The transmission of ancient music theory into the Middle Ages

Transcription

1 . 5. The transmission of ancient music theory into the Middle Ages calvin m. bower The chronicle of musical thought in the Latin world from the beginning of the Common Era through the first millennium of European history presents a metamorphosis of various intellectual traditions into what we today call music theory. The adjectives middle and dark hardly apply to these ages when one is writing the history of musical thought, for these centuries witness the beginning indeed the birth of that Western discipline which attempts to reflect systematically about given musical phenomena and apply these reflections to the analysis and composition of musical repertoires. While one might speak of a tradition of musical thought during the early Middle Ages, the integrity of that tradition is achieved not by any continuous thread that runs through the whole, but by a number of overlapping strands that give strength to a broad tradition. Often these strands forming the very core of musical thought draw their character from traditions other than music, and the continuity of musical reflections must be viewed from proximate perspectives. While the first millennium saw the birth of Christianity and the flourishing musical liturgy built principally around psalmody, 1 in the first centuries of the new millennium the study of music theory as a technical discipline remained largely isolated from the fresh artistic tradition. The development of musical learning in the Latin West basically grew from the technical subject formulated by the ancient Greeks, namely musica (µουσική) or harmonica ( ρµονικά). (see also Chapter 4, pp ). Hence in the early sections of this chapter, music theory as a general discipline will be referred to as musica to distinguish it from music, which would imply the totality of musical experience, practical and theoretical, or from music theory, which would imply some relation between a repertoire and systematic reflections concerning music. Since the transmission of ancient thought into these ages was both limited and enriched by the intellectual and spiritual contexts in which it was received, the history of musica in the early Middle Ages cannot be separated from the history of education, of philosophy, and of learning in general. The first part of this chapter, therefore, must describe the broad intellectual stage on which musica first appeared. Yet musica could not remain unmoved by the vital, contemporaneous culture of liturgical chant, particularly 1 For a lucid discussion of the rise of music in Christian worship, particularly as part of the Mass, see James McKinnon, The Advent Project: The Later Seventh-Century Creation of the Roman Mass Proper (Berkeley, Los Angeles, London: University of California Press, 2000). 136

2 The transmission of ancient music theory into the Middle Ages 137 as that movement gained momentum in the ninth and tenth centuries; hence the second section of this chapter will address the initial interaction between musica and cantus,and the intellectual and artistic synthesis that represents the beginnings of music theory. The brush strokes in this history covering more than a thousand years are of necessity broad, and many important details are never introduced into the narrative. Nevertheless the six sections of this two-part chapter may serve as a multi-focal lens through which one can gain a view of the intellectual and artistic forces that shaped musical thought during the first millennium of the Common Era. 2 Musica in the late Roman and early medieval worlds Musica in the Roman rhetorical tradition Musica first appeared in Roman education as a discipline fundamental to the formation of the orator that Roman patrician who was expected to lead and shape his society through eloquence and persuasion. Certain disciplines (artes) were considered essential to the training of the person born free of servile and commercial obligations (the homo liber), and these disciplines came to be known as the artes liberales, or the free or liberal arts. The great Roman encyclopedist Marcus Terentius Varro (first century bce), had written a seminal work on the disciplines appropriate to the education of the free man, Nine Books on the Disciplines (Disciplinarum libri IX), a work (now lost) that o ered introductions to nine disciplines: grammar, dialectic, rhetoric, geometry, arithmetic, astrology, music, medicine, and architecture. Traces of the Roman hortatory tradition of the study of the arts can be found in the Fundamentals of Oratory (Institutio oratoria)of Quintilian and in Vitruvius s On Architecture (De architectura). 3 Music and the other arts were hardly considered fields worthy of study for any noble end among the Roman orators. The principal goal for learning musica seemed to have been mastering a repertoire of facts and references that might be dropped in a speech at an appropriate moment, thereby making a favorable impression and giving the orator more credibility. The content of the brief sections on music among these 2 While the present narrative of music theory during the early Middle Ages is in many ways di erent from that of Michael Bernhard, I must express my debt at the beginning of this essay to the survey of ancient and medieval theory o ered by my colleague in Überlieferung und Fortleben der antiken lateinischen Musiktheorie im Mittelalter and Das musikalische Fachschrifttum im lateinischen Mittelalter. These two essays are fundamental to any history of medieval theory, and could be cited in virtually every paragraph that follows. 3 For a general introduction to the role of music in the Roman world, see Günther Wille, Musica romana. Die Bedeutung der Musik im Leben der Römer (Amsterdam: P. Schippers, 1967), and Einführung in das römische Musikleben (Darmstadt: Wissenschaftliche Buchgesellschaft, 1977); the lost work of Varro is placed in historical context in William Harris Stahl, Richard Johnson, and E. L. Burge, Martianus Capella and the Seven Liberal Arts, vol. i, The Quadrivium of Martianus Capella, Latin Traditions in the Mathematical Sciences, 50 B.C. A.D.1250 (New York and London: Columbia University Press, 1971), pp and passim.

