CHAPTER 3

Retheorizing Music

NEW FRANKISH CONCEPTS OF MUSICAL ORGANIZATION AND THEIR EFFECT ON COMPOSITION

MUSICA

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.

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 Greekinfluenced 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