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Music from the Earliest Notations to the Sixteenth Century


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

Formal introduction to Guillaume de Machaut (d. 1377), the greatest poet-musician of mid-fourteenth-century France, can wait until the next chapter. Suffice it for now to say that he was the chief extender of the trouvère tradition, to which he gave a new lease on life by channeling it into new styles and genres that would thrive for almost two centuries. Machaut carried on the tradition of the French love-song motet into the fourteenth century and applied to it all the new technologies of the Ars Nova. But since the Latin devout genre that stood closest to the tradition of fine amours was the antiphon to the Blessed Virgin Mary, it is not surprising to find that Machaut’s grandest, most rigorous essay in the most exalted genre available to him was an appeal to Mary in her role of divine “neck,” or intercessor.

This lofty, ambitiously structured work—Felix virgo/Inviolata/AD TE SUSPIRA-MUS—is harmonically amplified by a the addition of a contratenor, a fourth voice composed “against the tenor” and in the same range. It also has a more formal introitus than any we have as yet encountered: it comes to a full cadence, supported by the contratenor and the tenor, the latter playing “free” notes (that is, not drawn from the cantus firmus or color) for no other purpose than sonorous enhancement.

The color, once it gets under way, turns out to be a tune we know, albeit in a somewhat different version (or “redaction”). It is a phrase from a variant of a melody already encountered in chapter 3 (see Ex. 3-12b): Salve Regina, the eleventh-century Marian antiphon that stood closest, formally and melodically, to the contemporary Provençal lyric. Machaut selected a 48-note passage from the version of this dirgelike Dorian melody that he knew by heart, encompassing the words “…to you we sigh, mourning and weeping in this vale of tears. O, therefore, [be] our advocate …,” and applied to it a talea consisting of twenty rhythmic durations (sixteen notes and four rests) encompassing 36 tempora divided into two equal parts.

The first 18 tempora are organized into 6 longs under [O], the sign of perfection, and the second 18 are organized into nine longs under [C], the sign of imperfection, as shown in Ex. 8-5. It takes three such taleae to exhaust the color (3 × 16 notes = 48 notes), following which the whole color/talea complex is repeated in diminution, so that, relative to the motetus and triplum, the tenor now moves at the level of tempus, in breves and semibreves.

Machaut: The Occult and the Sensuous

ex. 8-5 Guillaume de Machaut, Felix virgo/Inviolata/AD TE SUSPIRAMUS, tenor talea

Everything we have observed about the tenor is true, in this motet, of the contratenor as well. Although a newly invented part rather than a cantus firmus (something that we can state with near certainty owing to its chromatic vagaries), the contratenor consists, like the tenor, of a color that is put through a double cursus, with each cursus encompassing a three-fold talea and with the second cursus in diminution. The contratenor’s talea is in fact the same as the tenor’s, except that it presents the two 18-tempora halves in the reverse or reciprocal order, with the imperfect longs under [C] preceding the perfect ones under [O]. Thus there is a constant interchange of time signatures between tenor and contratenor, and a perpetually maintained “polymeter” of perfect and imperfect mensurations. Because of their close relationship, we can be sure that the contratenor was composed at the same time as the tenor, and that both parts were conjointly laid out like a foundation to govern the proportions of the whole. In extremely formalized motets like this one, architectural analogies are virtually inescapable and in all likelihood envisaged aforethought.

Although the diminution of note values in the talea is quite salient to the ear (the more so because the texted parts choose that moment to break into hockets), the “polymetrical” superimposition and exchange of perfect and imperfect mensurations in the slow-moving lower parts is not. In this it resembles the harmonious orbits of heavenly bodies, which fit together according to the divinely ordained musica mundana, and which according to ancient tradition emit tones that the mind can infer, but that the senses cannot experience. Like the architectural analogy, this analogy too was surely present to the composer’s imagination as he planned the trajectories of his supporting voices. It reflected the neo-Platonic worldview of every master of science or magus (the word, not coincidentally, from which “magician” is derived.) As a magus, Machaut believed that

the world was hierarchically ordered, with intellectual elements occupying the highest realm; that superior elements in the hierarchy influenced inferior ones; and that the wise man might ascend through the levels of the world structure (or at least interact from below with higher levels) to gain special benefit from these influences.8

So writes Gary Tomlinson, a scholar who by means of musical parallels has sought to penetrate the arcane world of premodern occult philosophy. The fourteenth-century isorhythmic motet, possibly the most hierarchically conceived and rigorously ordered genre in the history of European music, was more concerned than any other to incorporate a representation of the higher “intellectual” elements and their controlling influence, which, being hidden from the senses, were in the most literal and etymological way occult. That is another way of interpreting the enormous value and emphasis that was placed on the “architecture” of the motet.

Machaut: The Occult and the SensuousMachaut: The Occult and the Sensuous

ex. 8-6 Guillaume de Machaut, Felix virgo/Inviolata/AD TE SUSPIRAMUS, mm. 1-40

And yet the other special attribute of the motet was its heterogeneity, its power of harmonizing contradictions. So none of what has been said about its occultism should imply neglect of the sensuous surface, which in Machaut’s hands was particularly and famously seductive, especially in the introitus, shown in Ex. 8-6. What made it so was an extraordinary harmonic idiom that, while emulated somewhat by the next generation or two of French composers, nevertheless remained Machaut’s unique and inimitable signature. It stemmed from the use of what we would call chromaticism, known in Machaut’s day as musica ficta (“imaginary music”) or musica falsa (“false music”).


(8) Gary Tomlinson, Music in Renaissance Magic (Chicago: University of Chicago Press, 1993), p. 46.

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. 18 Oct. 2021. <https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008011.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 18 Oct. 2021, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008011.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 18 Oct. 2021, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008011.xml