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Music from the Earliest Notations to the Sixteenth Century


CHAPTER 5 Polyphony in Practice and Theory
Richard Taruskin

To trace this trajectory we need to begin by reviewing some earlier, more or less scattered manifestations of written polyphony. As a performance practice associated with plainchant, polyphony makes its documentary debut (as noted briefly, with an example, in chapter 2) in the ninth-century treatise Musica enchiriadis. A contemporary commentary to it, called the Scolica (or Scholia) enchiriadis, describes two basic techniques of embellishing a melody harmonically. One consists of simply accompanying a melody in bagpipe fashion, with a drone on the final of the mode. That method—under the name of “ison chanting” after the Greek word for “the same note”—still survives as a traditional way of performing the so-called Byzantine chant of the Greek Orthodox church. The other technique consisted of “parallel doubling”—that is, accompanying melody with a transposition of itself at a constant consonant interval (for which the Greek term, used in the treatise, was symphonia). Three intervals were considered eligible as symphoniae for this purpose; they are the ones we still call “perfect” (fourth, fifth, and octave).

These methods are easy to describe and to illustrate (Ex. 5-1), and they seem eminently practical. In actual fact they were entirely “theoretical” and, in the case of the second, impracticable. As the examples in the Musica enchiriadis itself suffice to prove, these simple devices were actually practiced in a complex synthesis requiring considerable artistry—which, of course, is why a treatise needed to be written about them in the first place. That artistic synthesis—not (as often assumed) mere parallel doubling—was what the author of the treatise called organum.

“Symphonia” and its Modifications

fig. 5-1 Polyphonic or organal settings of the sequence Nos qui vivimus (We the living) in Scolica enchiriadis, ca. 850.

The reason why parallel doubling is not acceptable without modification can be expressed in a single word: tritones. If a given diatonic melody is doubled at a constant fourth or fifth below, then tritones will emerge whenever the note B has to be doubled at the fourth or the note F at the fifth. Adjustment of the doubling-voice (called the vox organalis) at these places produces a built-in discrepancy between its mode species and that of the original chant (vox principalis). The result is “polytonality”—quite literally so, given that parallel lines by definition never meet, and so two voices in strict parallel motion at any interval except the octave will appear to end on different finals.

Consider Ex. 5-1b, the demonstration of “the symphonia of the diapente” (parallel doubling at the perfect fifth) in the Scolica enchiriadis. The ending note of the vox organalis (G) contradicts the Dorian final, and the B-natural in the vox principalis (a psalm tone) is answered in the vox organalis by a B-flat. If the vox principalis is modified with a B-flat to agree with the vox organalis (and to smooth the contour between its highest note and the F of its own medial cadence), then an E-flat (a note not present in the normal diatonic system) must be introduced beneath it, which creates a new discrepancy between the voices. (It can never be erased; if the vox principalis takes over the E-flat, the vox organalis will need an A-flat, and so it will go on forever.)

“Symphonia” and its Modifications

ex. 5-1a Transcriptions of Scolica enchiriadis examples (Fig. 5-1), Double diapason

“Symphonia” and its Modifications

ex. 5-1b Diapente

“Symphonia” and its Modifications

ex. 5-1c Diatessaron

“Symphonia” and its Modifications

ex. 5-1d Composite

To “hear” (that is, aurally conceptualize) strict parallelism at the fifth without any sense of “polytonal” contradiction, one must be able to imagine “fifth equivalency” on a par with the octave equivalency we have all learned to take for granted as a listening norm. The author of the Musica enchiriadis recognized as much and even constructed a scale that exhibits fifth equivalency as the basis for “the symphonia of the diapente” (Ex. 5-2a). Instead of reproducing interval species at the octave, this scale duplicates interval sequences at the fifth. Just as one encounters discrepancies in fifth-size (perfect vs. diminished) when harmonizing within the “normal” diatonic scale, so in the Musica enchiriadis scale there will be uniform fifths but discrepancies in octave-size (perfect vs. augmented).

