The Art of Fugue, BWV 1080: Contrapunctus VIII [with analysis]

Описание: This is the first "triple fugue" (i.e. fugue with three subjects) in the Art of Fugue. I have provided my motivic analysis with the following color code:
Subject 1 - red
Subject 2 - green
Subject 3 - blue
Fragment of countersubject 1 - dark red

By labeling the three subjects as 1 2 3, respectively, we can see how Bach uses the permutation matrix[1] as a structural device, which is revealed at the very end. As far as I know no one has discussed the use of the permutation matrix in Contrapunctus VIII.

The piece is extremely rich with motifs/fragments and their transformations that if I labeled everything the score would be too busy. Most instances of the BACH motif (and its inversion HCAB) are indicated.

I hope this video can provide a glimpse of Bach's structural genius and what I see as I'm playing his music. (I don't have synesthesia; I only see patterns.)

[1] The discovery of Bach's use of the permutation matrix in Contrapunctus XIV, the unfinished fugue, is due to Zoltán Göncz. "The Permutational Matrix in J. S. Bach's Art of Fugue. The Last Fugue Finished?" Studia Musicologica Academiae Scientiarum Hungaricae T. 33, Fasc. 1/4, 109-119 (1991)
https://doi.org/10.2307/902439

Die Kunst der Fuge, BWV 1080 by Johann Sebastian Bach (1685-1750)
Contrapunctus VIII
Typesetter: Ruoshi Sun (2022)
Analysis: Ruoshi Sun (2022)
Piano: Ruoshi Sun (2022) on CLP-785

[Score download] https://imslp.org/wiki/Special:Revers...
[Art of Fugue playlist]    • The Art of Fugue, BWV 1080  

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Errata
b.5: Subject 1 should end at the first note.
b.98: Subject 3 should end at the first note.
b.145: The last note in the bass should be C# (played correctly); hence there is no BACH motif.