The last page of J. S. Bach’s The Art of Fugue, BWV 1080. (x)

A note from his son C. P. E. Bach, “Über dieser Fuge, wo der Name B A C H im Contrasubject angebracht worden, ist der Verfasser gestorben.” (At the point where the composer introduces the name B A C H [B♭-A-C-B♮] in the countersubject to this fugue, the composer died.)

This great composition is actually unfinished, even the title

Fuga a 3 soggettiwas given by Johann’s son. Scholars dispute this piece and it’s intention. Many believe it is meant to be a fugue of 4 subjects, not 3 as titled. One, Indra Hughes, proposed that this was intentionally unfinished (not just because Bach happened to die).The Permutation Matrix theory

was formed by Zoltán Göncz from an attempt to figure out how Bach would have introduced his 4th subject. This is an easy/simple representation of the mathematics behind this work, as Bach (to put it lightly) based much of his compositional style in math and its relation with music.

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