Music from the Earliest Notations to the Sixteenth Century

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. 6-1 a. 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.

EX. 6-1A    Trochaic    pattern notated with    “modal” ligatures

EX. 6-1B    Iambic  pattern notated with    “modal” ligatures

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