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Music from the Earliest Notations to the Sixteenth Century


CHAPTER 6 Notre Dame de Paris
Richard Taruskin

The major works of the Perotin generation differ from those of the previous generation in one fundamental respect. They are written for more than two parts—or, to make the point in most essential terms, they are written for more than one part against the Gregorian tenor. That is why contemporary theorists called their style organum cum alio (“organum with another [voice]”) to distinguish it from organum per se (“organum by itself”).

The presence of the added voice or voices changed everything. They moved at the rate of the duplum, not the tenor (so they were called the triplum and, when present, the quadruplum). Two or three parts moving at a similar rate are in effect in discant with one another, regardless of whether there is a long-held tenor note, and so they had to be notated throughout in strict modal rhythm (modus rectus, as it was called). Everything now had to move in countable perfections; there could be no spontaneous coordination in performance, the way there could be with a single cantor in the driver’s seat, ad-libbing “freely” and giving all necessary signals to his subordinates on the tenor line.

For an example of organum cum alio at its most luxuriant, we can examine the four-part setting (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 W2 (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.

Organum Cum Alio

fig. 6-4 Opening of Viderunt omnes, set as organum quadruplum by Perotinus for performance in 1198 (Flo, fols. 1–2).

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.

Organum Cum AlioOrganum Cum Alio

ex. 6-4 Viderunt omnes a 4 (attributed to Perotin), first syllable of setting

In context, of course, the chord is heard as implying its resolution to the normative consonance. Note that in making the resolution, every voice proceeds by step. The dissonant second between the triplum and quadruplum arises not out of some “non-harmonic” medieval way of hearing (as we are sometimes tempted to imagine it), but out of the implied voice-leading rule that dissonance proceeds to consonance by step. We have, in short, the beginnings of a cadential practice here, in which the motions of the individual parts are subordinated to an overall harmonic function (maximum dissonance resolving to maximum consonance). This is the beginning of harmonic tonality (or, if you prefer, of tonal harmony). It exemplifies textural integration, control, and planning.

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 sacre gestas.)

A dactylic foot consists of a long and two shorts. In contrast to the trochee (LB), which contains three tempora (2+1), the normal dactyl (LBB) contains four (2+1+1), which would make it longer than a “perfection.” To accommodate the dactylic foot to what had become the de facto ternary meter of modal rhythm, it was stretched out over two perfections, becoming inherently a modus ultra mensuram, a “mode beyond (normal) measure.” The first perfection was entirely occupied by the long, now perfect by definition. The remaining perfection was divided unequally between the two breves, one of them becoming a so-called brevis altera (“altered” or “alternate” breve) containing two tempora. Thus the six tempora occupied by the LBB of the dactylic foot was apportioned 3+2+1 or 3+1+2, with the latter much more frequently described (or prescribed, which amounts to the same thing) by mid-thirteenth century theorists, and that is the pattern commonly employed in modern transcriptions, though the other is not by any means precluded.

Organum Cum Alio

fig. 6-5 Opening of Alleluia Nativitas, set as organum triplum by Perotinus (W1, f. 16).

One of the most widely circulated dactylic pieces is the Alleluia Nativitas, an organum triplum for the Mass of the Feast of Mary’s Nativity (an especially important feast at “Our Lady’s” own church, Notre Dame), attributed to Perotin in Anonymus IV. Its first page, as given in W1, is shown in Fig. 6-5; Ex. 6-5 is a transcription of three significant excerpts, beginning with the word “Alleluya” (Ex. 6-5a).

Organum Cum AlioOrganum Cum AlioOrganum Cum Alio

ex. 6-5a Alleluia Nativitas (attributed to Perotin), mm. 1-63

Organum Cum AlioOrganum Cum Alio

ex. 6-5b Alleluia Nativitas, mm. 72-104

Organum Cum Alio

ex. 6-5c Alleluia Nativitas, mm. 168-89

The basic ligature pattern for this rhythmic mode consists of a nota simplex, representing the first perfect long, followed by a series of ternariae. This pattern is very clearly set out at the beginning of the Alleluia Nativitas, but gives way at various points, particularly near the ends of sections, to the more fluid trochaic pattern. (Look, for example, at “-YA,” the concluding portion in Fig. 6-4.) Remarkable in this composition is the sheer number of rhythmically active clausulae in the verse. There are half a dozen of them, including one (on Ex semine) that is of great historical significance for a reason we will discover in the next chapter (Ex. 6-5b). The last clausula, on “IU-” (Ex. 6-5c), is also of special interest for the way the 12-note tenor is put through a second cursus in diminution: irregular ordines of duplex and perfect longs give way to an uninterrupted and self-evidently climactic run of perfect longs that end the composition on a note of maximum excitement.

But while this remarkable run ends the composition, very narrowly defined, it does not end the Alleluia, or even the verse. The chorus must sing its brief response (including the melisma on the name of “David” that recapitulates the melody of the jubilus, the enormous melisma at the end of the choral repetition of the word “Alleluia”; it, too, will figure again in a later chapter). And then the whole Alleluia with jubilus must be repeated, either with polyphony (as some of the sources direct) or without. A polyphonically outfitted liturgical chant as sung at Notre Dame, though far more elaborately composed than any other polyphonic music of its time, is still not a composition in our modern sense. It is not solely the product of an author’s shaping hand but the complex response to a variety of ceremonial and artistic demands, some seemingly in mutual contradiction.

Citation (MLA):
Richard Taruskin. "Chapter 6 Notre Dame de Paris." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 4 Aug. 2021. <https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-006005.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 6 Notre Dame de Paris. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 4 Aug. 2021, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-006005.xml
Citation (Chicago):
Richard Taruskin. "Chapter 6 Notre Dame de Paris." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 4 Aug. 2021, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-006005.xml