Measures 41 to 80

The longest section of this canon begins in measure 41. The subject is transformed by inversion or contrary movement.

Original subject:

Inverted subject:

Measures 37 to 40 are in the key of D minor. The upper voice is imitated by the lower voice in measures 41 to 44 in the key of A minor. Let’s see how Bach manages to harmonize the same melody in both keys:

Remarks:

Measures
37 to 40	The use of rests and long notes in the upper voice of bars 37 to 40 helps Bach to harmonize the passage in both D minor and A minor.
37 and 41	The G# of the second and third beat of measure 37 becomes the third of the dominant chord of A minor in measure 41.
38 and 42	The minor v degree of D minor in measure 38 becomes the A minor tonic in measure 42.
39 and 43	The D and F in the first beat of measures 39 and 43 are harmonized with the D minor tonic chord in measure 39 and with the A minor vii degree of in measure 43. The harmonic ambiguity of the third beat of measure 39 is needed to maintain the A minor key in measure 43.
40 and 44	By using the A and E notes only in the upper voice in measure 40, Bach is able use the D minor dominant in measure 40 (with C#) and the A minor tonic chord in measure 44 (with C natural).

It is amazing how Bach manages to overcome harmonic obstacles with effective melodic solutions!

Bach returns to D minor in measure 61 and repeats the original canon. Measures 41 to 80: