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Music from the Earliest Notations to the Sixteenth Century

CHAPTER 3 Retheorizing Music

New Frankish Concepts of Musical Organization and their Effect on Composition

CHAPTER 3 Retheorizing Music
Richard Taruskin

Richard Taruskin


When musicians thought “theoretically” about music—that is, made systematic generalizations about it—before the tenth century, they usually did so in terms of the quadrivium, the late-classical postgraduate curriculum, in which music counted as one of the arts of measurement. What was measurable was what was studied: abstract pitch ratios (we call them intervals) and abstract durational ratios (we call them rhythms, organized into meters). Reducing music to abstract number was a way of emphasizing what was truly “real” about it, for late-classical philosophy was strongly influenced by Plato’s doctrine of forms. A Neoplatonist believed, first, that the world perceived by our sense organs was only a grosser reflection of a realer world, God’s world, that we perceive with our God-given capacity for reasoning; and, second, that the purest form of reasoning was numerical reasoning, because it was least limited to what our senses tell us. Education meant the development of one’s capacity to transcend the limitations of sense and achieve comprehension of “essences,” purely rational, quantitative concepts untouched by any “stain of the corporeal.”1 A medieval treatise on music theory, then, emphasized musica speculativa (we may call it Musica for short), “music as reflection of the real” (from speculum, Latin for looking glass or mirror).2 Such a treatise had as little to do as possible with actual “pieces of music,” or ways of making them, for such music was merely music for the senses——unreal and (since real meant divine) unholy. The two most-studied late-classical texts on Musica were De musica (“About Musica”) by none other than St. Augustine (Aurelius Augustinus, 354–430), the greatest of the Fathers of the Christian Church, and De institutione musica (“On the organization of Musica”) by Anicius Manlius Severinus Boethius (ca. 480–ca. 524), the Roman statesman and educational reformer who first proposed the division of the liberal arts curriculum into the trivium and the quadrivium. Both of these books, but especially the one by Boethius (which was virtually rediscovered by the Franks), were mainstays of the Carolingian academic curriculum instituted by Alcuin.

Chapter 3 Retheorizing Music

fig. 3-1 St. Augustine, depicted in an eleventh-century French manuscript of his treatise “On Baptism,” disputing in 411 with Felicianus of Musti, a Donatist bishop, who represented a schismatic sect that practiced rebaptism of the righteous (comparable to the “rebirth” of Protestant fundamentalists in later periods).

St. Augustine’s treatise, completed in 391, is the sole survivor from an enormous projected set of treatises that would have encompassed the whole liberal arts curriculum. It covers nothing but rhythmic proportions (quantitative metrics) and contains a famous definition of music——as bene modulandi scientia, “the art of measuring well”—that was quoted as official doctrine by practically every later medieval writer. The treatise ends with a meditation, reminiscent of Plato’s dialogue Timaeus, on the theological significance of the harmonious proportions with which it deals, and the way in which they reflect the essential nature of the universe. (The Timaeus, translated by Cicero, was the only Platonic text known to late-classical Latin writers.) Boethius’s treatise covers much more ground than Augustine’s. It consists largely of translations from the Hellenistic writers Nicomachus and Ptolemy. (The term “Hellenistic” refers to the Greek-influenced culture that flourished in the non-Greek territories conquered by Alexander the Great.) It thus became the sole source of medieval knowledge of Greek music theory, which included the Greater Perfect System, a scale constructed out of four-note segments called tetrachords; and also the Pythagorean classification of consonances (simultaneous intervals). The treatise also contained directions for representing pitch intervals in terms of spatial ratios, which made possible the construction of “laboratory instruments” called monochords (later to be described in more detail) for demonstrating number audibly, as sound.

While Greek music theory still involved practical music for Nicomachus and Ptolemy (who lived in the second century ce in Arabia and Egypt, respectively), by the time of Boethius the actual music practiced by the ancient Greeks had fallen into oblivion, along with its notation. Accordingly, Boethius’s treatise concerns not practical music but abstract Musica, as the author declares quite explicitly.

