Even if the poet Leonius was Anonymus IV’s (or rather, the Paris university lecturer’s) Leoninus, that still would not guarantee the story’s status as fact. A famous church poet would in fact be the ideal mythological creator of Notre Dame polyphony, for the great glory of that repertory in the eyes of its latter-day practitioners was the fact that it was metrical. That is to say, it managed to incorporate precise time-measurement into musical composition and notation, and it did so by adapting to musical purposes the principles of “quantitative” poetic meter.
This, too, shows the connection between musical practice at Notre Dame and the University of Paris curriculum. By the twelfth century, quantitative meter—defined by syllable-length rather than by “accent” or stress—was no longer used by contemporary poets, even when writing in Latin. But it was studied academically as part of the quadrivium, often from the famous textbook by St. Augustine suggestively titled De musica (“About music”—that is, the “music” or sonic organization of verse). The rhythmic practice at Notre Dame was based on similar principles of versification.
In a quantitative meter, one assumes at least two abstract durations—one “long,” the other “short”—that are related to each other by some simple arithmetic proportion. The simplest proportion is a factor of two: a long equals two shorts. That already gives the gist of the earliest abstractly conceived musical meter, as practiced at Notre Dame. Two note-lengths were assumed: a nota longa (shortened in normal parlance to longa, or in English, a “long”) and a nota brevis (shortened to brevis, or in English, a “breve”). A long was assumed to equal two breves, and the simplest way of turning their relationship into a metrical pattern (called an ordo, plural ordines) was simply to alternate them: LBLBLBLBLBL …; in effect “tum-ta-tum-ta-tum-ta-tum-ta-tum-ta-tum …,” and so on. This was the basic modus (or “rhythmic mode,” or “way of doing rhythm”) in use at the time of the “Leonin” generation.
So the standard musical “foot” (pes) was like the classical “trochee”: a long followed by a short. The difference between a pes (mere building-material) and an ordo (an actual “line” of musical poetry) was that the ordo ended with a “cadence” on the long, after which a pause (for the sake of scansion or simply for a breath) could take place. The basic pattern, then, was not LB but LBL, “tum-ta-tum.” The shortest finished “line” of rhythmicized melody, consisting of one of these patterns, was called the “first perfect ordo.” (Thus LBLBL, or “tum-ta-tum-ta-tum,” was the “second perfect ordo,” the third was LBLBLBL, or “tum-ta-tum-ta-tum-ta-tum,” etc.)
The beautifully elegant thing about this abstractly conceived “modal” meter was that its notation did not require the invention of any new signs or shapes. The old “quadratic” chant neumes could be adapted directly to the new purpose. There was no special sign for a long or for a breve. There was no need for one, because the unit of notation was not the note but the ordo, the pattern. And the most efficient way of representing such a pattern of measured sounds was by a pattern of familiar neume shapes—that is, “ligatures,” in which two, three, or more pitches were “bound together” in a single sign.
Generically, a ligature of two notes (whether ascending or descending) was called a binaria, one of three notes a ternaria, of four notes a quaternaria. An ordo was represented by a particular sequence of these shapes. The basic modus, described above as “trochaic” meter, was shown by an initial ternaria followed by any number of binariae, as in Ex. 6-1a. If one wanted the opposite metrical arrangement (“iambic” rather than trochaic meter), in which the basic foot is BL and the first perfect ordo is BLB, all one had to do was reverse the pattern of ligatures. Now there will be a series of binariae followed by a ternaria, as in Ex. 6-1b.
Comparing Ex. 6-1a with Ex. 6-1b, one readily sees that the rhythmic significance of a given neume shape is not stable or immanent, but depends on the context. The ternaria in Ex. 6-1a is read LBL, while the ternaria in Ex. 6-1b has exactly the opposite meaning: BLB. The fact that the binariae in both are read BL should not be regarded as an inherent property of the sign, but as the coincidence or overlap of two different contexts. Later, as the result of a new notational refinement, shapes—both of single notes and of ligatures—did acquire inherent meanings. At that time the binaria did finally assume the “proper” meaning BL. But the invention of that refinement, like all inventions, had to await its necessity.
To observe Notre Dame polyphony in action, rhythm and all, we can begin with a two-part setting (organum duplum; or, as some theorists called it, organum per se) of the kind associated in Anonymus IV with the original “great book” of Leonin. The obvious choice for this purpose is the original two-part setting of the Gradual Viderunt omnes, used variously, as we have seen, at Christmas and at the Feast of the Circumcision (January 1), and eventually recomposed as a quadruplum.
The two-part Viderunt is the great book’s opening piece as preserved in all its extant sources, since they are all organized according to the church calendar, which begins with Advent, the lead-up to the Christmas season. Fig. 6-3a reproduces the original chant from the Liber usualis, until 1963 the official modern chant book of the Roman Catholic church. Fig. 6-3b shows the organum, as found in its most lavish source, a codex copied in Paris during the 1240s, now kept in the Medici library in Florence. (It is usually called the “Florence manuscript,” and is known to its friends as Flo or simply as F.) As befits its pride of place, the organum is decorated with an impressive “illuminated” capital V containing a three-part illustration or triptych. Reading from the top down, the three panels illustrate three successive phases of the Christmas story: the Adoration of the Magi, the Flight into Egypt, and the Slaughter of the Innocents. The tenor corresponds to the chant, and it is evident at a glance that the Notre Dame style gave new meaning to the word “melisma.” The first syllable of text (“Vi-”) carries an outpouring of more than forty notes of duplum. That’s “intrasyllabic melodic expansion” with a vengeance!
A second glance discloses something that may seem puzzling. The organum setting is drastically incomplete. After the opening pair of words, “Viderunt omnes,” the organum skips all the way to “Notum fecit,” the beginning of the verse. The verse is set almost complete but is missing just the final pair of words, “justitiam suam.” What happened to the rest? The asterisks in the chant text as given in the Liber usualis are our clue. They are the cues that show how the soloist and choir divide up the text in this responsorial chant. The opening respond, once past the incipit (the opening pair of words), belongs to the choir. The verse, excepting the final melisma, belongs to the soloist.
Putting that information together with the polyphonic setting reveals that the composer set as organum only the soloist’s portion of the chant. The two-voice polyphony thus represents a multiplied soloist, so to speak. The parts sung by the choir are not set but were supplied in performance from memory. Since the choristers did not need to learn their part from the book, the book does not contain their part. Materials were expensive and space was at the highest premium.
From all of this we learn that polyphony at Notre Dame was the art of virtuoso soloists—the cantor and his assistant, the succentor. (And that is why only responsorial chants—matins responsories, Graduals, Alleluias—were set as organum there.) The astonishingly expansive treatment of the incipit is something of a counterpart to the illuminated capital: a rich decoration.
Again comparing the chant in Fig. 6-3a with the organum in Fig. 6-3b, we notice that when the soloist’s portion of the chant has its own melismas (at “om-” of omnes and especially at “Do-” of Dominus in the verse), the organum tenor notes are written in clumps, taking up far less space (=time). The primary motivation for hurrying the tenor along at such spots was undoubtedly practical: just imagine how long the music would have to last if every tenor note were held out like the first few! But what begins in necessity often ends in play—that is, in “art.” It was precisely these hurried-along sections of the organum, where the tenor is melismatic, that evoked from the composers what we would call the greatest artfulness or creativity. We will be tracing the repercussions of that creative response for the next three chapters.
The ratio of notes in the duplum to notes in the tenor in such sections becomes much closer; we are now obviously dealing with a type of discant. It is here, too, that we are most apt to find the clear organization of ligatures in the duplum voice into “modal” patterns, invoking the abstract metrical schemes described above.
From this we learn that in organum duplum or organum per se, the kind associated in Anonymus IV with the name of Leonin, measured rhythm is essentially an aspect of discant. In sections where the tenor is held long, called organum purum—“pure (or plain) organum”—to distinguish it from the discant, the rhythm is not organized in this way. The notes are sung “freely,” as in chant. But not entirely freely, of course. Guides to organum emphasize that notes forming consonances with the tenor were or could be sung longer than those forming dissonances. This habit, or rule, was probably what prompted the adoption of trochaic (long-short) patterns as the rhythmic norm: the note that in the added voice intervenes between two harmonic consonances is often dissonant (a “passing” or “neighbor” tone, as we now call such things), hence sung short.
In a style where “organal” and discant sections are so radically contrasted in rhythm, meter, and (consequently) tempo, it is not surprising that there is an intermediate texture as well, called copula (from the Latin for “something that binds,” like a string). In a copula, the duplum sings (usually) two phrases in regular modal patterns over sustained tenor notes. In Viderunt omnes this happens most clearly over “-de-” and “-runt.” In Ex. 6-2 you can see the two copulae in transcription, following the notation in a manuscript roughly contemporaneous with Flo but copied in England or Scotland for the Augustinian abbey of St. Andrews. (It is now the older of two Notre-Dame codices kept at the former ducal library in the German town of Wolfenbüttel, for which reason it is known to its adepts as W1.) The modal ligatures are somewhat clearer in W1 than in Flo.
