic status of the person delivering the lecture or a deviation from the customary horarium governing the times of ordinary and cursory lectures. Ordinary lectures were delivered by regent masters in the early hours of the morning. If a master lectured apart from this time, even in the ‘ordinary’ manner with commentary and resolution of objections, such a lecture was deemed ‘extraordinary’. According to a 1309 statute from the University 9! James A. Weisheipl, ‘The Parisian Faculty of Arts in Mid-Thirteenth Century’, American Benedictine Review, 25 (1974), 200-17; Malcolm B. Hackett, The Original Statutes of Cambridge University (Cambridge, 1970), 133-42; Bruno Laurioux and Laurence Moulinier, Education et cultures dans l'Occident chrétien (Collection ‘Prépa Capes-Agrégation’; Paris, 1998), 81-8; Claude Lafleur, Quatre introductions à la philosophie au XIIF siècle: Textes critiques et étude historique (Montréal and Paris, 1988), 141-61; Alfonso Maierù, ‘Les Cours: Lectio et lectio cursoria (d’après les statuts de Paris et d'Oxford)’, in L'Enseignement des disciplines à la Faculté des arts (Paris et Oxford, XIII-XIV" siècles), 373-91; Daly, The Medieval University, 151-6. 52 Olga Weijers, Le Maniement de savoir, 39-59 (‘Les Cours: méthodes et pratiques’). 9 Statuta Antiqua Universitatis [Statuta Antigua Vniversitatis] Oxoniensis, ed. Strickland Gibson (Oxford, 1931), 56 and Ixxxi. Though Robert de Courçon had distinguished between the logical works read ‘ordinarie et non ad cursum' on dies legibiles, it is not clear that the diesfestivi lectures were thereby intended to be cursory (CUP i. 78). 5% Mariken Teeuwen, The Vocabulary of Intellectual Life in the Middle Ages (Turnhout, 2003), 304-6 (‘ordinarius/-ie, extraordinarius/-ie’ ). 5 Alan B. Cobban, English University Life in the Middle Ages (Columbus, Ohio, 1999), 173. 56 Hackett, The Original Statutes, 135.

of Toulouse, lectures on physica realis delivered by non-regent masters or by ‘bachelors so designated by the regent masters’ were considered ‘extraordinary’.” A Parisian statute (1255) cautioned masters not to turn ordinary lectures into ‘extraordinary’ ones by rushing through the final portions of a required text in order to finish it within the assigned period, or (worse still) shirking their obligation to elucidate the text Another Parisian statute dated between 1270 and 1274 reiterated the norm in a way that equated extraordinary with cursory: ‘no master ought to finish his ordinary lectures cursorie’.°? Since it is inconceivable that a master would change from one text to anotherin the middle of a course, the regulation must apply to the manner of lecturing, not to the text on which the lecture was given.” Thus it cannot be assumed that the extraordinary lecture was a vehicle for the introduction of a parallel university curriculum, one that perhaps included speculative musica. Another objection to the presence of music in the Parisian curriculum arises from a 1275 statute that required bachelors who wished to lecture cursorie on any book to have previously ‘heard’ a lecture (presumably an ordinary one) on that book at Paris. If the bachelor ‚game from another studium generale, two lecture courses on the book were required.” One cannot guess how strictly this regulation was enforced, but unless there were frequent ordinary lectures on music at Paris—or even more frequently elsewhere—there could be no cursory ones either (at least by bachelors)—a dilemma epitomized by the phrase ‘catch 22’. Michel Huglo drew attention to the presence of the word ‘auditor’ in several music theory treatises, suggesting that this term might point, in the direction of the university as an intended venue for the texts in question.”Although “auditor” did gain currency during the era of the universities, often as a designation of a newer student stillin the listening” phase of his education, it had a long history of usage in a more general sense.” In the prologue to Ars cantus mensurabilis, Franco of Cologne (fl. mid to late 13th c) promised that he had formulated his teachingin such a way as to make it comprehensible to learners (‘auditorum facillimam apprehensionem)). ° Petrus Picardus (Ars mottetorum compilatio brevior, late 13th c.), acknowledging his indebtedness to the teaching of Franco and Johannes de Burgundia, observed that ‘novi auditores appreciated brevity; hence he provided only the basic information necessary for Ÿ “Item de physica reali legantur extraordinarie complete libri qui sequuntur per magistros regentes in dicto studio, seu per alios sufficentes magistros, seu bacalarios a magistris regentibus ad hoc deputatos’; Les Statuts et priviléges des universitésfrançaises depuis leurfondation jusqu’en 1789, ed. Marcel Fournier, 4 vols. (Paris, 1890-4), i. 465 (no. 542). ‘Insuper nulli liceat legere lectiones ordinarias plures duabus, nec eas extraordinarias facere, nec eas nisi hora ordinaria et in habitu ordinario legere CUPi. 278 (no. 246); Thorndike, University Records, 66. 39 CUPi. 518 (no. 455). 60 Cambridge University statutes forbade a lecturer to ‘convert an ordinary lecture into an extraordinary one or vice versa, unless he has previously received permission from the masters of his faculty’ (‘leccionem ordinariam in extraordinariam vel econverso nullus convertat, nisi a magistris sue facultatis prius licenciatus’); Hackett, The Original Statutes, 201. ©! CUP i. 531 (no. 461). 62 Michel Huglo, ‘L’Enseignement de la musique dans les universités médiévales’, in Pompilio et al. (eds), Atti del XIV congresso della Società Internazionale di Musicologia, i. 30-7 at 33, repr. in id., La Theorie de la musique antique et médiévale (Variorum Collected Studies Series, 822; Aldershot, 2005, no. XIII). es Olga Weijers, Terminologie des universités au XIII" siècle (Lessico intellettuale europeo, 39; Rome, 1987), 283—7; see also Teeuwen, The Vocabulary, 224-5 (Although both auditor and audire were part of the vocabulary of the schools before the period of the universities (that is, before the thirteenth century), they became widely used only in the context of the universities; ... auditor is then distinguished from the more advanced student [scolaris])’. 6% ‘Nec dicat aliquis nos hoc opus propter arrogantiam, vel forte propter propriam tantum commoditatem incepisse, sed vere propter evidentem necessitatem et auditorum facillimam apprehensionem necnon et omnium notatorum ipsius mensurabilis musicae perfectissimam instructionem’; Franco of Cologne, Ars cantus mensurabilis, ed. Gilbert Reaney and André Gilles (Corpus Scriptorum de Musica, 18; [Rome], 1974), 24.

