I’m continuing my journey through rhythmic analyses of canonical classical works with Metrical Displacement and Metrically Dissonant Hemiolas by Channan Willner. One of the pieces that Willner analyzes is the Gigue from Bach’s English Suite No. 5 in E minor, played here by Glenn Gould.
A gigue is a Baroque dance descended from the Irish jig. As with all of Bach’s dance pieces, this one is a few levels of abstractions removed from something you might actually dance to. Willner devotes a lot of analysis to a peculiar rhythmic event 43 bars into the Gigue where Bach interrupts the smooth flow of eighth and sixteenth notes with some crazy syncopation. (He also does it a second time.) Willner describes this disruption as a “cadential hemiola.”
The cadential hemiola in mm. 43 and 44 of the Gigue from Bach’s E-minor English Suite… completely disrupts the momentum which the Gigue had built up during its first reprise (see the box and the schematic reduction for Example 2b).
I reproduced Willner’s illustration here:
And here’s the passage in MIDI piano roll view:
Willner goes on:
Here the hemiola is quite incompatible with its surroundings: it replaces the Gigue’s perpetual motion of running scalar sixteenths with sustained chordal eighths that span almost the entire range of both hands. The disjunctive miniature silence that the hemiola’s eighths introduce is remarkable on many counts; there is nothing quite like it among the many movements of Bach’s dance suites (p. 89).
What does this mean? Willner says that when Baroque composers do this kind of hemiola, they are displacing the “effective, thematic meter” earlier or later. In so doing, the short-term sense of “metrical dissonance” can create a longer-term sense of “durational consonance.”
The Gigue has the structure of a fugue, whose subject is its first five bars plus one beat of the sixth bar. Willner says that the metrical structure of the Gigue makes more sense if you think of it as being in 6/8 rather than 3/8, and if you mentally insert a bar of silence (“bar 0“) at the beginning, so that the subject actually starts halfway through a double-length bar.
Within the framework of the Gigue ‘s displacement – counting, that is, the missing bar 0 as an integral part of the subject in 3/8 time – one would parse the subject not as a five-bar phrase with a closing downbeat but as a six-bar phrase that continues into the downbeat of a seventh measure (p. 112).
The countersubject comes in at bar five. But if you count the way Willner does, then it actually starts in the second, “strong” measure of the subject.
Owing to the way in which the countersubject and its continuation later combine with the subject, they help foster (rather than forestall) the emergence of apparent periodicity in the Gigue… [F]ar from preventing a foursquare periodicity from building up, the constant elision of measures at the end of the subject and the countersubject, and at the end of each episodic sequence, combined with the countersubjecťs delayed entrance, all promote what one might call an approximate or simulated periodicity (p. 112).
The metrical displacement caused by the hemiola is really an overlap of two phrases, which actually “undisplaces” the music into proper metrical consonance. Bach alternates between having the meter be displaced by one bar or undisplaced over the course of the Gigue, giving “the impression of on-again, off-again quadratic periodicity” (p. 113).
As always, I hear these things more clearly when everything is at a steady tempo, supported by some tight beats. I made a remix using the breakbeat from “Vital Transformation” by the Mahavishnu Orchestra.
Let’s have a look at the counterpoint in the first 48 bars, shall we? The MIDI piano roll is great for this purpose. The top track shows the entire MIDI file. I manually split up the three voices and color-coded them.
I’d like to make an explainer video of all of this, but I don’t have the resources or the time to do this properly. Who wants to collaborate with me?