I came across this fun "quarantine project" by Dan Tepfer, who is a classically trained Jazz pianist: #BachUpsideDown. He is recording himself playing Bach's famous Goldberg variations on a high-tech player piano. His Yamaha Disklavier is a grand piano with a recording function that can very accurately reproduce a performance. But Dan programmed it to perform the pieces "upside down," i.e. inverted.

A melodic inversion is when a melody is reflected symmetrically around a fixed pitch, e.g. the middle C on the great stave, as in this example in a Bach fugue:



The idea is simple: if the original interval goes up, when inverted it goes down, so that an ascending line becomes a descending line and vice versa. Bach and other composers before and after have used inversion in inventive ways, sometimes alternating or staggering inverted voices, other times playing them in unison. Goldberg variations have a number of such examples, e.g. in Var. 12 - an "inverted canon," where the second voice is an inversion of the first. (Guess what happens when it's played "upside down"?) The technique is used extensively in modern serial (12-tone) music. Dan Tepfer has written a primer where he popularly explains the technique both for melody and for harmony.

The example above is diatonic inversion, which differs from strict or chromatic inversion in that the inverted intervals do not exactly mirror the original. The thing about strict inversion is that it changes harmony, turning major into minor, minor into major, etc. Diatonic inversion attempts to preserve the harmonies of the original, and it is something of an art in that you have some choices to make.

Anthony Tommasini, a longtime New York Times music critic, in his very complementary article about Dan Tepfer's project makes it sound like he did something complicated with the music, but actually Dan used the simpler kind of inversion that can be easily automated. Some commercial music applications have this function, and apps that can "flip" a MIDI file can even be found online. You can have some fun with these, or search Youtube for #MIDIFLIP.

Of course, what Dan Tepfer does on his Disklavier, though not formally complicated, is on a different level musically. The results sometimes sound odd, sometimes surprisingly compelling, but never boring. Give it a listen! My favorites are variations 13 through 15.

By the way, though he mostly works in jazz, Dan Tepfer has a history with Goldberg Variations (not surprising: you don't just learn and masterfully perform one of the most difficult classical music works in a couple of months on quarantine!) Earlier he has performed and recorded the entire Goldbergs with his own jazz improvisations added after every piece, a project he called Goldberg Variations / Variations. He has written a wonderful article about the experience: Doing It Bachwards: my unexpected Goldberg Variations.