3 138 calvin m. bower Table 5.1 Late Roman and early medieval authors and texts Cicero (d. 43 bce) Varro (d. 27 bce) Vitruvius (d. before 27 bce) Quintilian (d. c. 100 ce) Censorinus Calcidius (4th c.) Macrobius (c. 400) Martianus Capella (before 439) De re publica Displinarum libri IX De architectura Institutio oratoria De die natali (238 ce) Timaeus... translatus commentarioque instructus Commentarii in somnium Scipionis De nuptiis Philologiae et Mercurii Augustine ( ) De musica (387 89) De ordine De doctrina christiana Favonius Eulogius (5th c.) Boethius (early 6th c.) Cassiodorus (after 540) Isidore (d. 636) Disputatio in somnium Scipionis De institutione arithmetica De institutione musica Institutiones Etymologiae authors reflects a superficial understanding of Greek tonal systems, enumerates notable persons from Greek antiquity who were inventors of musical instruments or able performers, and repeats various myths and accounts of the a ective potential of instrumental and vocal music. The arts designated as liberal were by no means a canon among ancient Latin authors, and the number of arts seems to have varied to fit the occasion. Thus it is remarkable that music is invariably counted among the disciplines worthy of the free man among ancient authors (see Table 5.2). The figure who seems to have been instrumental in establishing the number of arts at seven and indeed in establishing the canon of the arts for the later Middle Ages was the North African writer Martianus Capella. 4 While writing in the early fifth century, Martianus clearly reflects several aspects of the Roman rhetorical tradition: the order of the arts (excluding medicine and architecture) is similar to that of Varro; the chapters on the individual arts are relatively brief and represent little more than basic introductions to the disciplines; and the treatment of the last four arts arithmetic, geometry, astronomy, and music shows little grasp of the underlying mathematical principles developed by earlier Greek authors. 4 Concerning Martianus Capella, see James A Willis, Martianus Capella and His Early Commentators (Ph.D. diss., University of London, 1952); Stahl, Johnson, and Burge, Martianus Capella; Danuta Schanzer, Three Textual Problems in Martianus Capella, Classical Philology 79 (1984), pp ; and A Philosophical and Literary Commentary on Martianus Capella s De Nuptiis Philologiae et Mercurii Book I (Berkeley, Los Angeles, London: University of California Press, 1986).

4 The transmission of ancient music theory into the Middle Ages 139 Table 5.2 The place of musica in the liberal arts Varro Martianus Boethius Cassiodorus Isisdore (1st c. bce) (5th c. ce) (6th c. ce) (6th c. ce) (7th c. ce) i Grammar Grammar Grammar Grammar ii Dialectic Dialectic Rhetoric Rhetoric iii Rhetoric Rhetoric Dialectic Dialectic iv Geometry Geometry Arithmetic Arithmetic Arithmetic v Arithmetic Arithmetic Music Music Geometry vi Astrology Astronomy Geometry Geometry Music vii Music Harmony Astronomy Astronomy Astronomy viii Medicine Medicine ix Architecture Yet the tone of Martianus s presentation is strikingly di erent from that of the earlier Roman patricians. Martianus s treatise is entitled The Marriage of Philology and Mercury (De nuptiis Philologiae et Mercurii); Philology and Mercury symbolize human and divine intellect, and their wedding represents the union of the human intellect with that of the gods. The arts in Martianus s allegory are wedding gifts personified as maidens, and each of the maidens represents an art by which the human intellect may rise to the level of the divine. The arts of medicine and architecture are rejected because they deal with mortal matters and their skills are mundane. 5 Throughout Martianus s allegory harmony (or musica) holds a unique position, for the order of the cosmos itself is set out according to harmonic principles, and music, unlike some of the other arts, is treated in the first two books that set the stage for the allegory as well as the last book that reveals Harmonia herself: in the final book she is presented as a bridesmaid particularly cherished in the heavenly realm. 6 Thus Martianus transformed the Roman rhetorical tradition of the arts as evidence of humane erudition into a tradition in which the arts were intellectual disciplines that enabled the human mind to rise to the level of divine intellect. This new status of music and the other arts resonated well with an essentially Platonic exposition of music and the other mathematical disciplines that had developed in the time between Varro s introduction to the artes liberales and Martianus s allegory. 7 Musica and the late Latin Platonists In the first century bce, Marcus Tullius Cicero concluded his philosophical treatise The Republic (De re publica) with a moving account of the ascent of the soul to 5 De nuptiis 339, 3 7; all textual references to Martianus follow the page and line numbers in the Willis edition 6 Ibid. 339, Concerning the place of Martianus in medieval Platonism, see Stephen Gersh, Middle Platonism and Neoplatonism: The Latin Tradition (Notre Dame: University of Notre Dame Press, 1986), pp

