This is a fun idea, although I think referring to these inventions as "inverted" is a bit misleading because the notes still all go in the same directions. It's just a matter of shifting one part down a few octaves and the other up. However, you could say that having an idea like this tossed my way was like having a pebble tossed into a pond. A Lilypond, to be precise.
Because all of the Inventions are readily available online in Lilypond format, I snagged the notes for the F Major Invention No. 8 demo'd above and, because Lilypond is magic, did some quick little operations to:
- truly invert the two parts (down is up and up is down)
- play the original backwards (retrograde)
- combine the inversion and retrograde operations
The results are more satisfying than I expected, although I admittedly have quirky tastes. Of course, Bach's tonal relationships work in such a way that flipping things upside down distorts a lot of the original context. Major often becomes sort of minor, final chords end up without the root on the bottom, etc. But I decided not to try to "fix" anything, but rather remain perversely faithful to the original. One might think of these "compositions" or "variations" as negative space defined by what Bach actually wrote.
There are dissonant moments that sound like they could come straight from a 20th century contrapuntal master like Shostakovich, but I also think the pure energy of Bach shines through. Rather than write much more about them now, I'll just present this little "Theme and Variations" for your enjoyment (variations 2-4 are where the real fun begins):
THEME:
VAR. 1 - HANDS SWITCHED:
VAR. 2 - HANDS SWITCHED & INVERTED:
VAR. 3 - RETROGRADE:
VAR. 4 - RETROGRADE INVERSION:
Again, even if you don't like everything, I hope you'll find a few passages here and there to spark your interest.
Here's another example of me re-inventing some Bach:
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