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Contents

Music from the Earliest Notations to the Sixteenth Century

PUTTING IT INTO PRACTICE

Chapter:
CHAPTER 8 Business Math, Politics, and Paradise: The Ars Nova
Source:
MUSIC FROM THE EARLIEST NOTATIONS TO THE SIXTEENTH CENTURY
Author(s):
Richard Taruskin

So much for the theory, which like all scholastic theory had to be exhaustive. The implications of all this tedious computation for musique sensible, by appealing contrast, were simple, eminently practical, and absolutely transforming. To begin with, maximodus was pretty much a theoretical level (except in the tenors of some motets) and can be ignored from here on. Moreover, in practical music it was the breve, rather than the minim, that functioned as regulator. Its position in the middle of things made calculations much more convenient. Lengths could be thought of as either multiples or divisions of breves. But then, as the “tempus” value, it had long been the basic unit of time-counting. Petrus de Cruce’s use of “division points” (puncta divisionis) had already established it as the de facto equivalent of the modern “measure” (or bar, as the British say, and as we say when we aren’t being too fastidious). It was this measure and its divisions, then, rather than the unit value and its multiples, that defined mensurations for practical musicians and those who instructed them.

So we can henceforth confine our discussion to the levels of tempus and prolation—that is, the number of semibreves in a breve and of minims in a semibreve. The former level defines the number of beats in a measure; the latter, the number of subdivisions in a beat. And that, by and large, is the way we still define musical meters. (One must include the qualifier “by and large” because our modern concept of meter includes an accentual component that is not part of Ars Nova theory.)

We end up with four basic combinations of tempus (T) and prolation (P):

  1. 1. Both perfect (tempus perfectum, prolatio major)

  2. 2. T perfect, P imperfect (tempus perfectum, prolatio minor)

  3. 3. T imperfect, P perfect (tempus imperfectum, prolatio major)

  4. 4. Both imperfect (tempus imperfectum, prolatio minor).

The first combination, with three beats in a bar and three subdivisions in a beat, is comparable to our modern compound triple meter . The second, with three beats in a bar and two subdivisions in a beat, is like “simple” (or just plain) triple meter . The third, with two beats in a bar and three subdivisions in a beat, resembles compound duple meter ; and the fourth, with two beats in a bar and two subdivisions in a beat, is like our “simple” (or just plain) duple meter .

The resemblance between these Ars Nova mensuration schemes and modern meters is notoriously easy to overdraw. It is worth repeating that “meter,” to us, implies a pattern of accentuation (strong and weak beats) whereas mensuration is only a time measurement. And it is also worth pointing out that when modern meters are compared, or when passing from one to another, it is usually the “beat” (the counterpart to the semibreve) that is assumed to be constant, whereas in Ars Nova mensuration the assumed constant was either the measure (the breve) or the unit value (the minim).

Because the beat (called the tactus, the “felt” pulse) was a variable quantity within the Ars Nova mensuration scheme, and because authorities differed as to whether the measure (tempus) was also a variable, an ineradicable ambiguity remained at the heart of the system that had to be remedied over the years by a plethora of ad hoc auxiliary rules and signs. Eventually the whole field became a jungle and a new notational “revolution” became necessary. (It happened around the beginning of the seventeenth century, and we are still living with its results.) Still, the extraordinary advance Ars Nova notation marked over its predecessors in rhythmic versatility and exactness is evident, and unquestionably amounted to technical progress. Everything that was formerly possible to notate was still possible under the new system, and a great deal more besides. As Jehan des Murs triumphantly observed, as a result of the Ars Nova breakthroughs “whatever can be sung can [now] be written down.”

But do not confuse progress in notation with progress in music. In particular, do not think for a moment that duple meter was “invented” in the fourteenth century, as often claimed, just because the means of its notation and its “artful” development were provided then—as if two-legged creatures needed the elaborate rationalizations of the Ars Nova in order to make music to accompany marching or working or dancing. As Jehan’s triumphant claim itself implies, “musique sensible” surely employed regular duple meter long before there was a way of notating it—and had, no doubt, since time immemorial. The unwritten repertory was then, and has always remained, many times larger than the literate repertories that form the main subject matter of this or any history text.

But even if the “imperfect mensuration” of the Ars Nova had had its origins in speculation about musical analogues to squares and cubes, and ultimately in speculation about how music might best represent God’s cosmos, it nevertheless made possible the unambiguous graphic representation of plain old duple meter, and willy-nilly provided a precious link between what had formerly been an unwritable and historically unavailable practical background and the elite “artistic” or speculative facade. Lofty theory—the loftiest yet and perhaps the loftiest ever—had inadvertently provided the means by which musical art could more directly reflect the music of daily human life.

Citation (MLA):
Richard Taruskin. "Chapter 8 Business Math, Politics, and Paradise: The Ars Nova." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 5 Dec. 2019. <https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008003.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 8 Business Math, Politics, and Paradise: The Ars Nova. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 5 Dec. 2019, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008003.xml
Citation (Chicago):
Richard Taruskin. "Chapter 8 Business Math, Politics, and Paradise: The Ars Nova." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 5 Dec. 2019, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008003.xml