More about 2 over 3

December 04, 2015

After writing last time about 2-beat groups in triple meter (in the aria "Öffne dich" from Bach's Cantata BWV 61 Nun Komm, der Heiden Heiland), I started thinking about other examples. One that came to mind was the Invention No. 8 in F Major. This piece is obviously much more widely known than "Öffne dich", and the way in which Bach plays around with the meter in this case is easier to grasp.

The work starts out with a pickup, which must be performed as such (articulation and so forth), or the listener will experience a slightly jarring effect around bar 4.

Bach uses a simple and effective metrical trick starting at the downbeat of bar 8, and ending at the downbeat of bar 12. There are in this span 4 measures of 3/4 time, equal to 12 beats. This number 12 is fairly important in music, generally speaking. 12 is of course rich in divisors: 1, 2, 3, 4, 6, 12, which made it a favorite of number theorists since time immemorial. In this case, it makes sense to look at what happens here almost as a meter change to 4/4 at bar 8. Not only do we have 4 measures of 3/4 time here, we also have 3 measure of 4/4 time. This is clear not only by the contrapuntal rhythm but also the harmonic rhythm, leading to cadence on the dominant. Let your ear follow the upper voice and you'll see what I mean.

The piece proceeds decidedly in 3/4 until four bars from the final downbeat, where the metrical trick is used again, this time leading to the closing cadence on tonic.

Probably this piece will be easier to remember, should you ever want to call to mind an example of music that has some fun pretending to be duple meter for a while within a triple meter.

BTW, the latest offering from All of Bach features an interview with the conductor and soloists that includes some commentary about this same topic in the Cantata BWV 196 Der Herr denket an uns.

Regards,
Aaron