“Symphonia” and its Modifications

ex. 5-2a Disjunct tetrachord scale from Musica enchiriadis

“Symphonia” and its Modifications

ex. 5-2b Hypothetical conjunct tetrachord scale

Unlike the octave system, with a scale constructed (as we saw in chapter 3) out of alternately conjunct and disjunct tetrachords, the Musica enchiriadis scale is constructed entirely out of disjunct tetrachords. Beginning with the familiar tetrachord of the four finals, d–e–f–g, you add a disjunct tetrachord below, and thus obtain the B-flat in Example 5-1b. Add a disjunct tetrachord above and you get the B-natural as part of the same scale. Add another tetrachord above that and F-sharp appears. Above that there will be a C-sharp. (This much is actually demonstrated in the treatise. If one were to extend the scale at the bottom, of course, one would keep adding flats, beginning with the E-flat hypothetically added to Ex. 5-1b.) The result is a scale altogether without diminished fifths. An analogous hypothetical scale composed of nothing but conjunct tetrachords would eliminate augmented fourths; it is not given in the treatise but can be easily deduced: see Ex. 5-2b.

These scales produce perfect parallel counterpoint in theory but bear no relationship to normal oral (that is, aural) practice. And that is why strict parallel doubling, though conceptually as simple as can be, is literally utopian. It occurs nowhere in the “real world” of musical practice. Polyphonic music actually composed according to the Musica enchiriadis scales (to quote a wry comment of Claude Debussy on a piece the young Igor Stravinsky showed him in 1913) “is probably Plato’s ‘harmony of the eternal spheres’ (but don’t ask me on which page); and, except on Sirius or Aldebaran or some other star, I do not foresee performances … especially not on our more modest Earth.”3

On our modest Earth, in other words, compromise with theory—that is, with imagined perfection—is usually required. The author of the Scolica enchiriadis tacitly recognized this crucial point when constructing an example to illustrate “the symphonia of the diatessaron” (parallel doubling at the perfect fourth). The counterpoint in this case (Ex. 5-1c) has been “cooked,” precisely so as to avoid the “polytonal” situation encountered in the case of fifths. The two lines end on the same final; that is to say, they end on a unison. In order to meet, of course, they must stop being parallel. Instead, they approach the final note in contrary motion. Such an approach is called an occursus, literally “a meeting.”

In order to smooth the way to the occursus (and also to avoid the B-flat from the Musica enchiriadis scale, which would produce an augmented fourth against the E in the vox principalis), the vox organalis behaves, in the second half of the example, like a drone—or like a sequence of drones. Instead of following the contour of the vox principalis, the vox organalis hugs first the D and then the C, moving from the one to the other when the opportunity presents itself to recover the correct symphonia (perfect fourth) against a repeated note in the vox principalis. The voces organales above and below the vox principalis in Ex. 5-1d, a composite organum simultaneously demonstrating octaves, fifths, and fourths, behave similarly.

Curiously (and rather characteristically), the author of the Scolica enchiriadis does not actually explain the modifications—the drones, the occursus—by which the purely conceptual idea of parallel doubling is transformed into the actual practice of organum. Acknowledging that the case is not as straightforward as the other examples, the author refers the discrepancy to “a certain natural law about which we shall speak later” (but of course “we” never get around to it), meanwhile counseling the student 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-`a-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 Ex. 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.


(3) Claude Debussy, letter to Igor Stravinsky of 18 August 1913, facsimile and transcription in Avec Stravinsky, ed. Robert Craft (Monaco: Éditions du Rocher, 1958), pp. 200–201. The work of Stravinsky’s that elicited the comment was Zvezdoliki (Le Roi des Étoiles).

(4) Ring Lardner, The Young Immigrunts (1920).

Citation (MLA):
Richard Taruskin. "Chapter 5 Polyphony in Practice and Theory." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 23 Feb. 2024. <https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-005002.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 5 Polyphony in Practice and Theory. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 23 Feb. 2024, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-005002.xml
Citation (Chicago):
Richard Taruskin. "Chapter 5 Polyphony in Practice and Theory." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 23 Feb. 2024, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-005002.xml