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 W 1 .) The modal ligatures
are somewhat clearer in W 1 than in Flo.
EX. 6-2 Transcription of -derunt from organum setting shown in Fig. 6-3bIn 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 threetempora 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