The music for these two movements is well known today in instrumental settings with the name "Jesu, Joy of Man's Desiring." Here are the first five measures for these two movements.
One does not need to analyze deeply the famous stream of eighth notes to find within it the chorale tune's opening three notes (B-C-D), as shown below: they occur on beats 2, 3, and 1 in mm. 1-2.
The B-C-D progression—also on beats 2, 3, and 1—also occurs in the bass in mm. 3-4, as shown on the bottom of the full score provided above. In fact, these two pairs of measures enjoy a closer relationship. Below are just the soprano and bass onsets for these six beats. The first six notes, if retrograded and diatonically inverted around middle C, becomes the next six notes. The inverted clef and signatures at the end of the system also indicate this: if you turn this figure 180°, it looks exactly the same.
A "table canon"—whereby a line of music is placed on a table in between two performers, who read it from either side—also contains this kind of symmetry. This reduction of Bach's music could be performed by placing either of the two lines above on a table between a treble performer and a bass performer.
