That cadence incorporates both the Cé and the Gé, resolving in parallel to D and A, the notes that define the Dorian “pentachord.” The defining or “structural” notes are each thus provided with a leading tone, the strongest possible preparation. For this reason such a cadence has been dubbed the “double leading-tone cadence.” Thanks to its great stabilizing power it became the standard cadence in fourteenth- and early fifteenth-century music.
What gave it that stabilizing and articulating (form-defining) power had only partly to do with the doubled leading tone, however. More fundamentally, the structure of the cadence goes back to the earliest days of discant, when cadence was synonymous with occursus, the coming together of two parts in contrary motion. The earliest variation on the occursus (already endorsed by Guido in the eleventh century) was its inversion, in which the two parts moved out to the octave in contrary motion; and that basic cadential frame endured until the end of the sixteenth century. In the cadence we are now examining, at the end of the introitus to Machaut’s motet, the essential two-part motion takes place between the motetus and the tenor, which move outward from the sixth e/c♯’ to the octave d/d’.
No matter what else the other voices may be doing, no progression can be called cadential unless that “structural pair” is present in two voices (one of them, in keeping with the history of discant, almost invariably the tenor). The “double leading-tone” cadence, then, is only one of a number of possible ways of filling out the cadence-defining frame. It had its moment of popularity and was replaced in the mid-fifteenth century by another standard cadence type, and by the beginning of the sixteenth century by still another. We will take them up in due course, but it is worth pointing out up front that all of them incorporated—or, more strongly, were constructed around, or in various ways embellished—the old discant pair that went all the way back to Guido.
For a final technical point, it is worth observing that it was the structure of the cadence, defined by an imperfect consonance moving by step in contrary motion to a perfect one, that gave rise to the convention of subsemitonium modi, the use of cadential leading tones. The idea was to egg on the resolution of the imperfect consonance to the perfect one by making it larger—that is, closer in size to the perfect one. It was called, in fact, the “rule of closeness” (or, more fancily, “the rule of propinquity” after the Latin propinque, “near at hand”).
The reason for raising C to C♯ before a cadence on D, then, was to make a major sixth with the tenor. The same effect could be achieved by lowering the tenor to E♭, making a major sixth with the unaltered triplum or motetus. There were times when that solution was preferable, but they were in the minority. The more striking alteration was the one that affected the higher part. As already noted, that type of alteration lasted into the era of “tonal” harmony in the form of the harmonic minor, which borrows its dominant function, replete with leading tone, from the major. Here we see the first step in that direction, and the reason for it.
- 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. 4 Dec. 2016. <http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008013.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 4 Dec. 2016, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008013.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 4 Dec. 2016, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008013.xml