5 140 calvin m. bower knowledge of its own immortality; Cicero s narrative is known as the Dream of Scipio (Somnium Scipionis). When viewing the marvels of the cosmos, Cicero s soul inquires concerning the nature of the wondrous sound filling its ears, and is told that the harmony results from the motion of the spheres that are spaced according to musical ratios. Only souls who search for truth, along with certain musicians who can imitate the heavenly order in their playing and singing, are able to hear these celestial tones. 8 To ancient and medieval scholars in the Platonic 9 tradition to which Cicero s philosophical works belong 10 the ratios that governed the highest order of the physical universe and the metaphysical world itself were those that determined musical concord, and the degree to which sensual music was shaped by these ratios, was the degree to which the soul was led away from rank sensuality to contemplate eternal truths. The most important source for a narrative of the creator s application of arithmetic ratios and musical intervals was found in Plato s account in Timaeus of the creation of the world soul. 11 In the fourth century, Calcidius translated this section of Timaeus into Latin, replete with arithmetic and musical commentary and diagrams concerning the ratios and intervals. 12 Early medieval scholars sensed the resonance between Cicero s Somnium Scipionis and Plato s Timaeus; Macrobius (c. 400) and Favonius Eulogius (fifth century) both wrote commentaries on Cicero s text that emphasized the mathematical ratios and musical intervals, and that discussed at length the ratios Plato s demiurge applied in creating the world soul. 13 The figure of Augustine, the famous saint of North Africa and bishop of Hippo, was a dominating force in the intellectual history of the Middle Ages, and, albeit indirectly, a powerful influence on musical thought during that formative period. Augustine s much celebrated conversion in 387 marked the major turning point in his intellectual as well as his spiritual life, and more than one modern scholar has suggested that the conversion was as much to neo-platonism as to Christianity. 14 In the months and years immediately 8 See De re publica vi (Keyes edn., pp ). 9 In this essay I use the term Platonist very broadly to embrace both pure Platonism (if there is such a thing) and the neo-platonism of the early common era; properly speaking, most of the authors treated in this chapter would be termed neo-platonists. 10 Concerning Cicero s place among Platonists, see Gersh, Middle Platonism and Neoplatonism, pp See Francis M. Cornford, Plato s Cosmology, The Timaeus of Plato Translated with a Running Commentary (New York: The Liberal Arts Press, 1957); Jacques Handschin, The Timaeus Scale, Musica disciplina 4 (1950), pp For a concise summary of Calcidius, see Thomas J. Mathiesen, Apollo s Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages (Lincoln, NB and London: University of Nebraska Press, 1999), pp For a general discussion of Macrobius, see Introduction to Stahl trans.; See also Mathiesen, Apollo s Lyre, pp Concerning the role of Platonism in the Christian formation of the young Augustine, see especially John J. O Meara, The Young Augustine: The Growth of St. Augustine s Mind up to his Conversion (Staten Island: Alba House, 1965), esp. pp ; see also Dominic J. O Meara, The Neoplatonism of Saint Augustine, in Neoplatonism and Christian Thought, ed. D. J. O Meara (Norfolk: International Society of Neoplatonic Studies, 1982), pp For a broader study of Augustine, see Peter Brown, Augustine of Hippo: A Biography, new edn. with an epilogue (Berkeley and Los Angeles: University of California Press, 2000).

6 The transmission of ancient music theory into the Middle Ages 141 following the famous scene in the garden of Milan, Augustine surrounded himself with austere and high-minded Christian scholars, and during these years he wrote a series of works that are distinctly philosophical in character. One was a treatise on music. In his On Music (De musica) Augustine allies himself with the Pythagorean tradition of ancient Greek musical thought and the Platonic philosophical tradition. The matter of musical discipline is number, specifically the ratios that govern musical consonances. The first five books of Augustine s treatise apply the theory of ratios not to musical pitch or consonances, but to quantitative verse, that is, to the metrics of the corpus of Latin poetry beloved and taught by the young Augustine. The final book of On Music, on the other hand, uses number and ratios as a way to lead the reader away from the corporeal world of sound; for the ratios first encountered in poetic meters can lead the soul to appreciate harmony as abstract truth, and thence to philosophical knowledge, indeed to knowledge of God. 15 While music as a manifestation of beauty appears repeatedly in the works of Augustine, and while he was obviously moved by song, 16 his chief role in the development of musical theory lies in his establishing two traditions within early Christian thought: (1) in On Christian Doctrine (De doctrina christiana)and Order in the Universe (De ordine) as well as in several other works Augustine justified secular learning, in particular the liberal arts, as integral to the proper formation of the Christian; (2) in these works, and more specifically in his De musica, he set forth the principle that music was one of the disciplines that enabled the mind to transcend sensual reality and rise to a knowledge of rational truth, to a knowledge of the divine. In a civilization that could have all too easily taken a turn toward the suppression of secular learning, Augustine s episcopal and spiritual authority became a crucial apology for preserving and cultivating ancient knowledge concerning the arts, particularly musica. Anicius Manlius Severinus Boethius ( /26) was the most prolific and the most influential scholar in the Platonic tradition of the early Middle Ages. 17 Greatly influenced by Greek writers such as Nicomachus, Ptolemy, Euclid, Plato, and Aristotle, the young Boethius set out to write works treating arithmetic, music, geometry, and astronomy as disciplines that lead the soul to its first encounter with incorporeal knowledge. He expressed little interest in the Roman liberal arts of grammar, rhetoric, and dialectic; 18 in the introduction to his De arithmetica, however, he defined an educational program in the mathematical disciplines that influenced the study of musica for over a millennium. Boethius, following Pythagorean and neo-platonic 15 For a general survey of Augustine s view of music, see Herbert M Schueller, The Idea of Music: An Introduction to Musical Aesthetics in Antiquity and the Middle Ages (Kalamazoo: Medieval Institute Publications, Western Michigan University, 1998), esp. pp See, for example, the famous passage from the Confessions x.33, trans. James McKinnon in SR, pp For a thorough examination of Boethius s thought, see Henry Chadwick, Boethius: The Consolations of Music, Logic, Theology, and Philosophy (Oxford: Clarendon Press, 1981). 18 I imply not that Boethius was not interested in logic, but that logic was not merely an art of elocution for Boethius as it was for earlier Roman writers; indeed, Boethius s translations of Aristotle s Prior and Posterior Analytics testify to Boethius s view of logic s position in philosophy.

7 142 calvin m. bower e.g. (1) (2) (3) (4) 256 : 243 : 216 : 192 = 9 : 8 and 9 : 8 E F G A Figure 5.1 The Pythagorean tetrachord authors before him, held that quantity was divided into two basic genera: discrete quantity or multitude; and continuous quantity or magnitude. The monad,or unity, was the source of discrete quantity, and this genus could increase into infinite multitude; yet its basic element, unity, remained indivisible. Magnitude, or continuous quantity, might be represented by the line or a shape, which was delimited with respect to increasing and growth, but could be infinitely divided. The two basic genera of quantity were, in turn, subdivided into two species: multitude is best represented by number, and every number can be considered in and of itself (even, odd, perfect, square, cube, etc), or it can be considered in relation to another (in ratios and proportions e.g., 2:1, 3:2, or 6:4:2); magnitude is best represented by shapes, and some shapes are fixed and immobile (e.g., a line, a triangle, a cube), while others are in motion (e.g., the sun, the moon, the heavenly spheres). Four areas of study were thus defined by the very nature of quantity: arithmetic pursued number in and of itself; music examined number in ratios and proportions; geometry considered immobile magnitudes; astronomy investigated magnitudes in motion. Boethius described these four disciplines as the quadrivium, the fourfold path by which the soul was led from the slavery of sensual knowledge to the mastery of knowing immutable essences. Musica thus became a necessary prerequisite to the study of philosophy. 19 Boethius opens his Fundamentals of Music (De institutione musica) with a grand juxtaposition of sensual experience and reasoned truth that is worthy of the Roman rhetorical tradition. Of all the mathematical disciplines, music is unique; for music is the most sensual of the arts, and can thus influence behavior, can determine character. Boethius proceeded to develop a theory of sound that was quantitative, and argued that the rational person must cultivate a music structured according to principles that were themselves rational, principles that reflected the most consonant essences found in that species of quantity expressed in beautiful ratios and proportions. For Boethius and indeed for the Pythagoreans and neo-platonists those essences were discovered neither by rational deduction nor by induction from sensual experience; they were revealed truths. The following account represents a condensed paraphrase of the myth from Fundamentals of Music i.10: Pythagoras had long sought the rational criteria that determined musical consonances. One day, by divine guidance, he passed a smithy from which the sounds of musical harmonies emerged. He approached the place with amazement, for pitches sounding consonant with each other seemed to come from the hammers. He examined the weights of 19 See De institutione arithmetica i.1; De institutione musica ii.3.

8 The transmission of ancient music theory into the Middle Ages 143 the hammers and discovered that one weighed 12 pounds, a second 9 pounds, a third 8 pounds, and a fourth 6 pounds. The hammers of 12 and 6 pounds sounded the octave that interval in which the two pitches were most identical. The hammers of 12 and 8 pounds, as well as those of 9 and 6 pounds, sounded the fifth an interval which, next to the octave, was most beautiful. The hammers of 12 and 9 pounds, as well as those of 8 and 6pounds,soundedthefourth thatintervalwhichseemedtobethesmallestconsonance. In this manner Pythagoras discovered the ratios the immutable essences of musical harmonies: the octave lay in the ratio of 2:1; the fifth was determined by the ratio of 3:2; and the fourth was found in the ratio of 4:3. Moreover, since the basic building block of music, the tone, was the di erence between a fourth and a fifth, the ratio of that interval was the di erence between 3:2 (or 12:8) and 4:3 (or 12:9), thus 9:8. 20 The roots of this myth so fundamental to the history of Western musical thought are buried within ancient values and archetypes that can never be fully fathomed. The empirical data o ered in the myth is wholly specious, for hammers of comparable weights would not sound the musical intervals presented in the story. 21 However, the myths and dreams of a civilization are judged not by their empirical truth or falsity, but by the expression of intellectual and spiritual complexes they reveal within a culture. Given the four mathematical values revealed in the myth of the hammers, and given the position that sound was quantitative and that musical intervals could be scientifically measured only by ratios, the Pythagoreans and Platonists unfolded the musical cosmos of the diatonic scale and developed an arithmetic apparatus that presented some of the most rigorous mathematical reckoning known in antiquity and the Middle Ages. The fundamental building block of the Pythagorean scale was the tetrachord, four notes three intervals defined by the fourth. The diatonic tetrachord contained two tones (each 9:8) plus a remainder (limma), which was called the semitone not because it was half of a tone, but because it was less than a whole tone (see also Chapter 4, pp ). The ratio of the remainder, the semitone, was 256:243, a measure defended as the legitimate interval of the semitone at excessive length by Boethius following other Pythagoreans. In keeping with traditional Greek tetrachordal structures, the semitone was the lowest interval of a tetrachord (Figure 5.1). Boethius o ered a history of the Greek tonal system (i.20) that is as mythic in tone as the history of Pythagoras and the smithy but myth had been established by Plato himself as a primary vehicle for leading the reader toward philosophical truths. Two fundamental collections of pitches unfold built on the principle of conjunct and disjunct tetrachords: (1) a two-octave, disjunct system, and (2) an octave-plus-fourth, conjunct system (Table 5.3) For the Latin text of this myth, see Friedlein edn., ; for complete text in English see Bower trans., pp Also see Chapter 10, p See Claude V. Palisca, Scientific Empiricism in Musical Thought, in Seventeenth-Century Science and the Arts, ed. H. H. Rhys (Princeton: Princeton University Press, 1961), pp ; see also Walter Burkert, Lore and Science in Ancient Pythagoreanism, trans. E. L. Minar, Jr. (Cambridge, MA: Harvard University Press, 1972), pp For the Latin text of this mythic history see Friedlein ed., ; for English text, see Bower trans., pp

9 Table 5.3 Disjunct and conjunct systems from Fundamentals of Music Two-octave system (systema teleion) Octave-plus-fourth system (systema synemmenon) Names Names Letters for pitches Modern Xof notes of tetrachords of notes of tetrachords iv.6 11 iv.14 iv.18 pitches XProslambanomenos Proslambanomenos A P A (disjunct) (disjunct) XHypate hypaton Hypate hypaton B A O B XParhypate Parhypate C B N C XLichanos Lichanos E C M D XHypate meson (conjunct) Hypate meson (conj.) H D L E XParhypate Parhypate I E K F XLichanos Lichanos M F I G

10 XMese Mese (conj.) O G H a (disjunct) Trite synemmenon Q bb XParamese diezeugmenon X H G b XTrite Paranete Y T K R c XParanete Nete CC V L E d XNete hyperboleon (conjunct) DD M D e XParanete FF N C f XTrite KK X B g XNete LL O A a 1

11 146 calvin m. bower After all mathematical essences had been exhaustively examined in the course of the first three books of his treatise, Boethius took up the division of the musical ruler (division of the canon), a line divided geometrically over which a string can be placed and notes may be tested by positioning a movable bridge at points of division (see also Chapter 6, pp ). Boethius undertakes this division (1) to demonstrate how the Pythagorean arithmetic and geometric apparatus can shape a whole musical system and (2) to confirm the veracity of the ratios to the sense of hearing. 23 In the course of the monochord division Boethius uses ancient Greek notation, a notation he takes up again when discussing the ancient Greek modes; but equally significant indeed more significant to the history of music theory, Boethius employs various letters to represent geometric points in the division of the ruler, points which in turn designate and represent specific strings or notes. A single pitch within a collection could thus be assigned a discrete symbol, and could be noted by that symbol in subsequent discussions of functions within the collection. 24 While Boethius had no intention of using these letters as any form of notation, the abbreviated, objective representation of a function within a set of pitches clearly becomes possible; a basic step in the development of noting pitches within a collection had been taken. In the opening chapters of his treatise, Boethius developed his threefold division of music: cosmic music (musica mundana), which was subdivided into the harmony of the spheres, the concord of the elements, and the consonance of the seasons; human music (musica humana), which was subdivided into the harmony of the soul and the body, the consonance of the parts of the soul, and the concord of the parts of the body; and instrumental music (musica in instrumentis constituta), which is subdivided into string, wind, and percussion instruments. 25 In the closing chapter of the first book, Boethius elaborated his threefold division of those who might be named musicians : instrumentalists (or performers), poets (or composers), and those who adjudicate performers and composers; only the last class is a true musician, according to Boethius, for only this class is concerned with knowing, through reason, the fundamental essences which determine the value of performances and compositions. 26 Boethius s justly famous divisions of music and musicians link him most closely with the Platonic tradition of musical thought: the essences expressed in ratios pervade every level of being, and by coming to know these essences even in the corporeal world of sound the mind is able to transcend cursory sensory experience and rise to a higher level of knowing; it is reminded of these essences as it comes to know its own 23 While divisions of the chromatic and enharmonic genera are appended to this diatonic division, they are merely ancillary: the diatonic division clearly holds primary position in the theoretical consciousness of the Pythagorean, and the intervals necessary for these divisions (the second semitone and the quarter tone) are derived from diatonic intervals. 24 For Boethius s exposition of Greek notation, see De institutione musica iv.3 4 (Friedlein edn., ; Bower trans., pp ). Boethius employs Latin letters to represent pitches throughout the work, but develops this aspect of theory very extensively in Book IV. 25 See Friedlein edn., ; Bower trans. pp Ibid., ; p. 51.

12 The transmission of ancient music theory into the Middle Ages 147 being and as it studies nature and the cosmos. The goal of learning musica is to ascend to the level of reason. The fundamental principle motivating Platonic music theory is knowing, the acquisition of pure knowledge, and Boethius s threefold division of music and three classes of musicians resonate consistently with that principle. Every legitimate facet of musica was subject to quantification by Boethius: every function in the collection of pitches was calculated with a point on the ruler, was assigned a discrete number, and was noted with a geometric symbol (a letter); even basic elements in the theory of ancient tonality (the tonoi and the harmonia) were reduced to expositions of species of fourth, fifth, and octave quantitative reductions that reveal little of musical function or e ect. The beauty of this theoretical system if one may so speak lies in its internal consistency and its congruence with Platonic ontology and epistemology. Yet the limitations of quantification in ancient musical thought must be recognized. The values that the Boethian musicus applied in his judgments were a priori principles grounded in abstract thought, not principles grounded in experience of actual music. The diatonic system derived from a limited number of ratios was computed with little indeed no reference to a musical repertoire. The names of the notes and tetrachords obviously had some functional correspondence in their origins, yet in the Latin theoretical tradition of the early Middle Ages no musical function or character is ascribed to any note; the construct exists as an abstract entity determined by arithmetic principles. While the Platonists including Boethius cannot be described as philosophical puritans taking no pleasure in song, they can be accused of abstracting values and principles from sound and moving ever upwards toward pure reason, thereby never returning to describe and analyze the structures and functions that dwelt in the sonorous matter of the music that, in the beginning, had so moved them. Musica and the early medieval encyclopedists Two writers occupy a crucial position in the transmission of ancient musical thought in the later Middle Ages, not because of the originality or significance of their thought, but because of the particular intellectual tradition within Western Christendom that they cultivated with respect to musica. Cassiodorus (c ) and Isidore (c ) were Christian intellectuals deeply influenced by the tradition of Christian humanism formulated by Augustine in such works as De ordine and De doctrina christiana. Each in his own way set out to pass secular learning on to his community and to posterity. Cassiodorus had originally intended to found a Christian university in Rome, but following the decline and conquest of Rome around the middle of the sixth century, he retired to his native estate in the south of Italy and established a monastery where he compiled a great library of sacred and secular learning. Cassiodorus wrote a great twovolume encyclopedic work for his community, the Introduction to Divine and Human Readings. His first book examined Biblical and patristic scholarship, while his second

13 148 calvin m. bower book discussed secular learning. The seven liberal arts represented the organization of secular learning for Cassiodorus (see Table 5.2); his extended treatment of the first three arts grammar, rhetoric, and dialectic links his program of secular learning to the Roman rhetorical tradition. Yet he describes the arts of Boethius s quadrivium as mathematica, and, while their treatment is much more cursory than the arts of elocution, their sequence and organization reflect elements of the Platonic and neo- Pythagorean tradition. 27 Isidore, an influential secular bishop residing in Seville, compiled his Etymologies in the early seventh century, and this encyclopedic work became one of the most universally known books of the Middle Ages. The Etymologies commences with a treatment of the liberal arts. And while Isidore obviously owes a great debt to the work of Cassiodorus, his order and treatment of the arts is rather distinctive: musica is given the rather unusual position of the sixth art, placed between geometry and astronomy (see Table 5.2). 28 Both Cassiodorus and Isidore were leaders of Christian groups who wrote principally as a means of establishing an intellectual tradition within their respective communities a monastery for the former, a diocese for the latter. Because of their o ces and their spiritual characters, they introduced two new dimensions into reflections concerning music: (1) the presence of music in Biblical literature and (2) the centrality of singing in Christian worship. Both writers draw on Biblical passages to demonstrate the power of music, thereby supplementing pagan myth with Judeo-Christian narratives. Both authors are clearly moved by the singing of psalms in the liturgy, and begin to integrate the spheres of secular learning concerning musica with the sacred tradition of singing in worship. Cassiodorus considers the discipline of music essential to the study of the psalms, particularly since they make reference to so many musical instruments; moreover he discerns the active presence of musical concord in the singing of psalms, active both in the harmony immediately present in singing and the harmony achieved between the soul and God brought about through prayer and praise. 29 Isidore recognizes the ecclesiastical o ce of cantor, and seems so influenced by the practical activity of singing that subtle but fundamental changes in basic definitions are found in his writings: music is defined as skill ( peritia) rather than knowledge (scientia), 30 and musica is said to consist in songs and chants. 31 These authors thus began to break 27 Concerning Cassiodorus, see Günter Ludwig, Cassiodor: Über den Ursprung der abendländischen Schule (Frankfurt, 1967); James O Donnell, Cassiodorus (Berkeley, Los Angeles, and London: University of California Press, 1979); Jacques Fontaine, Cassiodore et Isidore: L évolution de l encyclopédisme latin du vi e au vii e siècle, in Atti della settimana di studi su Flavio Magno Aurelio Cassiodoro (Cosenza-Squillace settembre 1983), ed. S. Leanza (Catanzaro: Soveria Mannelli, 1986), pp ; Ubaldo Pizzani, Cassiodoro e le discipline del quadrivio, in ibid., pp Concerning Isidore, see Jacques Fontaine, Isidore de Séville et la culture classique dans l Espagne Wisigothique, 2nd rev. edn., 3 vols (Paris: Etudes Augustiniennes, 1983), esp. vol. i, pp See Expositio psalmorum, ed M. Adriaen, Corpus Christianorum (1958), Series latina 98, p Etymologies iii.15: musica est peritia modulationis sono cantuque consistens. 31 Ibid., I.2: musica quae in carminibus cantibusque consistit.

14 The transmission of ancient music theory into the Middle Ages 149 down the boundaries that isolated the ancient discipline of musica that collection of facts known by the orator and that Platonic sphere of learning leading to abstract knowledge from the practice of music that was rapidly becoming an ever more significant part of the liturgy. They also played a crucial role in cultivating the tradition established by Augustine that secular learning, particularly the liberal arts, was an integral part of Christian education. Formation of a medieval theoretical tradition in the Carolingian and post-carolingian eras The reception of ancient theory in the ninth and early tenth centuries In the closing years of the eighth century and the opening decade of the ninth, Europe achieved a degree of cultural and political unity under Charlemagne (d. 814) that remains exceptional in the entire history of the West. Every aspect of culture clerical and secular education, the Latin language, theology, the liturgy and the chant sung therein, scriptural texts, even the script employed in copying manuscripts was subject to the Carolingian principle of unification through established order and style. Alcuin of York (d. 804), one of the leading scholars brought into educational reforms by Charlemagne, set both the intellectual tone and the program of study for his age when he compared the seven liberal arts with the seven pillars of Salomon s temple, and described them as seven steps leading to wisdom. 32 Thus Alcuin grounded Carolingian intellectual and spiritual formation in both the Roman rhetorical tradition and the Platonic tradition of the early Middle Ages, and gave musica an important place in that program. The acquisition of manuscripts formed an important part of Charlemagne s conquests, and scholars such as Alcuin and Theodulf of Orléans (d. 821) encouraged the transport of manuscripts from remote boundaries of the new empire to Aachen, the intellectual and geographical center of the Carolingian court. The court library itself drew more scholars to the court, and the scholars in turn brought additional texts with them that became part of the library. 33 An important textual movement referred to by scholars as the (Delta) tradition was introduced to the Carolingian court through the second book of Cassiodorus s Introduction to Divine and Human Readings. 34 This tradition brought together the justification for secular learning formulated by Cassiodorus, 32 De vera philosophie (PL 101, ), 852b 853b. 33 On manuscript culture in the Carolingian period, see Bernhard Bischo, Manuscripts in the Age of Charlemagne, in Manuscripts and Libraries in the Age of Charlemagne, trans. and ed. Michael Gorman (Cambridge: Cambridge University Press, 1994), pp ; and The Court Library of Charlemagne, in ibid., pp Concerning the tradition, see Bischo, The Court Library of Charlemagne, p. 62.

15 150 calvin m. bower Table 5.4 Authors and texts in Carolingian and post-carolingian eras Johannes Scotus Eriugena (c. 810 c. 877) Remigius of Auxerre (c. 841 c. 908) Aurelian of Réôme Glossa maior in musicam Boethius Annotationes in Marcianum Commentum in Martianum Capellam Musica disciplina (lost half of 9th c.) Regino of Prüm (c ) Epistola de harmonica institutione (c. 900) Musica et Scolica enchiriadis (late 9th c.) Hucbald of Saint-Amand (c ) Musica (c. 900) Berno of Reichenau (c ) Prologus in tonarium (after 1021) Hermanus Contractus ( ) Musica (before 1054) Wilhelmus of Hirsau (d. 1091) Musica (before 1069) Theogerus of Metz (d. 1120) Musica (before 1120) [Pseudo-Odo] Dialogus de musica (c. 1000) Guido of Arezzo (c. 900 c. 1050) Prologus in antiphonarium (before 1025) Micrologus (1025/26) Regule rhythmice (1025/26) Epistola ad Michahelem (after 1028) a number of excerpts from Augustine emphasizing the value of education (from On Music, On Christian Doctrine, The Order of the Universe, The City of God, and First Meanings in Genesis), and a précis of Boethius s Fundamentals of Arithmetic. Thus the principle of including secular learning specifically the liberal arts in Christian education established by Augustine and developed by Cassiodorus was taken up by scholars surrounding Charlemagne, and the liberal arts were given a privileged position in Carolingian learning. Two works that were particularly significant in the tradition of musica began to be copied in and around the court of Charlemagne and dispersed throughout the empire: Martianus Capella s Marriage of Mercury and Philology and Boethius s Fundamentals of Music. An explicit reference to Boethius s musical treatise is even found among the texts brought together in the textual tradition of Cassiodorus used in the royal library. From these works early Carolingian scholars learned basic elements of Greek musical theory within the context of liberal learning. But both of these works were transcendent in tone rather than practical, and in their early reception they did little to focus the scholar s attention on the vital tradition of liturgical chant that was as integral to Carolingian civilization as the liberal arts. The nature of the early ninth-century reception of musica can be traced using the extensive commentary copied into the margins and between the lines of manuscripts containing Martianus s and Boethius s treatises. The writers of these glosses were obviously scholars and philosophers, not musicians; for their primary concerns were

16 The transmission of ancient music theory into the Middle Ages 151 (1) explanation of Greek proper names and places using medieval principles of etymology, (2) definitions and explanations of technical terms inherited from the Greeks, (3) discussion of basic elements of Greek music theory particularly the basic building blocks of the Greek musical systems, and (4) relating the whole of the discipline of music to the broader issues of philosophy. These scholars were particularly attracted to the advanced mathematical problems discussed in Boethius s text, and wrote numerous commentaries on the semitone, the apotome (2,187 : 2,048), and the Pythagorean comma (531,441:524,288). Their interest in ratios led them to an obsession with musical pitch, with the consequence that other parameters of music were largely ignored. Conspicuously absent from the early ninth-century commentaries on classical musical texts is any extended discussion of practical music. 35 As the Carolingian kingdom was divided among his sons following the death of Charlemagne, and as the political unity of Europe waxed and waned during the course of the ninth century as kingdoms were repeatedly divided and unified, the vital culture that had originally been associated with the court moved into monasteries. The manuscript traditions originally associated with scholars not necessarily attached to a given location became established in monastic centers such as Corbie, Saint-Riquier, Saint- Denis, Fleury, Tours, Saint-Amand, and Ferrières. While monastic scholars were by nature drawn to theories of transcendence set forth in the Platonic tradition of musica, the singing of the liturgy played such a central role in their daily lives that they were unable or unwilling to divorce musical speculation from liturgical practice. Thus in the marginal commentaries on Boethius s musical treatise formulated in the late ninth century, musical intervals defined by ratios are likewise exemplified by musical examples taken from chant. 36 Pythagoras s discovery of the four ratios governing musical consonances is allegorized to represent the four tonal (or modal) qualities of liturgical chant: protus, deuterus, tritus, and tetrardus. 37 In short, monastic scholars began to connect concrete musical practice with abstract musical thought, and the synthesis that was to become medieval musical theory had begun. The closing decades of the ninth century and the opening decade of the tenth also witness the beginnings of writing music theory; for two theorists from these years may be cited: Aurelian of Réôme and Regino of Prüm. Yet while treatises have been preserved associated with the names of these two monastic scholars, the nature of the texts associated with their names resembles more a centonization of musical thought than the purposeful writing of systematic theory. The textual traditions of treatises 35 On the nature of these commentaries, see Calvin M. Bower, Die Wechselwirkung von philosophie, mathematica und musica in der karolingischen Rezeption der Institutio musica von Boethius, in Musik und die Geschichte der Philosophie und Naturwissenschaften im Mittelalter, ed. Frank Hentschel (Leiden, Boston, Cologne: Brill, 1998), pp ; and Mariken Teeuwen, Harmony and the Music of the Spheres: Ars musica in Ninth-century Commentaries on Martianus Capella (Ph.D. diss., University of Utrecht, 2000). While no references to practical music are found among the glosses on Boethius, Teeuwen has found references to organum and sequentia among ninth-century glosses on Martianus; nevertheless no systematic discussion of practical music is found in any of the early glosses. 36 See, e.g., Glossa maior in musicam Boethii i,3, Ibid., i,10,143; i,10,146; i,10,151; i,10,153.

