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n Music 105, you learned the basic principles governing the construction of harmonic cycles: tonal harmonies progress from tonic to dominant along the descending circle of thirds, returning to the tonic by way of a few special progressions (V!I, vii°!I, IV!I, etc.). You also learned that this basic system can be enriched with secondary dominants and modulation. However, the system of harmonic cycles is just the first of three separate syntactical systems operating in functionally tonal music. The other two, though somewhat less central, play an important role in the style. You certainly need to be conversant with them if you want to understand Bach, Mozart, Haydn, etc. The second system, “fauxbourdon” or the system of parallel triads, will be described in this handout.1 The third system, the system of sequential tonality, will be discussed in the next handout. 1. History of fauxbourdon. Interestingly, the second system is the longest-lasting of the three, dating back to the early Renaissance, and extending to the present day.2 Starting in the 1400s, one finds passages in which first-inversion triads move in parallel, particularly in the music of Guilliam Dufay (1397–1474). See, for instance, the following excerpt (stolen from the Wikipedia article, which is pretty good), where the only harmonies are “open fifths” (such as D3-A3-D4) and first inversion triads, with the latter always moving in parallel and almost always stepwise. Fauxbourdon passages can also be found in jazz (which often uses parallel triads, particularly in “drop 2” or “locked hands” piano style), and popular music. For instance, the Pixies’ “Wave of Mutilation” moves from IV to I through parallel stepwise motion: IV!iii!ii!I. 1 “Fauxbourdon” is often translated as “false bass,” with bourdon referring (I believe) to a certain kind of organ pipe often used for the bass notes. 2 The system of harmonic cycles starts in the early 1600s, and is often associated with Monteverdi. Sequential tonality starts around the same time, and is often associated with (the eldest) Gabrielli. Functional tonality has three fathers! 2. Fauxbourdon in functional tonality. Fauxbourdon plays an important role in Baroque and classical music, where one often finds composers employing brief passages of stepwise triads that do not obey any clear functionally tonal laws. I’m not aware of any good theoretical treatments of this particular subject, so what follows is my own take. If you can think of anything to add, let me know! A. Passing interpolations. One natural way to use the technique is to slide between two chords that might otherwise be directly connected. In the following passage, Haydn connects IV6 (at the start of bar 3, decorated with a suspension) to vii°6 by a series of parallel first- inversion triads. One can think of these triads as passing chords: the progression IV!vii° is perfectly sensible on its own, and the iii-ii-I just decorate the basic progression. (Note that the iii chord is perfectly usable in Fauxbourdon contexts, though forbidden in the system of harmonic cycles.) In the consequent, the same technique connects V6 to I6. 6 6 E : I IV (iii6 ii6 I6) vii° V ! 6 6 V (IV6 iii6 ii6) I This technique works well with descending-thirds progressions (IV6!ii6), descending-fifths progressions (as in the Haydn), and, more rarely, descending fourth progressions (IV6!I6, typically moving on to ii6). B. Sorbet. Here’s a really long passage in parallel first inversion triads from the last movement of the first Mozart sonata. We’re in G major, and the passage connects IV6 to I6. I think the first-inversion triads have the function of cleansing the listener’s palate3, giving us a little break from the incessant recirculation of harmonies. However, you can also see this passage as an extravagant way to connect the initial IV6 to the final ii6 . Note that the passage works, in large part, because it leads to a stereotypical cadence: ii6!I!!V!I, which reorients our ears and reintroduces the system of harmonic cycles. (In other words: if you’re going to use a long chain of first-inversion triads, make sure you end up somewhere really recognizable.) For a similar example, see the opening of the third movement of Beethoven’s first C major piano sonata. For another example, see the Trio of Beethoven’s first piano sonata, or the Rondo of his second piano sonata. When writing fauxbourdon, make sure that your melody makes sense, and that the parallel motion leads somewhere recognizable—usually to a strong dominant or a strong cadence. It may help to think of fauxbourdon as a kind of “thickened melody.” C. I6 as a neighbor to ii6. Here’s a passage from Mozart’s B major piano sonata (K333) where a phrase ends with a ii6-I6-ii6-vii°6 progression; you can think! of the I6 as a kind of “neighbor chord” appearing within the sequence of stepwise triads. 6 6 ii6 I6 ii vii° This particular figure is pretty common in Mozart. In fact, the first piano sonata begins with what can be construed as a ii6!I6!ii6!V progression, where the I6 is again neighboring.