We use cookies to enhance your experience on our website. By continuing to use our website, you are agreeing to our use of cookies. You can change your cookie settings at any time. Find out more


Music from the Earliest Notations to the Sixteenth Century


CHAPTER 8 Business Math, Politics, and Paradise: The Ars Nova
Richard Taruskin

In keeping with the idea of discordia concors, which emphasized belief in a hidden order and unity behind the world’s apparent chaos, composers of Ars Nova motets placed particular emphasis on subtle patterning that unified and reconditely organized the heterogeneous surface of their work. One can bring this aspect of Tribum/Quoniam/MERITO to light by comparing mm. 10–13 in the transcription with mm. 34–37. The repetition thus uncovered initiates an interlocking series of periodicities that crosscut the more obvious periodicity of the tenor. The same melodic phrases in the triplum and duplum will turn up again in mm. 58–62, and the triplum-duplum combination in mm. 22–25 will recur in mm. 46–49 and again in mm. 70–73. Every one of these spots corresponds to a progression in the tenor from E to D, which crosscuts the tenor’s more obviously repeating rhythmic ordo or talea (since in every case the E is the end of an ordo and the D is the beginning of another). And the thrice-recurring pair of alternating repetitions in the upper voices—mm. 10–13/22–25, 34–37/46–49 and 58–62/70–73 (ABABAB)—crosscut the tenor’s double cursus, which begins right between the members of the middle pair (just after our example breaks off). This is an especially significant hidden periodicity, for it imposes on the structure of the motet at its most encompassing level a “perfect/imperfect” duality (three repeated pairs vs. two tenor cursus) that reflects the duality of note-value relationships at the heart of the Ars Nova system.

That duality is “thematized”—made the subject of demonstration—in a later motet by Vitry, Tuba sacre/In Arboris/VIRGO SUM (Fig. 8-4; Ex. 8-3), which displays with a special elegance the peculiar, highly persuasive combination of seriousness and playfulness that was so characteristic of the Ars Nova.

Here the tenor consists of a chant fragment (color) bearing the incipit Virgo sum, (“I am a virgin”), a verse that figures meekness and purity, supporting (and “coloring,” in the sense of commenting on) a pair of solemn meditations in the triplum and motetus concerning the mysteries of Christian doctrine and the necessity of reconciling faith with reason. These earnest sermons, for all their gravity, are nevertheless cast in graceful melodies full of the characteristic “prolation lilt” that we encountered in the previous motet as well, and that must reflect the style of the contemporary song repertory. (Vitry is known to have composed French songs in addition to Latin motets, but neither they nor any other French songs survive from the period of his main activity.) Also songlike are the mode and the harmonic idiom. Up to the final cadence in each cursus—which comes as a harmonic surprise—the tunes in the upper parts depart from and cadence on the note C, so that they are in the functional equivalent of our major mode. As Giraldus Cambrensis (quoted in chapter 5) remarked at the end of the twelfth century, that mode was used in unwritten musics far more prevalently than in chant-influenced literate ones. There is no better example of Vitrian C-major “poplyricism” than the unaccompanied motetus melisma that launches the introitus to this very high-minded motet. And no less emphatically sweet are the harmonies at strategic moments. Note the long-sustained full triads (the first we’ve seen) at tenor entrances and cadences such as mm. 16, 25, 43, and 46. Also self-evidently playful are the hockets between the triplum and the motetus that regularly recur at the ends of taleae. A motet with such prominent hockets (to recall a comment by Johannes de Grocheio) is at once high-minded and hot-tempered. Entertainment values are unabashedly summoned to assist lofty contemplation.

More Elaborate Patterning

fig. 8-4 Phillippe de Vitry, Tuba sacre/In arboris/VIRGO SUM (Ivrea, Biblioteca Capitolare, MS 115, fols. 15v–16). The tenor notes that appear gray are notated in red ink to show a hemiola (3:2) proportion.

More Elaborate PatterningMore Elaborate PatterningMore Elaborate Patterning

ex. 8-3 Philippe de Vitry, Tuba sacre/In Arboris/VIRGO SUM

As for the tenor, its rhythms are cast in no simple modal ordo, but in an arbitrary arrangement of values adding up to 24 breves, as follows (a number in italics indicates a rest): 4 2 2 2 2 3 2 1 2 4. Note the odd number in the middle. The composer might have indicated that one perfect long within a prevailing duple modus by simply dotting it—as we still do, even if we do not know that we are following the method introduced by the Ars Nova for converting imperfect values into perfect ones. Another way of indicating the perfect long would have been by applying to it an explicit mensuration sign. The way that Vitry actually did it was playfully ostentatious. He supplied the tenor with a supplementary performance direction—called a rubric (after the red ink in which such things were often entered) or a canon, meaning “rule”—that reads, Nigre notule sunt imperfecte et rube sunt perfecte (“The little black notes are imperfect and the red ones are perfect”). Like so many of Philippe de Vitry’s innovations, this one became standard practice. As a later theorist wrote, “red notes are placed in motets for three reasons, that is, when they are to be sung in some other mode, or other tempus, or other prolation than the black notes, as appears in many motets composed by Philippe.”7

In every talea, then, six breves’ worth of musical time is organized by perfect longs (that is, in “perfect minor modus”), requiring the use of red ink. It is here, of course, at the tenor’s friskiest moment, that the hockets appear in the texted parts. Their rhythms, like the rhythm of the tenor, are the same each time. After three taleae, the note values are halved to coincide with the second cursus of the color, so that the tenor proceeds twice as “fast,” and the red notes denote six semibreves’ worth of time organized in perfect tempus. The frisky tempus shift becomes much friskier, since the perfect breve that now begins the red-ink patch crosscuts the basic tempus unit, producing a true syncopation—something that had never before been possible in notated music. Needless to say, the hockets in the upper parts get friskier, too; and again these puckish rhythms reappear each time the tenor syncopation returns. This passage introduces what was a permanent stylistic acquisition for fourteenth- and fifteenth-century music. “Coloration” (the use of a contrasting ink color, or, later, the filling in of notes ordinarily left “white”) became a standard way of changing tempus in midstream to produce fascinating rhythms.


(7) Aegidius of Murino in Coussemaker, Scriptorum, Vol. III, p. 125.

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. 4 Oct. 2015. <http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008008.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 4 Oct. 2015, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008008.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 4 Oct. 2015, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008008.xml