In discant sections or clausulae, where the tenor moves rapidly against the “modal” rhythms of the duplum, it too must be organized into notes of determinate length. The usual method was to have each note of the tenor equal a metrical foot in the duplum. Such a note would equal the sum of a long and a breve. So now we are dealing with three durations: a breve consisting of one tempus or time unit, a long consisting of two tempora, and a tenor note consisting of three tempora, which defines the length of a foot.
Different theorists called this longest value by different names. The varying nomenclature reveals a change in attitude. Some writers were content to call the three-tempora length a longa ultra mensuram, which simply means “a long beyond (normal) measure.” Others, however, called it a “perfect” (that is, completed) long, recognizing it as the primary unit, of which the shorter values were now both regarded as subdivisions. Theorists began to speak abstractly of “perfections”—time units measured out in advance, as it were, waiting to be filled. Such a concept corresponds in some ways to our modern idea of a “measure.” Ex. 6-3a is a transcription of the big discant clausula on the chant melisma “Do-” as shown in Fig. 6-3b, from the Florence manuscript. Note that the perfect longs in the tenor group the notes of the chant melisma irregularly: 6, 4, 4, 6, 4, 4, 4, 6, 5, etc. (The barring of the transcription follows this grouping, set off in the manuscript by vertical lines called tractus, which look like bars and eventually developed into bars, but which are actually rests at this point.) But also note that the opening pattern of 6+4+4, when repeated, corresponds to a melodic repetition in the tenor. The overall organization of the discant section is clearly being “modeled” on that of the chant melody. And yet the most conspicuous component of the clausula, the duplum melody, does not participate in the repetition. The cantor, in other words, sings a continuously evolving, quasi-improvisatory string of ordines over the highly organized tenor.
Ex. 6-3b shows the same “Do-” clausula as it is found in a different manuscript, also copied in Paris but about two or three decades later than Flo. (This is the later of the two now kept in Wolfenbüttel, known as W2.) Although the Viderunt organum as a whole is more or less the same in the two sources, this particular clausula is altogether different. It is a later insert, much more tightly organized into short ordines than its predecessor, and the tenor participates fully in the modal rhythm with a mode of its own that is based on groups of perfect and “duplex” or double-measure longs (the latter designated D).
These tenor notes are organized according to a pattern reminiscent of the classical “spondee.” The spondaic foot consists of two long syllables, and the tenor’s rhythmic mode organizes the spondaic foot into two alternating perfect ordines: the first consists of a single spondaic foot with a cadential long (LLL+rest); the other ties the initial foot into a duplex (DL+rest). This modal pattern is now allowed to override the melodic repetition in the original chant. The repeated phrase is still discernible, but its notes now have different metrical placements: as the rhythm becomes more abstract and independent as an organizing factor, pitch and rhythmic organization are somewhat dichotomized. The more abstract the organization, one might say, the more “artificial” (in the sense of “artful”) the resulting musical shape. This clausula, with its regular tenor patterns of four “perfections” each, can be conveniently transcribed into our modern compound-duple meter.
The same clausula is found in Flo as well, but in a special section that contains no fewer than ten clausulae on the “Do-” melisma: a set of spare parts, so to speak, for insertion into the organum at pleasure. Just about anything can happen in these playfully (“artfully”) imaginative discants. One of them (Ex. 6-3c) puts the tenor through a double cursus in strict LLL ordines while the duplum carols away ever more decoratively, its notes “broken up” into extra breves by a process called fractio modi, literally “breaking the rhythmic pattern.” (One of the easiest ways of doing this was to add a little stroke called a plica or “fold” to a neume. The stroke usually stood for a breve on the next higher or lower note in the scale, its duration “folded” into that of the long to which it is attached. In the transcription, plicae are indicated by little strokes through the note stems.) There is even an especially souped-up clausula (Ex. 6-3d) in which both duplum and tenor contain longs and breves in ordines similar to the “iambs” shown in Ex. 6-1b.
- 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. 21 Oct. 2014. <http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-006003.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 21 Oct. 2014, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-006003.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 21 Oct. 2014, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-006003.xml