‘ipsis novis auditoribus’.” The generic sense of the term occurs also in the De musica of Johannes de Grocheio, who cited the monochord and musical hand as a teaching tool suitable for ‘novi auditores et pueri. Though the question of the ‘audience’ to whom the music treatises of the Middle Ages were directed still awaits a comprehensive study, one can be very certain that they were not addressed to academics. ‘DE FORMA AND UNIVERSITY LECTURES Several texts known as ‘introductions to philosophy’ and other sources related to the university curriculum identify certain quadrivial books as being ‘de forma’. Eight of them can be associated with the University of Paris (an identification made explicit in the Divisio scientiarum of Arnoul de Provence); 1. Compendium of Barcelona (c.1230—40): ‘Boethius is the author of this science [music], and it consists of five books. The first two pertain to the truth of the science. In the following three it is a matter of rejecting the opinions of others. ... However, two books of this entire science are read, because in these two, as already noted, the author expounds the science of all those things that he intends.’°® 2. Accessus philosophorum (c.1230-40): Musica consists of five books, but only two 9 569 are “de forma”. 3. Arnoul de Provence, Diuisio scientiarum (c.1200): “There are five books of Musica (which Boethius treated), of which two are “de forma” at Paris.’” 4. Questiones mathematice (c.1250): ‘Of the five books of Musica two are “de forma”. % ‘Quoniam nonnulli, maxime novi auditores, compendiosa brevitate letantur, quatuor tantum capitula mensurabilis musice, que quidem sunt ipsis novis auditoribus necessaria, breviter enodabo; dictaque mea arti magistri Franconis de Colonia necnon et arbori magistri Johannis de Burgundia, quantumcumque potero, conformabo'; Petrus Picardus, Ars motettorum compilata breviter, ed. F. Alberto Gallo (Corpus Scriptorum de Musica, 15; [Rome], 1971), 16; see also Wolf Frobenius, ‘Der Musiktheoretiker Franco von Köln’, in Albert Zimmermann (ed), Der Kölner Universitat im Mittelalter: Geistige Wurzeln und sociale Wirklichkeit (Miscellanea Mediaevalia, 20; Berlin and New York, 1989), 344-56. °° ‘Quidam autem istam artem depingunt in superficie [of the monochord], et alii in undeviginti iuncturis manuum undeviginti dictiones cum suis litteris et syllabis figurant, ut facilius novi auditores et pueri comprehendant’; Johannes de Grocheo, De musica, ed. Ernst Rohloff, in Die Quellenhandschriften zum Musiktraktat des Johannes de Grocheio (Leipzig, 1967), 128 (102). Even earlier, the pseudo-Oddonic Dialogus de musica drew a comparison between the monochord and the elementary teaching of the alphabet; Scriptores ecclesiastici de musica sacra potissimum..., ed. Martin Gerbert, 3 vols. (St. Blaise, 1784), 1. 252. 7 The citations concerning the quadrivial books have been conveniently assembled and analysed in Claude Lafleur with Joanne Carrier, ‘La Réglementation “curriculaire” (“de forma”) dans les introductions à la philosophie et les guides de l’étudiant de la Faculté des arts de Paris au xm° siècle: Une mise en contexte’, in Claude Lafleur with Joanne Carrier (eds), L’Enseignement de la philosophie au XIII’ siècle: Autour du “Guide de l’étudiant’ du ms. Ripoll 109 (Studia Artistarum, 5; Turnhout, 1997), 521-48. I am indebted to Prof. Lafleur for providing me with a copy of this article and for many insights derived from his studies of 13th-c. intellectual history. The complete texts are edited in Lafleur, Quatre introductions; for summaries and outlines see ‘Les “Guides de l’étudiant” de la faculté des arts de l’Université de Paris au xım“ siècle”, in Hoenen et al. (eds), Philosophy and Learning, 137-99. 6° “Huiusmodi autem scientie [musice] Boetius est auctor. Et dividitur in .V. libros partiales. In primis duobus agitur de eis que pertinent ad scientie ueritatem. In tribus sequentibus agitur de ipsis reprobando opiniones aliorum. ... Leguntur autem duo libri huius totalis scientie, quia in istis duobus, ut dictum est, manifestat auctor omnium illorum scientiam de quibus intendit’ (Barcelona, Archive of the Crown of Aragon, Ripoll 109, fo. 135"); Lafleur and Carrier, Le ‘Guide de l’etudiant’d’un maître anonyme de la Faculté des arts de Paris au XIIT siècle: Edition critique provisoire du ms. Arxiu de la Corona d “Aragó, Ripoll 109, ff. 134ra-158va (Publications du Laboratoire de philosophie ancienne et médiévale de la Faculté de philosophie de l’Université de Laval, 1; Québec, 1992), $51. °9 “Sunt autem in Musica V. libri partiales set de forma tantum duo’ Lafleur, Quatre introductions, 204 (431-2). 7 Sunt autem quinque libri Musice quam tractauit Boetius, quorum duo sunt de forma Parisius’; ibid. 328 (408-9). ” ‘5 sunt libri in Musica duo de forma’ (Paris, Bibliothèque nationale de France [hereafter BNF‘, lat. 16390, fo. 204”); Claude Lafleur with Joanne Carrier, “Les Questiones mathematice (mss. Paris BNF, lat. 16390 et 16617): Un compendium de la Faculté des arts de l’Université de Paris au xm° siècle. Edition provisoire du texte intégral”, Cahiers du Laboratoire de Philosophie ancienne et médiévale de la Faculté de philosophie de "Université Laval, 6 (Québec, 2003), $164.

5. Communia ‘Visitatio: “There are five books in Musica, of which the first two are “de forma”; the other three are not. 6. Johannes Dacus, Divisio scientie (c.1250): “Note that there are five books of the Musica which Boethius handed down, of which two are “de forma”. ” 7. Anonymous (c.1270): *[ Musica] consists of five books...of these five, two are “de forma”. 8. Raoul le Breton, Questiones mathematice (c.1300): “Whence there are four principal mathematicals....And therefore there are certain books ordered to geometry and arithmetic, and especially to arithmetic; some indeed to astrology and music. Yet many of these books ordained to these [four] are not “de forma”. ... Now, just as there are four principal mathematicals, accordingly there are several introductory [texts] ordered to these four, like Algorismus, Spera, and Compotus [works of Johannes de Sacrobosco], etc. ; whence Algorismus, Spera, and Compotus—these are “de forma”? All these passages agree (in language so similar that a connection must be assumed) that only the first two of the five books of Boethius’ De institutione musica pertain to the ‘de forma’ requirement. A similar specification was applied to geometry, of which only the first six (of fifteen) books of Euclid’s Elementa were considered ‘de forma’. Claude Lafleur explained the meaning of ‘de forma’ in these texts with reference to a parallel passage in the Compendium of Barcelona, a collection of potential examination questions associated with Paris. The Compendium says that Boethius’ Musica consists of five books, but that only ‘two books of this entire science are read’ (no. ]). Since ‘legere’ normally denoted an ordinary lecture, Lafleur argued that, in all other contexts, ‘de forma’ was the equivalent of ‘legere’, an equivalency that pointed to the existence of regular lectures on music and the other quadrivial books so designated. This conclusion needs to be balanced against the silence of the contemporary Parisian statutes and other relevant documentation regarding the quadrivium. Raoul le Breton (no. 8) distinguishes between the traditional quadrivial texts written ‘ab a[u]ctoribus auctenticis’ and various introductory handbooks of more recent origin.”” He seems to say that many of the former were no longer ‘de forma’. This distinction was reserved for popular introductory texts like those of Johannes de Sacrobosco (fl. 1230), Algorismus, De spera, and Compotus—manuals on arithmetic, basic astronomy, and time computation respectively: ‘ista sunt de forma’. ” “Quinque sunt libri in Musica, quorum duo primi sunt de forma, alii uero tres non’ (Paris, BNF, lat. 7392, fo. 79"); Lafleur and Carrier, ‘La Réglementation “curriculaire””, 536. 73 “Est etiam sciendum, quod quinque sint libri Musice, quos tradidit Boetius, quorum duo sunt de forma’; Johannis Daci Opera, ed. Alfred Otto, 2 vols. (Copenhagen, 1955), 30 (1. 6-8). % Que [Musica] dividitur in quinque libros partiales . . .istorum quinque duo sunt de forma; Christian Meyer, ‘Un abrégé universitaire des deux premiers livres du De institutione musica de Boéce’, Archives d'Histoire Doctrinale et Littéraire du Moyen Age, 65 (1998), 91-121 at 111. ‘Unde mathematice principales sunt quatuor.... Et ideo quidam sunt libri ordinati ad geometriam et arismeticam, et maxime ad arismeticam, quidam vero ad astrologiam et musicam. Verumptamen multi istorum librorum ad istos ordinatorum non sunt de forma. ... Modo sicut sunt quatuor mathematice principales, ita sunt aliqua introductoria ordinata ad istas quatuor, sicut algorismus, spera et compotus et cetera. Unde algorismus, spera et compotus, ista sunt de forma’; Olga Weijers, La ‘Disputatio’a la Faculté des arts de Paris (1200-1350 environ): Esquisse d’une typologie (Studia Artistarum, 2; Turnhout, 1995), 166; also Lafleur and Carrier, ‘La Réglementation “curriculaire””, 537. 76 Raoul le Breton (fl. 1290-1320), who enjoyed a reputation as an outstanding logician, composed a large number of questiones on the standard university texts: Priscian, Boethius (De differents topics), the logical works of Aristotle (Topics, Categories, Perihermeneias, Prior and Posterior Analytics, Topics, Sophistici elenchi), as well as De anima, Physics, and Parva mathematicalia. Jean-Luc Deuffic, ‘Un logicien renommé, proviseur de Sorbonne au XIV" siècle, Raoul le Breton de Ploudiry: Notes bio-bibliographiques’, Pecia, 1 (2002), 45-154 (with lists of all the questions).

