Nova techniques, which had been developed specifically to serve the purposes of the motet genre, were
“bottom-up” techniques. That is, they were techniques geared toward the erecting of highly stratified
polyphonic superstructures over artfully contrived and elaborated foundations. And the foundations were
wrought in turn from cantus firmus melodies appropriated, as a rule, from the high-authority repertoire of
canonized church chant.
Machaut wrote some real masterpieces in this very formalized and architectonic idiom, the most
extended being a giant hoquetus on the melisma DAVID that comes at the end of the Gregorian Alleluia
Nativitas for the feast of the Virgin Mary’s Nativity, already the basis (as Machaut surely knew) of a
grandiose, “classic” setting in the Notre Dame style. (We know it, too: see Ex. 6-5.) Machaut’s hoquetus
was not meant as an appendage to that venerable composition, however. The DAVID melisma is sung not
by the soloist(s) but by the choir, and so would not have been performed polyphonically in church. This
was still music for “feasts of the learned,” who delighted in high-spirited intellectual games.
As shown in Ex. 9-1, Machaut divides his 32-note color by a twelve-note talea lasting 30 tempora,
and lets the two repetition-schemes run their course until they come out even (or in more evocatively
“Boethian” terms, lets the two bodies orbit in musical space until they come into alignment). It takes three
cursus of color and eight of talea, thus: 32 × 3 = 12 × 8 = 96. Then, as a sort of cauda, he sets the color
going once more to a shorter talea that divides its 32 notes evenly (8 notes in 27 tempora). Laying out the
ground plan just described had to precede the composition of the hocketing upper parts, just as the
foundation of an architectural edifice had to be laid before the rest could be erected. Instead of a full
score, Ex. 9-1 gives just the foundational materials, the color, and the taleae. They can be followed,
tracking each with one hand, while listening to a recorded performance. This will give a vivid idea of
Ars Nova “isorhythmic” foundational architecture at its grandest.
By way of transition from the more speculative Ars Nova genres to the lyric genres more peculiar to
Machaut, we may cast a sidelong glance at a whimsical hybrid: a motet in three texted parts, all in French,
in which the tenor is not a Gregorian chant but instead a traditional chanson balladé (“danced song”) or
virelai (Ex. 9-2: Lasse/Se j’aime/ POURQUOY). The song Machaut chose to do tenor duty was almost as
“canonical” as a chant, however, having a textual pedigree going back to the thirteenth century. It satirizes
courtly love as mere marital infidelity (“Oh God, why does my husband beat me? All I did was talk to my
lover”). Ex. 9-2 shows Machaut’s tenor in compressed note values (Machaut’s are longs and breves,
typical “tenor” values), with the constituent parts of the virelai—AbbaA, with “A” the refrain—labeled.
The upper parts, meanwhile, behave in characteristic motet fashion. They are rhythmically stratified—the
motetus moving in breves, semibreves, and occasional minims; the triplum in minims, semibreves, and
occasional breves—and serve as glosses (here, ironic rhymed ones) on the tenor: “Alas, how can I
forget/the handsome, the good, the sweet, the merry/[youth] to whom I’ve completely given/this heart of
mine?” “If I love him truly, and he truly loves me, do I deserve to be treated so?” Ex. 9-3 shows the
portion of the whole polyphonic texture corresponding to the tenor’s first refrain.
EX. 9-1 Guillaume de Machaut, hoquetus “DAVID,” color and taleae