Boethius inherited two transcendent ideas from the Neoplatonists: first, that Musica mirrored the essential harmony of the cosmos (an idea we have already encountered in Augustine); and, second, that owing to this divine reflection it had a decisive influence on human health and behavior. This was known as the doctrine of ethos, from which the word “ethics” is derived. Audible music (musica instrumentalis, “music such as instruments produce”) is thus only a gross metaphor for the two higher and “realer” levels of Musica, perhaps best translated in this context as “harmony.” At the top there was the harmony of the cosmos (musica mundana), and in the intermediate position there was the harmony of the human constitution (musica humana), which musica instrumentalis—depending on its relationship to musica mundana—could either uplift or put awry. All of this is most effectively expressed not in words but in a famous manuscript illumination of the thirteenth century, fully seven hundred years after Boethius (Fig. 3-2). In each of the three panels of this illumination, “Musica” points to a different level of her manifestation. In the top panel Musica points to a representation of the universe with its four elements: earth, air, fire (the sun), and water. The sun and moon further represent the periodic movements of the heavens, an aspect of measurable “harmony.” In the middle panel Musica points to four men representing the four “humors,” temperaments, or basic personality types—that is, the four types of “human harmony.” The proportions of these humors were thought to determine a person’s physical and spiritual constitution: the “choleric” temperament was ruled by bile, the “sanguine” by blood, the “phlegmatic” by phlegm, and the “melancholic” by black bile. The four humors mirror the four elements; thus, human harmony is a function of the celestial. In the bottom panel we find musica instrumentalis, the music that we actually hear. Musica is reluctant to point; instead, she raises an admonishing finger at the fiddle player, obviously no disciple of hers but a mere sensory titillator. Whatever its relation to actual sounding music, the idea of Musica had remarkable staying power.

One who has mastered Musica, Boethius concluded, and only such a one, can truly judge the work of a musician, whether composer or performer. The composer and performer are after all concerned only with music, a subrational art, while the philosopher alone knows Musica, a rational science. The stringent differentiation between music and Musica, and their relative evaluation, were easily translatable from Platonist into Christian terms and remained standard in music treatises until the fourteenth century and even beyond. The idea that music was ideally a representation of Musica remained current in certain circles of musicians, and in certain genres of music, even longer than that.

Chapter 3 Retheorizing Music

fig. 3-2 Frontispiece of a mid-thirteenth-century manuscript—Florence, Biblioteca Medicea Laurenziana, MS Pluteo 29.I—representing the musical cosmology described by Boethius in De institutione musica.

At the height of the Carolingian renaissance, the liberal arts were studied at the great Benedictine abbeys, such as St. Gallen (where the Irish monk Moengal instructed the likes of Notker and Tuotilo), St. Martin at Tours (where Alcuin himself taught beginning in 796), St. Amand at Tournai (now in the southern, French-speaking part of Belgium), and Reichenau (on an island in Lake Constance, Switzerland). The libraries of all of these monasteries contained copies of Boethius’s treatise on music, and Neoplatonist ideas about Musica were incorporated as theological underpinning into liturgical music study. At the same time, however, the pressures of liturgical reorganization and chant reform created the need for a new kind of theoretical study, one that served the purposes not of theological or ethical indoctrination but of practical music making and memorization. Beginning very modestly, this new theoretical enterprise, and the documents it generated, led to a complete rethinking of the principles not of Musica but of actual music, as we understand the term today. Its repercussions were nothing short of foundational to the tradition of “Western music,” however we choose to define that slippery term.


(1) Scolica enchiriadis, in Martin Gerbert, ed., De cantu et musica sacra, Vol. I (St. Blasien, 1774), p. 196.

(2) The informal distinction proposed here between music and Musica follows Hendrik van der Werf’s longstanding and useful habit. See, for example, “The Raison d’être of Medieval Music Manuscripts,” Appendix to his The Oldest Extant Part Music and the Origin of Western Polyphony (Rochester: H. van der Werf, 1993), pp. 181–209.

Citation (MLA):
Richard Taruskin. "Chapter 3 Retheorizing Music." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 2 Aug. 2021. <https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-chapter-003.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 3 Retheorizing Music. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 2 Aug. 2021, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-chapter-003.xml
Citation (Chicago):
Richard Taruskin. "Chapter 3 Retheorizing Music." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 2 Aug. 2021, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-chapter-003.xml