At least one Parisian source makes a clear distinction between ‘de forma’ and ‘legere’. De communibus artium hberahum, a compilation designed to assist students preparing for examinations, distinguishes between several (unnamed) books on astronomy that were ‘de forma’ and the only one that actually had to be ‘read’: Sacroboscos De spera.” Among the disciplines listed by De communibus as de forma’ are arithmetic, geometry, and astronomy, but no mention is made of music.” In this case, ‘legere’ might have meant (exceptionally) individual study or lectures offered privately to interested parties ‘hors programme’. A list of books required to be studied for inception (admission to the master’s degree) at Oxford joins ‘forma’ and ‘legere’ in a single phrase: ‘all these books and all the others that are de forma” are rightly to be readin school according to the requirements of inception’.”Thereis, however, no mention of music, though Boethius’ Arithmetica and De sphera were required. This conjunction seems to confirm Lafleur’s hypothesis even as the De communibus disjunction seems to contradict it. Fourteenth- and fifteenth-century statutes of Oxford University (later than the Parisian material heretofore cited) employ ‘forma’ in two different meanings: as a required course of studies (a very common usage) or in the general sense of an accepted procedure of doing something. Several Oxford formae (in the first sense) are preserved on stray manuscript leaves. While there „Is 1 no mention of music, Boethius’ Arithmetica and Sacroboscos De spera were required.” The second meaning is exemplified by statutes dated 1407 and 1409 that describein elaborate detail the ‘forma’ to be observed py the university in approving a bachelor for the right to ‘determine the question.”The regulations cover all aspects of the event: both the responsibilities of the university masters and those of the candidate. A ‘REPORTATIO’ OF THE TEACHING OF JOHANNES DE GARLANDIA? Christian Meyer has argued that four versions of the Musica plana Johannis de Garlandia are reportationes of Garlandia’s teaching,” but none identifies itself as a reportatio of a university lecture, the context that might be assumed by Meyer’s use of the technical term ‘reportatio.*Meyer concluded that the text displays‘une certain rigueur scolastique’ without neglecting ‘une approche quadriviale’. The first reportatio declares its 77 “De ista scientia [astronomia] non legitur inter libros de forma nisi unus liber, scilicet De spera...’; Claude Lafleur with Joanne Carrier, Un instrument de révision destiné aux candidats à la licence de la Faculté des arts de Paris: le De communibus artium liberalium’ (vers 1250?) (Cahiers du Laboratoire de philosophie ancienne et médiévale de la Faculté de philosophie de l'Université de Laval, 3; Québec, 1993), §206. 78 Lafleur and Carrier, ‘La Réglementation “curriculaire , 935-7; for the complete text see Lafleur and Carrier, Un 399 instrument de révision. 7 ‘Omnes isti libri et omnes alii qui sunt de forma legantur in scolis et rite secundum exigenciam materie’; Statuta Antiqua, ed. Gibson, 34. ° The list (‘Forma illorum qui incepturi sunt in artibus /Ordinacio de forma audiendi libros’), preserved on a flyleafin a manuscript at Worcester Cathedral Library (F.73), is published in John Kestell Floyer (comp) and Sidney Graves Hamilton (ed. and rev, Catalogue of MSS preserved in the Chapter Library of Worcester Cathedral (Oxford, 1906), 36, 176-7. See also Rodney M. Thomson, A Descriptive Catalogue of the Medieval Manuscripts in Worcester Cathedral Library (Woodbridge, 2001), 46-7. Two other Oxford formae (Corpus Christi College, MS 117, fo. 30° and Merton College, MS 261) were published in Rashdall, The Universities of Europe (iii. 480-2); on the latter see Fredrick M. Powicke, The Medieval Books of Merton College (Oxford, 1931), 34. Statuta Antiqua, ed. Gibson, 199-204. 82 The treatises have been editedin Musica plana Johannis de Garlandia, ed. Christian Meyer (Collection d’Etudes Musicologiques, 91; Baden-Baden, 1998). 83 A: reportatio ranged from a student’s hastily scribbled notes on a lecture or disputation to a more or less accurate record taken down by a professional stenographer for later correction and emendation by the master. (Even todayin British and American courts of law the official record of the proceedings is made by a court ‘reporter’) On the meaning of the term reportatio see Teeuwen, The Vocabulary, 333-5, and the bibliography cited there.

allegiance to Boethius, but at the same time promises a ‘declaratio musice practice’. There follows immediately a divisto scientiarum, but such classifications appear in a great variety of contexts, and this one offers nothing new.* The second reportatio defines music as ‘the knowledge of how to sing correctly and the capability of doing so (‘veraciter canendi scientia et facile ad canendi perfectionem vis’), a description that could not apply exclusively to speculative musica. The third reportatıo presents itself as an ‘art of plainsong, which is called immeasurable, the theory of which has been transmitted to us by ancient philosophers’ (‘ars plane musice que immensurabilis dicitur, que theorice est nobis tradita ab antiquis philosophis’), thus presuming to place the mantle of philosophy over basic chant instruction. The same reportatio mentions the monochord, a very unlikely reference in a university text, as would be a reference to finger reckoning or the abacus in connection with speculative mathematics. While these four texts might indeed reflect the teaching of Johannes de Garlandia, that teaching did not take place within university precincts. In a broad sense, they might be called ‘reportationes”, but not properly evidence of university lectures on music. ‘QUESTIONES DE MUSICA There exists a small corpus (insofar as one can judge from what has been discovered so far) of sources called with varying degrees of probability ‘student questions’. They provide a hint about what thirteenth-century Parisian students were expected to know in order successfully to pass the examination leading to the baccalaureate and the concomitant licentia determinandi (the right during the following Lent to ‘determine the question’ in a formal academic dispute—normally a master’s privilege). ‘The collection of student examination questions known as De communibus artium liberalium concludes with the statement that ‘these are the ordinary things to which those seeking to be licensedin arts are required tto respond’ (‘haec sunt communia quibus tenentur respondere licentiandiin artibus’).°° Significantly, this collection contains but a single, generic question pertaining to music: whether its subzectum may be defined as ‘numerus relatus ad sonos’. Such a question about the subzectum of a branch of knowledge was important, since the unicity of the object studied was a prerequisite for its being considered a scientia.”’ It is hardly specific to music. The largest collection of student questions, the ‘Compendium of Barcelona’, is so called after the city where it now resides in the Archive of the Crown of Aragon. A nearly identical series of questions occurs in another manuscript, identified by its incipit as Primo queritur Both point unmistakably to Parisian university 84 See Dyer, ‘The Place of Musica’,passim. 85 Musica plana Johannis de Garlandia, ed. Meyer, 39. ‘Queritur utrum numerus relatus ad sonos sit subiectumin musica’; De communibus artium liberalium (BNF, lat. 16390, fos. 194-200"); Lafleur and Carrier, Un instrument de révision, 54 (8249-56) ” Robert Kilwardby concluded his discussion of every branch of knowledge with a definition of its subject. For example, the comprehensive subject of speculative philosophy is ‘all knowable nature, that is, God and all that he created’. Geometry has a narrower subject: ‘magnitude or continuous quantity, not infinite but limited, abstracted from natural matter’; De ortu scientiarum, 13 and 62, ed. Albert G. Judy (Auctores Britannici Medii Aevi, 4; London and Toronto, 1976), 13 and 30. 88 On the Compendium see Martin Grabmann, ‘Eine für Examinazwecke abgefasste Quaestionensammlung der Pariser Artistenfacultät aus der ersten Hälfte des 13. Jahrhunderts’, Revue néoscolastique de philosophie, 36 (1934), 211-29. A ‘provisional edition of Ripoll 109 is available in Lafleur and Carrier, Le ‘Guide de l'étudiant’ d'un maître anonyme de la faculté des arts à Paris au XIII" siècle. For an edition of the second source see Claude Lafleur with Joanne Carrier, ‘Le Recueil de questions “Primo queritur utrum philosophia”’, in Lafleur and Carrier, L’Enseignement de la philosophie au XIII siècle, 381-419. I would like to thank Prof. Lafleur for providing me with copies of these editions. They were previously

conditions c.1240. The questions and the suggested responses to them are of lesser significance than what they imply about the musical knowledge expected of students.” The ‘musical’ questions have little to do with music per se. Instead, they concern themselves with the classification of music among the branches of knowledge and with testing the student’s prowess in logic. Three of the music questions (1, 2, 5) challenge the student to defend in one way or another the independence of music as a scientia. Question 1 argues that musical proportion, having been already considered in the second book of Boethius’ Arithmetic, need not be treated separately: music is thus not an independent scientia. Question 2 would subalternate music to arithmetic—a solution not repugnant to all philosophers, but one that raises questions about whether or not music can be considered an independent scientia. Question 5 objects that, because mathematics is concerned with abstract matters (‘de rebus abstractis’), it cannot include music, which concerns limited number (‘de numero contracto’), that is, two finite numbers related to each other that exemplify a specific consonance or dissonance. On this basis (it is argued) music must be excluded from the speculative sciences. Questions 3, 4, and 6 demand some limited familiarity with the non-technical chapters of De institutione musica. Questions 3 and 6 associate musica humana, construed as vocal music, with sounding music (poetics and rhythm) and hence with natural science, not with speculative musica. Question 3 asks why musica humana (again vocal music) cannot be subsumed under the category of musica instrumentalis. Question 6, noting that sounds and melodies take place in time, asks why the musicus does not consider sound in the same manner as a natural scientist would, thus proposing to eject music from the quadrivium. The response to this question distinguishes between sounding music, which can fall into the domain of the natural scientist, and abstract proportion, which is the proper concern of the musicus. Question 4 brings up the problem that musica mundana cannot be heard. Since empirical investigation—the foundation of every scientia—is utterly impossible in the case of musica mundana, at least one of Boethius’ ‘musics’ must be eliminated. The suggested response to this question does not cast the existence of musica mundana completely into doubt, for eminent ‘philosophi’ (Pythagoras, Plato, Boethius) had affirmed its existence. It repeats the not uncommon explanation that humans cannot hear its dulcisona harmonia’ because of the enormous distance that separates earthbound creatures from the source of musica mundana.” After facing the challenge of these questions, the student might have greeted question 7, ‘whence derives the name “music”? (‘Unde dicatur musica’) with more thana little relief: etymological inquiry had been one of the staples of medieval knowledge since the time of Isidore. The final question of Primo queritur, ‘Quot sint symphonie in musica’, inquires about the number of musical consonances, a topic that in the Compendium of Barcelona forms part of the introduction. The proposed response paraphrases a section near the edited in Max Haas, ‘Studien zur mittelalterlichen Musiklehre I’, 323-456 at 354-9 (= ANOQM in the Thesaurus Musicarum Latinarum database). 8° These and other questions with their proposed responses will be analysed in greater detail in my “University Examinations and Questions on Music in Thirteenth-Century Paris, forthcoming in Studies in Musicfrom the University of Western Ontario (2009). “Mundana percipitur in sonoritate partium mundi et maxime corporum supercelestium: posuerunt enim philosophi quod dulcisona est armonia in corporibus superioribus, que forte non auditur a nobis propter nimiam distantiam inter nos et illa’; Compendium ($50). In the Physics (2.9) Aristotle scoffed at the whole notion of ‘celestial music’.

end of the second book of Boethius De institutione arithmetica (2.48)? It maintains that the diatessaron (4:3) 1s a proportion produced by a proportion between 6:3 and 6:2 (‘hec colligatur ex proportione que est inter sex et tria et sex et duo [the reading of Primo quentur]”). In the passage to which this makes reference Boethius gives the following illustration ‘of which the extreme terms are duplex, and another after it, of which the extremes are triple’:”” | | 3 6 —1&aO 2 | 6 I Boethius then explains that ‘six is the duplex of three in the first set, and six is the triple of two in the second set. If we put together the differences of these and compare them to each other, the epitrita proportion is assembled, from which resounds the symphony of the diatesseron’.”’ This conclusion confirms Boethius' earlier claim that the proportion of the diatessaron ‘which is the principal one...is found in harmonic medial proportions’. The difference between the two proportions thus results in a 4:3 proportion. The proportion of the diapente, correctly given as 6:4 or 3:2, is said by the Compendium to equal ten, a peculiar notion supported by an etymology that confuses the Greek preposition ‘dia’ (through, by means of, because of) with the Greek word for the number two (dyo): ‘the fifth is so called from dia, which is “two”, and “penta”, which is five, because it is two times five’, a curious conclusion not present in Primo queritur. (The student who parroted this answer before knowledgeable examiners would not have fared too well.) ‘The octave is correctly described as a duple proportion. A triple proportion (2:4:6) includes both octave (4:2) and fifth (6:4).°* While this response to the question of the number of symphonie seems to reflect a generally adequate comprehension of proportion—apart from the questionable etymology—one could imagine a simpler, more direct answer, or even one simply quoting De institutione musica. Practically speaking, none of the questions requires more than a superficial familiarity with Boethius’ Musica, which could have been picked up without serious study of the text. Far more useful for successfully passing this examination on ‘music’ would have been knowledge of the principles behind the thirteenth-century classifications of knowledge and a command of logical argument. ‘QUESTIONES DISPUTATE An academic exercise of only slightly lesser significance than the lecture was the academic dispute (‘determining the question’); it was an essential tool for sharpening 9! Ancius Manlius Severinus Boethius, De institutione arithmetica libri duo, ed. Gottfried Friedlein (Leipzig, 1867), 155-6 (2.48); De Arithmetica, ed. Heinrich Oosthout and Johann Schilling (Ancii Manlii Severini Boethii Opera, 2; Corpus Christianorum: Series Latina, 94A; Turnhout, 1999), 200-4. ° «Sint enim eiusmodi armonicae medietatis termini, quorum extremi dupli sint; et rursus alia huiusmodi dispositio, quorum extrema tripli; ed. Friedlein, 155; ed. Oosthout and Schilling, 200-1; trans. Michael Masi, Boethian Number Theory: A Translation of the De Institutione Arithmetica (Studies in Classical Antiquity, 6; Amsterdam, 1983), 177. % “Senarius igitur ad ternarium duplus est, idem autem senarius in alia dispositione ad binarium triplus. Horum igitur si differentias colligamus et ad se invicem comparemus, epitrita proportio colligetur, unde distessaron symphonia resonabit’; Friedlein, 155; Oosthout and Schilling, 201. * “In triplici quoque dispositione simul diapente et diapason symphonia componitur’ (‘a triple [disposition] contains two consonances, namely the diapente and the diapason’); Friedlein, 156; Oosthout and Schilling, 202; trans. Masi, 178.

the intellectual acumen of students and masters alike. The question was usually couched in the form of a dubium (whether such and such is true or not). After a statement of the question and its implications, the respondens presented a provisional solution; opponentes then presented arguments attacking this conclusion, sometimes citing authorities (mainly Aristotle) in their favour. The respondens, in turn, introduced counterarguments that rejected the objections. This procedure continued for some time—perhaps to the point of exhaustion, if the length of some published questions are any indication.” It was the master’s responsibility effectively to determine the question under dispute, but he had no obligation to do so immediately. On a subsequent day (often the day after the public dispute), the master presented his determination that ideally imposed a coherent scheme of organization on the viva voce session. Later, he might publish a record of the dispute as a questio disputata, preserving in some measure the ‘live’ quality of the original event (‘sed tu dubitabis’—‘sed tu quaeres—‘ed tu dubitando dices’). Eventually, the questio disputata evolved into an exclusively literary genre with extraordinarily elaborate responses. Had there been some interest in speculative musica at the University of Paris, one might expect to encounter a quantity of questiones disputate de musica, but such is not the case. Those that do exist take up themes that do not differ from the student questions (Compendium of Barcelona/Primo queritur) already cited. The Questiones super algorismum et computum et questiones communes mathematice et etiam geometrie of Raoul le Breton, mentioned above in the discussion of ‘de forma’, supply responses that reach a level of sophistication approaching that of the questio disputata. The questions on music and their responses, subtle as they are in the art of argumentation, require no specialized knowledge of speculative musica?” 7. Whether there are only four mathematical sciences (‘Utrum sint tantum quatuor scientie mathematice”) 8. Whether astrology and music are more natural than mathematical (‘Utrum astrologia et musica sint magis naturales quam mathematice’) 39. Whether music is a science (‘Utrum musica sit scientia’) 40. Whether music is a single science (‘Utrum musica sit una scientia’) 41. Whether music is useful (‘Utrum musica utilis est’) 42. Concerning the subject of music (‘Circa subiectum musice”) The first two questions (7 and 8) concern the place of music within the quadrivium. The response to question 7 argues that there are four sczentie mathematice, two of which (arithmetic and geometry) are purely mathematical, two of which are ‘partim mathematice et partim naturales’, i.e. scientie medie, as they were sometimes classified. Question 8 asks whether astrology (i.e. astronomy) and music are ‘more natural than mathematical’, a question that first arose because of a faulty Latin translation of a passage in Aristotle’s Physics, which made the Philosopher seem to hold that optics, ° See the outlines in Weijers, Le Maniement du savoir, 239-49 and 61-75 (‘La méthode de la “questio””); ead., La ‘Disputatio’a la Faculté des arts de Paris, esp. 25-40. The published questiones disputate are more than a little removed from the lively—at times chaotic—interchanges of the public academic dispute. % The prologue and a list of the questions are edited in Olga Weijers, La Disputatio’à la Faculté des arts de Paris, 162-7]; for an edition of the questions concerning music (7-8, 39-42) see Hentschel, Sinnlichkeit und Vernunft, 281-300; Raoul’ questions and two other collections are treated in Frank Hentschel with Martin Pickave, ‘Quaestiones mathematicales: Eine Textgattung der Pariser Artistenfacultät im frühen 14. Jahrhundert’, in Jan A. Aertsen, Kent Emery, Jr., and Andreas Speer (eds), Nach der Verurteilung von 1277: Philosophie an der Universität von Paris im letzten Viertel des 13. Jahrhunderts (Miscellanea Mediaevalia, 28; Berlin and New York, 2001), 618-34.

harmonics, and astronomy were ‘more physical than mathematical’ (‘magis physica quam mathematica”)”” The Arab commentator Averroés, with a correct text at his disposal, interpreted the passage according to Aristotle’s true intention: that music and astronomy were ‘the more physical of the mathematicals, and thus to be placed among mathematica. Raoul knew of this conclusion and aligned his own position with it, making the further distinction that the classification concerned not practical but speculative music.” The four questions that relate specifically to music (nos. 39-42) take up themes familiar from the Compendium/Primo queritur collection: whether music is a scientia, whether it is a single scientia, what is its usefulness, and its proper subject. The questions are generic: one could substitute almost any discipline for ‘music’ in them. The ‘utrum musica sit scientia’ question reappears in a collection of four Questiones musice (Padua, late fourteenth century), which must be the ne plus ultra of questiones disputate de musica.” The question receives a response of astonishing complexity. It first poses a dozen arguments why music should not be considered a sczentia. The response counters with four arguments that it should be so considered. The latter are then elaborated in seven lengthy articles, each subdivided into separate conclusiones. ‘The arguments, elaborate as they are, and far too involved to be discussed here, do not presuppose intensive study of De instituttone musica. Two anonymous Questiones mathematicales in a slightly later collection address two topics that concern music: (1) whether there can be more or less than four scientie mathematice, and (2) whether music and astrology are more mathematical than natural.!°® Both concern classification more than content, and both are already familiar from Raoul le Breton: 4. Whether it is possible for there to be more or fewer [than four] mathematical sciences (‘Utrum possint esse plures vel pauciores scientie mathematice”) 5. Whether music and astronomy are more mathematical than natural, or vice versa (‘Utrum musica et astronomia sint magis mathematice quam naturales vel econverso) The first question introduces six arguments that there are more than four mathematical sciences, followed by thirteen arguments that there are fewer. The stage thus set, reference is made to the authoritative determination of Boethius that there are four, a position that will be defended. The author thereupon explains the bases on which the question will be decided, proceeding to an examination of each argument in turn. A string of definitions and distinctions confirms the existence of only four mathematicals. Resolution of the ‘more mathematical than natural question (5) brings into play the full arsenal of the scholastic dispute. Undoubtedly, the author had some interest in music, but one could easily substitute ‘geometry’ for ‘music’ in the question and the responses would follow the same format. None of these questiones disputate de musica establishes speculative musica as a subject of curricular interest in the university. 97 Physica 2.2 (194*7), ed. Fernand Bossier and Jozef Brams (Aristoteles Latinus, 7.1; Leiden and New York, 1970), 51 (translatio vetus). In the Loeb Library edition Robert P. Hardie and R. K. Gaye translate correctly: ‘similar evidence is supplied by the more physical of the branches of mathematics, such as optics, harmonics, and astronomy’. ‘Sustineo opinionem Commentatoris et dico quod musica (non practica musica sed speculativa) et astrologia (non illa que est de iudiciis [astrology], sed speculativa) sunt magis mathematice quam naturales, quia scientia debet denominari a principiis suis magis quam a conclusionibus, quia principia sunt causa conclusionum’; Hentschel, Sinnlichkeit und Vernunft, 289. See also the discussion in Dyer, “The Place of Musica’, 60-9. ” This question has been published in Cecilia Panti, “The First “Questio” of ms Paris, B. N. lat. 7372: “Utrum musica sit scientia”’, Studi medievali, 33 (1992), 265-87 (introduction), 288-313 (edition). 100 Both questions are edited from the unique source (London, British Library, Harley 1, fos. 149-160") in Hentschel, Sinnlichkeit und Vernunft, 300—13.

TWO SUMMARIES AND A COMMENTARY ON ‘DE INSTITUTIONE MUSICA There are three texts that demonstrate the existence of some interest in Boethius on the part of masters and scholars of the medieval university. The first of these, a summary of the first two books of De institutione musica from the third quarter of the thirteenth century, called by its editor, Christian Meyer, ‘un abrégé universitaire’, was mentioned above in the discussion of ‘de forma’ (no. 7). This summary, prepared for readers not well versed in mathematics by a master fully conversant with the intricacies of proportion, is a simplified résumé, omitting the most formidably technical chapters of De institutione musica (1.24-5, 1.28-33, 2.18-20). Had Boethius been widely read, one might expect to find more summaries of this type or even more than three manuscript sources of this particular text. Whatever its purpose might have been, it possesses none of the features characteristic of the academic lecture or dispute (commentary, questions, objections, distinctions, responses). It is merely an ‘abrégé’ compiled for the intellectually curious. The summary of De institutione musica prepared by Johannes de Muris was destined to be widely copied, especially in Germany and Central Europe. Like the aforementioned ‘abrégé, Muris’s Musica speculativa (1323) treats Boethius in a manner designed to make his teaching comprehensible to those without advanced mathematical skills.” His statement that the mathematical books were no longer lectured on at Paris was cited earlier in this essay. He had sympathy for those who found Boethius’ teachings simply too challenging for their purposes, and for this reason he sought to explain them to a small circle of devotés interested in quadrivial music. Muris explains that the books of the ‘old philosophers’ (‘antiquorum philosophorum’) on music and other quadrivial disciplines were no longer read. For this reason he prepared for those who might be interested a ‘tractatus brevis’ with all of Boethius’ “conclusiones pulchriores”. Two versions of Musica speculativa are transmitted in the manuscript tradition. Version A begins with a prologue in which Johannes explained his intentions: It seemed to me a good idea to devise a short treatise from the Musica of Boethius, which I studied according the talents given me by God, and which I have been able (with God’s help) in some measure to comprehend; I will try to present [Boethius’] more excellent conclusions pertaining to the art of music in plain language and unambiguous meaning.” The presentation is adapted to the taste of the time, arranging the material in the form of theoremata (a term associated with geometry but not exclusive to it), thus supposing that the audience for Musica speculativa had the requisite preparation to appreciate such demonstrations. Version B begins with an entirely different prologue, self-borrowed from the first and second chapters of the author’s Notitia artis musice (1321)."°° This prologue explains 10 Die Musica speculativa des Johannes de Muris, ed. Falkenroth, 27-31 and 40-64 (list of manuscripts); the treatise has also been edited by Susan Fast: Johannes de Muris, Musica Speculativa (Musicological Studies and Documents, 6]; Ottawa, 1994). See also Ulrich Michels, Die Musiktraktate des Johannes de Muris (Beihefte zum Archiv für Musikwissenschaft, 8; Wiesbaden, 1970); Hentschel, Sinnlichkeit und Vernunft, 259-67 (‘Der Überlieferungskontext der “Musica Speculativa” als mathematische Klassifikation’); Laurence Gushee, ‘Jehan des Murs and his Milieu’, in Musik — und die Geschichte der Philosophie und Naturwissenschaften im Mittelalter, 339-71. For a concise overview of Jehan life and writings, see Lawrence Gushee and Matthew Balensuela, ‘Muris, Johannes de’, New Grove II, xvii. 409-13. “Visum est mihi bonum, ut ex musica Boethii, quam secundum vires a deo datas perstudui, eamque favente deo aliqualiter intellexi, tractatum brevem elicere[m], in quo conclusiones pulcriores ad ipsam artem musicae pertinentes cum sermonis claritate et evidentia sententiae manifestare conabor’; Die Musica speculativa des Johannes de Muris, ed. Falkenroth, 74. °° Ibid. 77-87.

music as sounding phenomenon (and hence outside the speculative context), for which three things are necessary: someone to strike an instrument, something to be struck, and a medium for striking it (‘ad generationem soni necessario tria requiruntur: percutiens, percussum, medium percutiend?), for example, a violinist, a violin, and a bow. Beginning in the late fourteenth century, Musica speculativa entered a very different academic climate from the one that prevailed at Parisin the thirteenth century. In the universities of Central Europe it became a prescribed text.!* Two-thirds of the time the treatise is transmitted not in the company of other music treatises (most oftenin Italian sources) butin company with quadrivial works (optics, astronomy, etc.), as one might expect in manuscripts assembledin a university milieu. 15 One of the manuscript sources (BNF lat. 7378A; Paris, after 1362) contains texts on algorism, geometry, astronomy, optics, and statics (de ponderibus). 106 A later hand added to the manuscript a series of thirty-five questiones on perspective, music, and statics (fos. 83-85”) couchedin the familiar ‘utrum’ format of the questio disputata. While most of the questions about music are technical (consonances and intervals), others inquire about matters that touch on natural science: whether the angle of incidence of sounds is equal to the angle of reflection, or whether sounds are multiplied (‘multiplicentur’) differently from lights and colours. Unfortunately, no responses are provided. The concepts behind these questions and the purpose for which they were framed are topics that invite further investigation. ‘COMMENTUM OXONIENSE’ Another witness to academic interest in De institutione musica in the later Middle Ages is a commentary on the text written at Oxford sometime after 1350 (Commentum Oxoniense). Definitely of English origin and transmitted in two English manuscripts from the first half and the middle of the fifteenth century respectively, only part of books 1 and 4 and all of book 5 survive from what must once have been a complete and extensive commentary on the entire text.”Version A of the Commentumis preservedin a manuscript accompanied by no other, texts. Version B is found in a manuscript whose contents are exclusively musical." 10% Gerhard Pietzsch, Zur Pflege der Musik an den deutschen Universitäten bis zur Mitte des 16. Jahrhunderts (1936, 1938; repr. Hildesheim and New York, 1971). Guy Beaujouan regards this as a new beginning after a ‘200-year eclipse’ of Boethius; see “The Transformation of the Quadrivium’ in Robert L. Benson and Giles Constable (eds.), Renaissance and Renewal in the Twelfth Century (Cambridge, Mass., 1982), 463-87 at 467. 105 Frank Hentschel singled it out as der einzige rein musiktheoretische Text, der aus der Zeit um 1300 überliefert ist; er fungierte überdies wohl an der Artistenfakultät als Textbuch’; Sinnlichkeit und Vernunft, 16 (a conclusion true only for a limited geographical area). Hentschel has analysed the manuscript tradition (pp. 259-67); the manuscripts and their contents are listed by Falkenroth (Die Musica Speculativa, 40-64), who distinguishes quadrivial from scientie medie manuscript collections (p. 29). $ For an index of the manuscript and a transcription of the questions see Pascale Duhamel, ‘L'Enseignement de la musique à l’Université de Paris d’après le manuscrit BnF lat. 7378A, Acta musicologica, 79 (2007), 263-89. I wish to express my thanks to Dr Duhamel for sending me an offprint of this important contribution. See also Johannes de Muris, Notitia artis musice, ed. Ulrich Michels (Corpus Scriptorum de Musica, 17; [Rome], 1972), 24-31. 107 Matthias Hochadel, Commentum Oxoniense in musicam Boethii: Eine Quelle zur Musiktheorie an der spätmittelalterlichen Universität (Bayerische Akademie der Wissenschaften, Verôffentlichungen der Musikhistorischen Kommission, 16; Munich, 2002). A brief introduction to the commentary by the same author appeared earlier as ‘Zur Rezeption der “Institutio Musica” von Boethius an der spätmittelalterlichen Universitat’, in Musik — und die Geschichte der Philosophie und Naturwissenschaften im Mittelalter, 187-206. See also Alexander Rausch, ‘Der Boethius-Kommentar in der Handschrift St. Florian XI 282’, Studien zur Musikwissenschaft, 48 (2002), 7-83. 8 For a description of ‘codex A (Oxford, All Souls College, MS 90) see Christian Meyer and Michel Huglo and Nancy C. Phillips, The Theory of Music, iv (RISM B III/4; Munich, 1992), 99. For ‘codex B’ (Oxford, Bodley 77) see Muris, Notitia artis musice, ed. Michels, 17-19; Johannis Wylde, Musica manualis cum Tonale, ed. Cecily Sweeney (Corpus Scriptorum de Musica, 28; Neuhausen-Stuttgart, 1982), 24-7; and RISM B III/4, pp. 102-3.

The preface to the Commentum Oxoniense, peppered with citations from dozens of authors, sacred and profane, ancient and medieval (identified by the editor of the commentary, Matthias Hochadel), extols the art of music. It cites scriptural passages, as well as Macrobius, Isidore, Hucbald, Guido, Peter of Blois, John of Salisbury (Policraticus), and Johannes Balbus (Catholicon, for definitions). The second section of the preface is framed as a classic accessus ad auctorem (‘ad sequentis operis intelligenciam faciliorem hec preconsideranda’) that explains what music is, whence its name, its purpose and usefulness, and the divisions of Boethius’ text. A curious feature of this exposition is the author’s decision to classify music under ethics, citing a statement made at the beginning of the Musica that ‘music 1s associated not only with speculation but with morality as well’, a theme familiar from ancient Greek sources that evokes the power of music to influence behaviour.” The main part of the Commentum paraphrases sections of Boethius’ text and explains individual words. A number of music theorists make an appearance, including the author’s countryman Walter Odington, whose Summa de speculatione musicae dates from c.1300. As is clear from Hochadel’s Índex auctorum, the commentary is also deeply indebted to the gloss tradition of De instituttone musica. A dozen passages were extracted from the florilegium Auctoritates Arıstotelis, a collection of citations from the works of Aristotle, and some of the other citations may well come from similar collections.” Despite the presence of citations from the nova translatio of the Metaphysics and a sprinkling of references to Aristotle’s works on natural philosophy, the Commentum Oxoniense lacks a philosophical ‘tone’. It is exclusively expository, raising none of the questions that might identify it as a product of the university environment. As a detailed glossing of the text accompanied by grammatical notes, it seems to be rather old-fashioned, a point acknowledged by Hochadel.!! ‘MUSICA IN ENGLISH AND CENTRAL EUROPEAN UNIVERSITIES The Commentum Oxomense raises the question of the role of speculative musica in the curriculum of the University of Oxford. By the first third of the fifteenth century, some study of quadrivial music was a requirement for promotion to the master’s degree. A 1431 statute (the first to mention music as part of the course of study at the university) lists all of the books to be heard previous to inception as a master: we assume that those presented to incept in arts and philosophy will have heard, ordinarily and attentively, the seven liberal arts and the three philosophies [natural, moral, metaphysical] for a period of eight years (each term consisting of 30 dies legibiles), according to the following course of studies [‘secundum formam’], ascending gradually by steps.!! 109 «Musica vero non modo speculationi, verum etiam moralitati coniuncta est’; Boethius, De institutione musica, ed. Friedlein, 179; trans. Calvin M. Bower, Fundamentals of Music (New Haven, 1989), 2. 10 Jacqueline Hamesse, Les Auctoritates Aristotelis: Un florilège médiévale. Etude historique et édition critique (Philosophes Médiévaux, 17; Louvain and Paris, 1974); ead., ‘Les Florilèges philosophiques du XII” au xv" siècle’, in Les Genres littéraires dans les sources théologiques et philosophiques médiévales: Définition, critique et exploitation. Actes du colloque internationale de Louvain-la-Neuve, 25-27 ma: 1981 (Louvain-la-Neuve, 1982), 181-91. !! ‘Aber auch von neueren theoretischen Entwicklungen, wie sie an anderen Universitäten in das Lehrprogramm aufgenommen wurden, sind kaum Spuren zu erkennen’; Hochadel, ‘Zur Rezeption der “Institutio Musica” von Boethius an der spätmittelalterlichen Universität”, 195. "2 Presentatos igitur ad incipiendum in artibus et philosophia supponimus. . septem artes liberales et tres philosophias per octo annorum terminos, termino quolibet ad minus continente xxx dies legibiles, secundum formam sequentem ascendendo gradatim, ordinarie et attente audisse’; Statuta Antiqua, ed. Gibson, 234-5 and xciv-xcv. For an annotated ‘bibliography’ of the main texts see James A. Weisheipl, ‘Curriculum of the Faculty of Arts at Oxford in the Early Fourteenth Century’, Mediaeval Studies, 26 (1964), 143-85, esp. 168-76.

The books listed combine the liberal arts, parts of the ‘old’ and the ‘new’ logic, with Aristotle’s works on natural science and moral philosophy (ethics). In the case of music, the statute specifies ‘musicam per terminum anni, videlicet Boecii, a unique example of a requirement that quadrivial musica be studied for a period of time (c.30 lectures) adequate for the understanding of its basic principles. Arithmetic was also required for a term; geometry and astronomy each received two terms. The existence of lectures on music is implied by the proviso that, ‘if any of the liberal arts is not taught [non legatur] in the schools assigned to that purpose, then let it be heard [audiatur] from a bachelor lecturing extraordinarie for the period of time allocated above to the same subject, whenever a suitable time for it becomes available”. This indicates that at Oxford music was one of the subjects on which bachelors were customarily allowed to deliver (extraordinary) lectures. These may have taken place outside the time of day reserved for ordinary lectures or in one of the colleges. The fact that music should be honoured at Oxford in the fifteenth century when such was not the case at Paris two centuries earlier is not surprising. The Oxford scholar Robert Grosseteste (c.1168-1253) mounted a strong defence of the value of music as a liberal art in his De artibus hberalibus, in which music takes up a considerable amount of space in a relatively brief treatise.’* Introductory remarks about proportions are followed by an explanation of the generation of sound as vibratory phenomenon, ‘cum enim corpus violenter percutitur’. Music and the other liberal arts possess the additional quality of utilitas, and Grosseteste goes on at some length about the power of music to restore the natural ‘harmony’ of soul and body.” Even wounds can be more quickly healed with music, but how effectively depends on the skill of the medicus in prescribing music of the right proportions so as to alter the ‘affect’ of the mind (‘in quos voluerit affectus animi permutare”). The Oxford savant Roger Bacon (c.1214-92) held very strong views about the essential role of mathematics in the acquisition of knowledge. Without the quadrivial sciences ‘the other sciences cannot be known or knowledge of things secured’."'° Given the paramount importance he attributed to mathematics, it is understandable that he would complain testily (as was often his wont) about the virtual neglect of the quadrivial disciplines at Paris: ‘Neglect of this branch now for thirty or forty years has destroyed the whole system of study of the Latins, since whoever is ignorant [of mathematics] cannot know the other sciences nor the affairs of this world.” Implicitly, Bacon would place mathematics above logic—a by no means conventional view in the thirteenth century. 113 “Si aliqua scienciarum liberalium ordinarie non legatur in scolis ad hoc deputatis, tunc a bachalario extraordinarie legente per tempus superius eidem sciencie limitatum audiatur, cum tempus congruum eis ad illud vacaverit’; Statuta Antiqua, ed. Gibson, 235. 4 De artibus liberalibus, ed. Ludwig Baur, in Die philosophischen Werke des Robert Grosseteste, Bischofs von Lincoln (Beiträge zur Geschichte der Philosophie des Mittelalters, Texte und Untersuchungen, 9; Miinster in Westf., 1912), 1-7; Baur’s edition is also available at <www.grosseteste.com>. See also Antonio Tognolo, ‘Il De artibus liberalibus de Roberto Grossatesta’, in Arts libéraux et philosophie au moyen âge, 593-97, and Cecilia Panti, Robert Grosseteste’s Theory of Sound’, in Musik — und die Geschichte der Philosophie und Naturwissenschaften im Mittelalter, 3-17. ° “Musicae ministerium in philosophia naturali non minus utile quam ad medendum, cum omnis aegritudo et in ordinatione spirituum et in temperantia curatur... musicis sanatur modulationibus et sonis, ut etiam credunt philosophi’; De artibus liberalibus, ed. Baur, 4-5. 1l6 “Et sunt quatuor scientiae magnae, sine quibus caeterae scientiae sciri non possunt nec rerum notitia haber?” Opus maius IV, dist. 1, ch. 1, in The Opus maius of Roger Bacon, ed. John Henry Bridges, 2 vols. (Oxford, 1897), i. 97; trans. Robert B. Burke, The Opus maius of Roger Bacon, 2 vols. (Philadelphia, 1928), 116. Opus matus, loc. cit.

Just how intensive and demanding the study of quadrivial music at Oxford was, or how seriously the average student was expected to take the subject, can be a matter of debate. John Caldwell hazarded that, with respect to music study at Oxford, ‘the statutes were more often honoured in the breach than in the observance, and that candidates [for the degree] could get by with the merest smattering of the subject’.!8 An early fourteenth-century memorandum records that an Oxford scholar went through two books of geometry in twelve days with one teacher and repeated the course in nine days with another. The first book of Boethius’ Arithmetic was polished off in twelve days.” The brevity of instruction in such difficult subjects seems inexplicable—basic computational efficiency cannot have been the goal. A Prague statute (rubrica) of 1367 (repeated in 1390) required study of all the books of Aristotle along with the quadrivial disciplines, lectures on which were forbidden on dies festivi, a prescription that exactly reversed the Parisian practice of a century and a half earlier. Evidently, speculative musica enjoyed high status at Prague as a subject permitted on ordinary lecture days. A subsequent rubrica required that lectures on ‘musica Muri’ be heard for the space of at least three weeks.” The 1390 statute prohibited anyone who had not heard ‘aliquid in musica et arithmetica’ from proceeding to the examination for the master’s degree.” By 1389, university students at Vienna were also expected to have heard ‘aliquem librum de musica) and one hundred fifty years later (1537), a reform statute of Ferdinand I (king of Bohemia and Hungary, 1527-56; Holy Roman emperor, 1556-64) ordained that a ‘primus mathematicus’ should have read ‘musicam Ptolomái, Boetii aut Joannis Muris. These regulations represent a revival of interest in the artes hberales in German-speaking and Central European university milieux rather than an inheritance from Paris. The teaching of musica on the banks of the Moldau and the Danube, far removed in time and place from thirteenth-century Paris, does not support the presence of a practice whose existence we have been unable to discover on the banks of the Seine. CONCLUSIONS Whatever was taught in the university classroom, intensely argued in academic disputes, and commented upon with unabated vigour embodied the intellectual interests of the time. The obligatory curriculum of the University of Paris was based on auctoritates, as medieval education always had been, even though now these authorities were subjected to critical scrutiny. The greatest of these was without question Aristotle, followed by his Arabic commentator, Averroés. Aristotle had little interest in music apart from a few comments about its social value; he never considered it extensively as sounding phenomenon. The mathematical orientation of speculative musica had little in common with Aristotle’s natural philosophy and non-mathematical conception of phenomena. "8 John Caldwell, ‘Music in the Faculty of Arts’, in James McConica (ed), The History of the University of Oxford, iii: The Collegiate University (Oxford, 1986), 203. 119 Rashdall, The Universities of Europe, iii. 482. 120 Pietzsch, Zur Pflege der Musik, 17-18. The existence of 15th-c. commentaries and accessus to Musica speculativa attest to its continued relevance; see Elzbieta Witkowska-Zaremba, ‘Music between Quadrivium and Ars canendi: Musica speculativa by Johannes de Muris and its Reception in Central and East-Central Europe’, in Cantus Planus: Papers read at the Fourth Meeting, Pécs, Hungary, 3-8 September 1990, 119-26. 121 Pietzsch, Zur Pflege der Musik, 17. 22 Ibid. 26. This late medieval reference to a music requirement seems to be applied generally to the Middle Ages in Klaus-Jürgen Sachs, Artes liberales”, MGG?, Sachteil, i. 91-2.

Ever lurking in the background was the fact that the disciplines of the quadrivium were also elementary studies. Children learnt arithmetic and could understand basic geometry and astronomy. Learning the Psalter at the very beginning of clerical studies meant learning how to sing it alongside the other chants required by the liturgy. So dominant was the awareness of music as sound that it resisted being defined solely as a quadrivial discipline. In Li livre du Trésor (1245), a classification of knowledge, Bruno Latini said of music, the second of the mathematical sciences, that it ‘teaches us how to sing and play in song and citoles and organs and other instruments that agree with each other, for the pleasure of people, and in church for the service of Our Lord’ (‘nous enseigne fair vois, sons en chant et en cytoles et en orghenes et en autres estrumens accordables uns contre les autres, pour delit des gens, et en eglise pour le service Notre Seigneur”). Thomas Aquinas elucidated how the ‘liberal’ arts could be effectively distinguished from the mechanical arts (weaving, navigation, etc). While both produced a ‘work’, in the case of the mechanical arts this might be a physical object (weaving) or a change in status or location (navigation, medicine), but ‘in speculative things themselves there is [also] something after the matter of a certain product, such as, for example, the construction of a syllogism, or of a fitting discourse, or the work of counting or measuring’.’** Thomas neglects to mention music. In his commentary on Boethius De Trinitate he affirms the importance of mathematics as a preparation for the study of natural science and metaphysics, but he excludes music and ethics.” In their survey of Thomas’s understanding of the liberal arts Frs Conway and Ashley concluded that he regarded music much as Aristotle did in the Politics: ‘Our fathers admitted music into education, not on the ground either of its necessity or utility... [but] for intellectual enjoyment in leisure, which is in fact evidently the reason for its introduction.’ !°° Hardly a ringing endorsement for the study of speculative musica! No medieval music theorist could aspire to the prestigious rank of an academic auctoritas, however highly he might be regarded by practical musicians. The biblical commentator Nicholas of Lyra (1270-1340) declared dismissively that ‘one need not pay much attention to the words of Guido, since he is without authority." Most likely, the question of Guido ‘authority’ never came up in academic circles. Music theory treatises, from the chant treatises of the early ninth century to the expositions of counterpoint and rhythm in the twelfth and thirteenth, addressed practical topics unlikely to have much appeal outside a circle of professional musicians. Reflecting on the complete absence of scholastic commentaries on medieval music treatises, Christian Meyer concluded quite correctly that they ‘were hardly ever the subject of academic lectures.. None of the extant derivatives of university teaching (lectures published as 23 As quoted in Glorieux, La Faculté des arts, 34-5. 124 Summa Theologiae I°-II°°, q. 57, a. 3, ad 3, as quoted in Pierre Conway and Benedict Ashley, “The Liberal Arts in St. Thomas Aquinas’, The Thomist, 22 (1959), 460-532 at 472. 125 Thomas Aquinas: The Division and Methods of the Sciences, Questions V and VI of his Commentary on the De Trinitate of Boethius, trans. Armand Maurer, 4th edn. (Mediaeval Sources in Translation, 3; Ottawa, 1986), 23 (q. 5, a. 1, ad 9). 126 As quoted in Conway and Ashley, “The Liberal Arts, 486; the reference is to Politics, 8; 1338°10. 27 Dicendum quod de dicto illius Guidonis non est multum curandum, cum nullius est auctoritas”; Biblia latina cum postillis Nicolai de Lyra et expositionibus Guillelmi Britonis in omnes prologos S. Hieronymi et additionibus Pauli Burgensis replicisque Matthiae Doering, 4 vols. (Venice, 1489). The comment appears in a postilla on 1 Kings 16: the response ‘ad tertium’ to the questio ‘Utrum demones virtute melodie possint expelli a corporibus obsessis’. For an edition and commentary see Joseph Dyer, “The Power of Music according to Two Medieval Philosophers’, in Dies est letitie: Essays on Chant in Honour of Janka Sendrei, ed. David Hiley and Gabor Kiss (Budapest, Regensburg, and Ottawa, 2008), 211-35. ‘ne faisaient guère l’objet de lectures scolaires’. Les Traités de musique (Typologie des sources du moyen age occidental, 85; Turnhout, 2001), 75.

commentaries, disputed questions, etc.) suggests strong interest in speculative musica or even music as a natural phenomenon. Still less is there much evidence that Boethius was carefully read. In the fourteenth century some masters and students at Oxford, Prague, and Vienna evinced a continuing (or more likely renewed) interest in De institutione musica. In thirteenth-century Paris, however, music had no place in either of the public forums of the University—the magisterial lecture or the formal academic dispute. ABSTRACT During the early Middle Ages quadrivial musica (the study of abstract mathematical proportion) was part of the educational programme in the liberal arts; the fundamental text was Boethius’ De institutione musica. With the rise of the universities in the thirteenth century, the goals of education and the content of the curriculum changed dramatically. Aristotelian logic and natural science virtually extinguished interest in the quadrivium—and necessarily music—at the university level. An analysis of the curriculum, teaching methods, questiones disputate (a derivative of the university dispute), and student examination questions at the University of Paris reveals that music had no place in the official instructional programme of the University. A few sources, however, indicate that Boethius De institutione musica still commanded interest in some circles, particularly at Oxford and in Central Europe in the fourteenth century.