not to ask questions but just to perform the example and learn to imitate its “smoothness of harmony.” This
deferral of explication should perhaps be viewed not as mere dogmatism (“‘Shut up,’ he explained,”^4 in
the immortal words of Ring Lardner). Rather, it reflects the author’s reliance on time-honored oral/aural
methods—hearing, repeating, imitating, applying, as opposed to “analysis”—in training musicians. It also
suggests that the technique being imparted was no recent invention but already a tradition, “oral” by
definition.
When the vox organalis moves in this modified, somewhat independent (though still entirely rule-
bound) way, using not just parallel motion vis-à-vis the vox principalis but oblique and contrary motion
as well, a variety of harmonic intervals are introduced into the texture, and the resulting line or voice-part
can be described as a true “counterpoint.” The intervals are still ordered hierarchically. In addition to the
actual symphonia (perfect consonance) of the fourth, Ex. 5-1c contains thirds and unisons. The organum
setting of the sequence Rex caeli from Musica enchiriadis, discussed in chapter 2 and shown in Ex. 2-6,
contains actual dissonances. The vox organalis begins with a dronelike stretch against which the vox
principalis rises by step from unison until the symphonia is reached. Its second note, then, forms a
“passing” dissonant second against the accompanying voice.
The thirds, “imperfect” consonances, are contrapuntally subordinate in Exx. 5-1c and 5-1d: a vox
organalis can move only to a perfect consonance; the thirds (like the second in Ex. 2-6) can occur only
over a stationary accompaniment. Thus the fourth, being unrestricted in its possible occurrences, is
“functionally consonant” according to the style-determining rules here in force, while the third is
“functionally dissonant.”
It has been worth our while to take a very close look at these primordial specimens of written
counterpoint because the principles we have observed in them will remain the bedrock principles of
Western polyphonic practice for centuries. The art of counterpoint (and of harmony as well, which is just
counterpoint slowed down) is most economically defined as the art of balancing normative harmonies
(“consonances”) and subordinate ones (“dissonances”), and elaborating rules for “handling” the latter.
The quotes around the terms are a reminder that criteria of consonance and dissonance are culture-bound,
hence relative and changeable, and are best described not on the basis of their sound as such but on the
basis of how they function within a style. The styles we all assimilate today in the process of
acculturation (otherwise known as “growing up”) teach us to hear—hence use—intervals a different way.
We have all been trained to “hear” thirds as consonances and fourths as dissonances.
The chief distinguishing characteristics of any contrapuntal or harmonic style, including those used
today, come down to two: the ways in which voices move with respect to one another (in terms of rhythm
as well as pitch direction), and the ways in which dissonance functions vis-à-vis consonance. To assess
any contrapuntal or harmonic style we need to make the same sorts of observations that we have been
making with regard to our primordial specimens.
GUIDO, JOHN, AND DISCANT
As if the achievements with which he has already been credited—the invention of the staff, the
operational rules of sight-singing—were not enough, Guido of Arezzo also made a decisive contribution
to the development of contrapuntal technique. It was yet another of that brilliant monk’s many impressive
contributions to the early rationalization of literate musical practice and its transformation into
transmissible technique. In his Micrologus (“Little treatise”), a guide to the rudiments of music theory,
Guido devoted one section to a very influential discussion of organum. The main emphasis was on
obtaining maximum variety in interval succession (though the fourth is still recognized as the primary