(organum quadruplum), attributed to Perotin in Anonymus IV and requested by Bishop Eudes de Sully for
performance at the Feast of the Circumcision, 1 January 1198 (we would say 1199, but the New Year was
celebrated in those days on 1 March). This was the recognized jewel in the Notre Dame crown, the
opening work both in Flo (where it faces the famous Boethian allegory we have already encountered in
Fig. 3-2) and in W 2 (according to its table of contents; the pages containing it have unfortunately been
lost). The setting of the incipit is shown in the original notation (from Flo) in Fig. 6-4; Ex. 6-4 is a
transcription of the part corresponding to the opening syllable.
This composition moves throughout in an especially stately version of the trochaic meter we first
observed in “Leonine” discant and copula. What makes it “stately” is the liberal admixture into the
rhythms of the upper parts of perfect and duplex longs. The basic modal pattern, established by a repeated
phrase in the quadruplum, consists of a ternaria plus a binaria, establishing tum-ta-tum-ta-tum (“second
perfect ordo”), but followed by a nota simplex, a freestanding note. That freestanding note, a long (since
it follows a long), forces the preceding note to be perfect. (It is itself “imperfected” by the tractus, the
breath mark, which takes the time of a breve and separates one ordo from the next.)
The first note in the duplum, triplum, and quadruplum alike is a duplex, indicated by the literal
elongation of the note’s oblong shape. The chord thus created (and no doubt held extra long for dramatic
effect) is a composite of all the symphoniae. There is an octave between the tenor and the triplum, a fifth
between the tenor and the duplum (or the quadruplum), a fourth between the duplum and the triplum, and a
prime or unison between the duplum and the quadruplum. This harmony (a sort of Pythagorean summary)
would be the normative consonance for polyphony in three or more parts until the sixteenth century. Not
every piece made such a spectacular opening display of it as this one, but every piece had to end with it.
From its original signification—harmoniousness, fitting-in, “e pluribus unum”—it came to signify
completion, consummation, achievement.
Notice now how at the outset every successive ordo re-achieves that normative perfect consonance.
And notice, too, how in every ordo the perfect long preceding the final consonance makes a calculated
maximum dissonance (asymphonia), both with respect to the tenor and within the upper parts themselves.
In the first ordo the next-to-last note (penult) in the quadruplum is D, a major sixth from the tenor (the
least consonant of the imperfect consonances as then classified). The penult in the triplum is E, a major
seventh from the tenor and a major second from the quadruplum; its dissonance speaks for itself. The
duplum’s penult is B-flat, a tritone from the triplum’s E. If isolated from its context and banged out at the
keyboard, the chord would startle even a twenty-first-century ear.