#### Final Measures

A new episode in measure 31 leads us to the presentation of a varied subject in measure 34:

The last episode begins in measure 36. Bass and alto use motive a inverted while the soprano plays CS-a:

The first time that the inverted subject and CS-a appear in the fugue is in measure 27. When we try to determine the inversion we find that it is neither and inversion at the tenth nor the twelve. The third inverts as fifth (alto and soprano) and seventh (bass and soprano):

Let's start with the alto and soprano. In order for a third to invert as a fifth and a ninth (or second) as a sixth we would need inversion at the seventh (3 + 5 - 1 = 7):

 This interval: 1 2 3 4 5 6 7 Inverts as: 7 6 5 4 3 2 1

In the case of the bass and soprano the third inverts as a seventh and the ninth as a octave. This is an inversion at the ninth (3 + 7 - 1 = 9):

 This interval: 1 2 3 4 5 6 7 8 9 Inverts as: 9 8 7 6 5 4 3 2 1

This episode leads to the final presentation of the subject, once more in stretto and with the use of countersubject CS-b. The final measures present motive a in its original and inverted forms doubled in thirds: