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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

Guillaume Du Fay (ca. 1397–1474) lived almost exactly a century later than his namesake Guillaume de Machaut, and like Machaut he will be reintroduced in a later chapter. It is very important to consider at least one of his works right here, however, in order to appreciate the direct generic and stylistic continuity that linked Du Fay’s creative output with that of his fourteenth-century precursors.

The reason for speaking in such urgent terms is that the beginning of “The Renaissance,” for music, is often—though, as we will see, arbitrarily—placed around the beginning of the fifteenth century, and major historiographical divisions like that can act as barriers, sealing off from one another figures and works that happen to fall on opposite sides of that fancied line, no matter how significant their similarities. Not only that, but (as already observed in a somewhat different context) an appearance of stylistic backwardness or anachronism—inevitable when sweeping categories like “Medieval” and “Renaissance” are too literally believed in—can easily blind us to the value of supreme artistic achievements such as Du Fay’s isorhythmic motets. They are not vestigial survivals or evidence of regressive tendencies, but a zenith.

The fact is, Du Fay’s career was very much like Philippe de Vitry’s a century earlier. He was a university-educated ordained cleric—in short, a literatus—whose musical horizons had been shaped by Boethius, by Guido … and by Philippe de Vitry. Like his predecessors, he thought in scholastic terms about his craft but in Platonic terms about the world. For him, no less than for the founders of the Ars Nova, the world was materialized number, and the highest purpose of music was to dematerialize it back to its essence.

Born in French-speaking Cambrai, near the border with the low countries, Du Fay followed in Ciconia’s footsteps to early employment in Italy. He may have first gone down there as a choirboy in the entourage of the local bishop, who attended the Council of Constance, where Francesco Zabarella, Ciconia’s patron, had shone. By 1420, when he was about 23, Du Fay was employed by the Pesaro branch of the notorious Malatesta family, the despots of the Adriatic coastal cities of east-central Italy. He joined the papal choir in 1428, and evidently formed a close relationship with Gabriele Cardinal Condulmer, who in 1431 became Eugene IV, the second pope to reign over the reunited postschismatic church.

Du Fay wrote three grandiose motets in honor of Pope Eugene. The first, Ecclesie militantis Roma sedes (“Rome, seat of the Church militant”), was composed shortly after the pope’s election, at a very precarious moment for the papacy. That motet, expressive of the political conflicts that beset the new pope, is a riot of discord, with a complement of five polyphonic parts (three of them texted), and a sequence of no fewer than six mensuration changes. The second motet for Eugene, Supremum est mortalibus bonum (“For mortals the greatest good”) is a celebration of a peace treaty between the pope and Sigismund, the Holy Roman Emperor. It is an epitome of concord, employing only one text and using a novel, sugar-sweet harmonic idiom of which (as we will see in chapter 11) Du Fay may have been the inventor. Near the end the names of the protagonists of the peace are declaimed in long-sustained consonant chords—concord concretized.

The third motet Du Fay composed for Eugene, Nuper rosarum flores (“Garlands of roses,” of which the dazzling close is shown in Ex. 8-8), is the most famous one because of the way it manipulates symbolic numbers. In 1434, the pope, exiled from Rome by a rebellion, had set up court in Florence. In 1436, the Florence cathedral, under construction since 1294, was finally ready for dedication. A magnificent neoclassical edifice, crowned by a dome designed in 1420 by the great architect Filippo Brunelleschi, it was dedicated, under the denomination Santa Maria del Fiore, to the Virgin Mary. Pope Eugene IV, resident by force of circumstances in Florence, performed the dedication ceremony himself, and commissioned a commemorative motet for the occasion from Du Fay. This was to be the musical show of shows.

Nuper Rosarum Flores is cast in four large musical sections, plus an “Amen” in the form of a melismatic cauda. The layout is remarkable for its symmetry. The first and longest section begins with an introitus for the upper (texted) voices lasting twenty-eight tempora. The Gregorian cantus firmus, the fourteen-note incipit of the introit antiphon for the dedication of a church (Terribilis est locus iste, “Awesome is this place”), now enters, carried by a pair of tenors that present it in two seven-note groups, answering each to each as in biblical antiphonal psalmody.

Du Fay: The Motet as Mystical SummaDu Fay: The Motet as Mystical Summa

ex. 8-8 Guillaume Du Fay, Nuper rosarum flores, mm. 141-70

Each of the succeeding sections presents the same 7 + 7 disposition of the tenor, and the same balanced alternation of duo and full complement (28 + 28 tempora, or 4 times 7 + 7). As in Ciconia’s motet, the pair of tenors is written out only once, with directions to repeat. And again as in Ciconia’s motet, each tenor statement is cast in a different mensuration: and (the part given in Ex. 8-8) . These mensurations stand in a significant proportional relationship to one another. A breve or tempus of contains six minims; a breve of has four. The line through the signature halves the value of the tempus, so that a breve under contains three minims as sung by the texted parts running above, and a breve under contains two. Comparing these signatures in the order in which Du Fay presents them, they give the durational proportions 6:4:2:3. As anyone trained in the quadrivium would instantly recognize, these are Pythagorean proportions. In musical terms they can easily be translated from durations into pitch, for they describe the harmonic ratios of the most consonant intervals. Given a fundamental pitch X, Du Fay’s numbers represent the octave (2X), the compound fifth, or twelfth (3X), the double octave (4X) and the twice-compound fifth (6X), as shown in Ex. 8-9.

Du Fay: The Motet as Mystical Summa

ex. 8-9 Proportional numbers in Nuper rosarum flores represented as pitch intervals

Perfect concord

Moreover, the complex of durational ratios also contains a symbolic perfect fifth (3:2) and a perfect fourth (4:3), all of it summed up in the final chord of the piece. Thus Du Fay’s motet embodies a hidden Pythagorean summa, or comprehensive digest of the ways in which music represents the enduringly valid harmony of the cosmos. With its four different integers, it is the most complete symbolic summary of its kind in any isorhythmic motet. (By way of comparison, the proportional ground plan of Ciconia’s motet, 3:2:2, incorporates only two integers, one of them repeated. The only harmonic intervals it can be said to express are the unison and the fifth.)

But that is by no means all. As Craig Wright has shown in detail (far more of it than we can pursue at the moment), the number symbolism in Du Fay’s motet, reaching far beyond the specifically musical domain, makes contact with a venerable tradition of biblical exegesis that bears directly on the circumstances that inspired the work and the occasion that it adorned.11 As we read in the second book of Kings, where the building of the great temple of Jerusalem is described, “the house which king Solomon built to the Lord, was three-score cubits in length, and twenty cubits in width, and thirty cubits in height” (2 Kings 6:2); that the inner sanctum, the “Holy of Holies,” was forty cubits from the doors of the temple (2 Kings 6:18); and that the feast of dedication lasted “seven days and seven days, that is, fourteen days” (2 Kings 8:65). These, of course, are precisely the numbers that have figured in our structural analysis of Du Fay’s motet. The durational proportions of the tenor taleae are precisely those governing the dimensions of Solomon’s temple (60:40:20:30 cubits:: 6:4:2:3 minims to a breve); and the length and layout of the chant fragment chosen as color correspond to the days of the dedication feast (7 + 7 = 14). The relationship of all of this to the dedication feast for the Florence cathedral could hardly be more evident—or more propitious, in view of the Christian tradition that cast Rome as the new Jerusalem and the Catholic church as the new temple of God.

And yet there is more. The Florence cathedral was dedicated to the Virgin Mary, as the motet text affirms. That text is cast in a rare poetic meter with seven syllables per line. The introitus before the tenor entrance in each stanza lasts 28 (4 × 7) tempora, and the section following the tenor entrance likewise lasts 4 × 7. Seven is the number that mystically represented the Virgin in Christian symbolism, through her sevenfold attributes (her seven sorrows, seven joys, seven acts of mercy, seven virginal companions, and seven years of exile in Egypt). Four is the number that represented the temple, with its four cornerstones, four walls, four corners of the altar, and—when translated into Christian cruciform terms—four points on the cross, the shape of the cathedral floor plan. Four times seven mystically unites the temple with Mary, who through her womb that bore the son of God was also a symbol of Christian sanctuary.

All of this is mystically expressed in the occult substructure of Du Fay’s motet, while on the sensuous surface, according to the testimony of the Florentine scholar Giannozzo Manetti, an earwitness,

all the places of the Temple resounded with the sounds of harmonious symphonies as well as the concords of diverse instruments, so that it seemed not without reason that the angels and the sounds and singing of divine paradise had been sent from heaven to us on earth to insinuate in our ears a certain incredible divine sweetness; wherefore at that moment I was so possessed by ecstasy that I seemed to enjoy the life of the Blessed here on earth.12

What could better serve the church, better spiritually nourish its flock, or better assert its temporal authority?


(11) C. Wright, “Dufay’s Nuper rosarum flores, King Solomon’s Temple, and the Veneration of the Virgin,” JAMS XLVII (1994): 395–441.

(12) Giannozzo Manetti, quoted in G. Dufay, Opera omnia, ed. Heinrich Besseler, Vol. II (Rome: American Institute of Musicology, 1966), xxvii.

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. 28 Oct. 2016. <http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008015.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 28 Oct. 2016, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008015.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 28 Oct. 2016, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008015.xml