To see textural integration, control, and planning from another perspective, compare the triplum in the
first ordo with the duplum in the second ordo, the triplum in the third ordo, the duplum in the fourth ordo,
the triplum in the sixth, and finally the quadruplum in the seventh. Now compare the triplum in the second
ordo with the duplum in the third, the triplum in the fourth, and the quadruplum in the fifth and sixth.
Elaborate voice exchanges of this kind, the most conspicuous of integrative devices, can be traced
throughout the piece.
For yet another, look at the third system of the first manuscript page in Fig. 6-4, halfway through the
syllable “-DE-” (in “Viderunt”) in the tenor. Now the motion has slowed down to an alternation between
“spondaic” perfect longs and the normative trochees. The figure C–D–C in longs, and its trochaic variant
C–D–E–D–C, are tossed back and forth between the duplum and triplum. Their exchanges are now
dovetailed so that the first note in one voice coincides with the third note in the other. In between, a note
in one voice coincides with a rest in the other. This kind of exchange between notes and rests (done
slowly here, but sometimes done with lightning speed, as we shall see) was a specialty of organum cum
alio and its derivative genres. For the singers this kind of controlled textural fragmentation was great fun,
as we can tell by the name they gave it: hoquetus—“hocket” in English—from the Latin for “hiccup,” no
doubt because of the way the rests interrupt the melodic lines like spasms. An even more radically
fragmented “hocket” texture comes over the first tenor note of “-RUNT.”
The spirit of creative exuberance, of delight in construction, so evident in this and every other Notre
Dame quadruplum led inevitably to an expansion of the repertory of rhythmic “modal” figures. The
obvious choice for a new metric foot to apply to music was the dactyl, the most widely cultivated foot for
contemporary Latin poetry. (It was the foot adopted by the poet Leonius, for example, in his Hystorie