17 152 calvin m. bower attributed to these authors is extremely complex, for many shorter sections of their texts have been preserved as fragments in other texts independent of the treatises as a whole. Moreover, fragments from commentary on Martianus Capella and Boethius, as well as excerpts from Cassiodorus and Isidore, are taken into these treatises with little or no acknowledgment of their sources. The texts associated with Aurelian and Regino thus reflect the active reception of musica in late ninth-century monastic circles, and the conscious association of musica with the musical practice of liturgical chant. Ultimately the act of music-theoretical texts being copied and circulated from one monastic center to another is more critical to the formation of a tradition of music theory than the fact of various texts being compiled by a single agent or author. Nevertheless important first steps in the development of a mainstream of later medieval theory are taken in the texts associated with Aurelian and Regino. A fundamental emphasis of these treatises is knowing the unchanging essences of Pythagorean ratios. The myth of Pythagoras as transmitted by Boethius is repeated in both treatises, and each develops the basic theory of ratios as a fundamental element in the theory of musica. The texts assembled by Aurelian 38 introduce the important distinction between musicus and cantor; following Boethius s definition of musicus, the text argues that the true musician knows music as a speculative discipline, while the cantor merely applies basic skills. 39 Yet the concept of cantor does not appear in the Boethian text, and the dichotomy between musicus and cantor reveals the degree to which the philosophical discipline of musica is being assimilated into the practical musical world of the ninth-century abbey. Regino, like Aurelian, draws heavily on the Platonic tradition of early musica, but does so in a manner original and appropriate to ninth-century monastic spirituality and practice. While the treatise attributed to Regino pulls together virtually every thread of early medieval musical thought including an explication of the Greek musical system it o ers a musical ontology that rationalizes the systematic study of chant as well as the ancient discipline of musica. Music exists on two levels: natural music and artificial music. Natural music (musica naturalis) is defined as that music sung by the human voice in divine praises 40 and that music which governs the celestial spheres; artificial music (musica artificialis) is defined as that music performed through human artifice, namely instrumental music. 41 Four tones (toni) form the origins of natural music, the four fundamental pitches (principia)that govern the tonal structure 38 Concerning Aurelian, see Lawrence Gushee, The Musica disciplina of Aurelian of Réôme: A Critical Text and Commentary (PhD. diss., Yale University, 1962); but see also Michael Bernhard, Textkritisches zu Aurelianus Reomensis, Musica disciplina 40 (1986), pp I follow Bernhard s revised (later) dating of the texts assembled under Aurelian s name. In a recent study Barbara Haggh argues for placing the origins of Aurelian s treatise as early as 843 and 856, with revisions of the treatise continuing into the next two decades; see Traktat Musica disciplina Aureliana Reomensis. Proweniencja I Datowanie, Muzyka 2 (2000), pp (with English summary pp ). Finally, see the discussion in Chapter 11, pp Aurelian, Musica disciplina, Chapter 7 (Gushee edn., p. 77). 40 Regino, Epistola de harmonica institutione, iii,1 (Bernhard edn., p. 42); v,5 (Bernhard edn., p. 45). 41 Ibid., v,91 93; p. 51.

18 The transmission of ancient music theory into the Middle Ages 153 of chant: protus, deuterus, tritus, and tetrardus; the four tones are described as fountains, from which eight tones flow, four authentic and four plagal. 42 Five tones and two semitones, on the other hand, govern artificial music, the intervals that form the basic content of musica,and one comes to know these intervals through instrumental music and through the study of arithmetic theory, i.e., through the liberal art of musica. 43 But these two levels of being are not independent of each other: the experience of artificial music through instruments and the study of musica as a liberal art are basic to the knowledge of natural music, for musical knowledge begins with the artificial and rises to the natural. Natural music is proved by the artificial; things invisible are demonstrated by the visible. 44 Fundamental to both of these early medieval theoretical treatises are the eight modes as tonal principles organizing music. Both treatises are associated with tonaries, extended catalogues of individual chants organized according to the four primary tones (protus, deuterus, tritus, and tetrardus) that are in turn subdivided into plagal and authentic species. Independent tonaries and catalogues of chants combined with musical treatises played a very significant role in the manuscript culture of cantus and musica during the Carolingian period, and they remained practical and theoretical tools for the cantor and musicus until the end of the Middle Ages. 45 The modes of liturgical music form a crucial new element in the systematic study of music in the ninth century, for they were unknown to the treatises discussed in the first section of this chapter. The introduction of the modes as a subject of systematic musical reflection is obviously an answer to the practical as well as theoretical needs of monastic culture in the ninth century, and the cross-fertilization between the philosophical tradition of musica and the practical tradition of chant defines a new chapter in the study of music theory. But before the initial phases of the new chapter can be traced, the four tones protus, deuterus, tritus,and tetrardus must be examined as fundamental parts of a musical system independent of musica. The special place of Musica enchiriadis and the four qualities Paths of transmission and reception have been easy to trace to this point in the history of music theory in the early Middle Ages; for, even if some textual transmissions are complex, the footprints of earlier texts, authors, and intellectual traditions have been easily identifiable. The case of a complex of texts and treatises that might be named the enchiriadis tradition is strikingly di erent. The name enchiriadis is taken from the musical treatise Musica enchiriadis,the musical text that was copied more than any other theoretical text during the ninth and tenth centuries. This treatise, the author of which 42 Ibid., iii, 2 4; p Ibid., iv, 2 6; p Ibid., v, 98 99; p. 51. Concerning the philosophical background of natural and artificial music, see Calvin M. Bower, Natural and Artificial Music: The Origins and Development of an Aesthetic Concept, Musica Disciplina 25 (1971), pp See Michel Huglo, Les Tonaires: inventaire, analyse, comparaison (Paris: Société Française de Musicologie, 1971).