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Music from the Earliest Notations to the Sixteenth Century


CHAPTER 8 Business Math, Politics, and Paradise: The Ars Nova
Richard Taruskin

These terms should not be taken too literally. Indeed, Philippe de Vitry himself, as reported in Ars Nova, cautioned that “false music” is not false but real “and even necessary.” All that the name implied was that the notes involved were not part of the gamut as defined long ago by Guido d’Arezzo, and that they had no predefined “vox,” or position within a hexachord. So in order to solmize them—that is, find a place for them among the ut–re–mi’s of traditional sight-singing—one had to imagine a hexachord that contained them, one that may have been “fictitious” with respect to the official theory of music, but whose sounding contents were fully presentable to the senses and in that respect altogether real.

And necessary, as Philippe de Vitry allowed, when their purpose was to make perfect a diminished fifth or an augmented fourth. As we know, a certain provision of this kind was made by the earliest theorists of harmony, when they incorporated B-flat into the modal system alongside B for use in conjunction with F.

But when an E was written against the B-flat, one had to go outside the system to harmonize it. And that was musica ficta. The required E-flat was not conceptualized as we might conceptualize it, as an inflection of E. Instead, it was conceptualized as the upper member of a melodic semitone, D–E♭, for which a solmization—mi–fa—could be inferred. So the E♭ a semitone above D was a fa, which placed it in an imaginary or “feigned” (ficta) hexachord with ut on B♭. Since the flat sign was itself a variant of the letter “B” to denote a B that was sung fa (in the “soft hexachord” on F) instead of mi (in the “hard hexachord” on G), so the flat sign in and of itself denoted fa to a musician trained to sing in hexachords. Thus a flat placed next to an E did not mean “sing E a half step lower,” it meant “sing this note as fa.” The result may have been the same so far as the listener was concerned, but understanding the different mental process by which the E♭ was deduced by the singer will make clear the reason why in most cases musica ficta did not have to be expressly indicated by the composer with accidentals. In many contexts the chromatic alteration was mandated by rule, and the rule was fully implied in the solmization, and so any singer who thought in terms of solmization would make the chromatic adjustment without being specifically told to do so, and, it follows, without even being aware of the adjustment as “chromaticism.” It was not a deviation from a pure diatonic norm, it was a preservation of pure diatonic norms (in particular, perfect fourths and fifths) where they were compromised by a well-known kink in the diatonic system.

Musica ficta introduced to preserve perfect intervals was musica ficta by reason of (harmonic) necessity (in Latin, causa necessitatis), and was considered perfectly diatonic. Just as automatic, and diatonic, was musica ficta by long-established conventions—conventions that have left a trace on familiar harmonic practice in the form of the “harmonic minor.” They mainly affected the Dorian mode, the one closest to our minor mode. For example, there was a rule that a single B between two A’s had to be a B-flat (and, though it rarely required any adjustment, that an F between two E’s had to be F natural).

Singers learned this rule as a Latin jingle: una nota super la/semper est canendum fa (“One note above la is always sung fa”). This adjustment had the effect of lowering the sixth degree of the Dorian scale, turning it into a sort of appoggiatura or upper leading tone to fifth degree, A, the note that formed the boundary between the principal segments of the scale. (And it turned the Dorian scale, for all practical purposes, into the minor scale.) It was a grammatical rule, not an expressive device; it was called into play automatically, and so it did not need to be written down.

There was a similar rule affecting lower neighbors to the final in Dorian cadences. Such notes were common enough in Dorian melodies to have a name: subtonium modi, as we may recall from chapter 3. The rule about neighbors raised the subtonium, a whole step below the final, to the subsemitonium, a half step below. The effect was similar to that of borrowing a leading tone in the minor mode and served the same purpose, strengthening the grammatical function, so to speak, of the cadence. By signaling a more definite close it made the final more “final.” For this purpose the auxiliary pitch had to be raised, not lowered, thus forming the lower note in a mi–fa pair. To indicate it, a sign was needed that would instruct the singer to “sing mi.” That sign, é, which we call a “sharp,” was originally derived from the “square B” or b quadratum that functioned specifically as mi in the “hard hexachord.” In places like Dorian cadences, where the subsemitonium modi or leading tone was called for by the routine application of a rule, it again could “go without saying.” It did not need to be explicitly notated, though (like necessary flats) it could be notated and frequently, if haphazardly, was.

So often were musica ficta adjustments taken for granted—so often, in other words, were they left to oral tradition—that the term is often loosely (and, technically, wrongly) employed to refer only to “chromatics” that were unnotated. Scholars who transcribe early polyphony for nonspecialist singers cannot assume that the singers for whom they are preparing the edition will know the oral tradition governing these adjustments, and therefore indicate them in writing (usually with little accidentals placed above the staff). They often call this procedure “putting in the ficta,” thereby implying that the word “ficta” applies only to what has to be “put in” in this way. They know better, of course. A C♯ is musica ficta whether it is explicitly notated or not, because there is no such note as C♯ on the Guidonian “hand.” A B♭ is not musica ficta but musica recta (or vera), again whether explicitly notated or not, because there is such a note on the hand.

So the accidentals that are explicitly signed, often very abundant in fourteenth century music and particularly in Machaut’s music, are just as much to be considered musica ficta (unless they are B♭s) as those mentally supplied by unwritten rule. Their purpose, however, was different. Instead of being musica ficta causa necessitatis (harmonically necessary adjustments), or even musica ficta arising out of conventions that all competent singers knew, they represented musica ficta causa pulchritudinis—chromatic adjustments made “for the sake of their beauty,” that is, for the sensuous enhancement of the music.

Look now at the introitus to Machaut’s motet (Ex. 8-6). The triplum has a signed C♯ at the moment when the motetus enters. It follows D. If it returned to D, then strictly speaking it would not need to be expressly “signed.” But it does not return to D; instead, it skips to a wholly unexpected note, G♯. This note is not called for by any rule. Its only purpose is to create a “purple patch” in the harmony, especially in view of the weird interval it creates against the F-natural in the motetus.

An augmented second is, strictly speaking, a forbidden interval on the order of the tritone (and for the same reason: one of the voices sings mi while the other sings fa). It is clearly intentional, however, and cannot be removed by adjustment causa necessitatis. There can be no question of adjusting the expressly signed G-sharp, of course; why sign a note only to cancel it? The F cannot be adjusted to F-sharp for two reasons. First, it would only produce another dissonance (and a worse one)—a major second instead of an augmented second. And besides, the F can be construed as a fa between two la’s (since E is la in the hard hexachord on G) and therefore cannot be raised.

So the throb is there for its own sake. It is, literally, a heartthrob, expressing love for the Virgin the way so many similar harmonic throbs express love for the lady in Machaut’s French songs. But it is also there for “tonal” reasons. All of the signed accidentals in the introitus are C♯s or G♯s. These tones at once depart from and emphasize the basic Dorian pitch set because they are “tendency tones,” pitches altered chromatically in such a way as to imply—hence demand—cadential resolution to crucial scale tones. When the resolution is evaded or delayed—as it is in the case of the triplum’s first Cé (and even the Gé, whose resolution to A is interfered with by a rest where one is least expected)—a harmonic tension is engendered that will not be fully discharged until the introitus reaches its final cadence.

Citation (MLA):
Richard Taruskin. "Chapter 8 Business Math, Politics, and Paradise: The Ars Nova." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 31 Mar. 2020. <https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008012.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 8 Business Math, Politics, and Paradise: The Ars Nova. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 31 Mar. 2020, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008012.xml
Citation (Chicago):
Richard Taruskin. "Chapter 8 Business Math, Politics, and Paradise: The Ars Nova." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 31 Mar. 2020, from https://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008012.xml