In March, the jazz pianist and composer Dan Tepfer found himself confined to his apartment in Brooklyn with all his bookings canceled for the foreseeable future, like musicians everywhere. So he decided to work seriously on an idea he had long been toying with.
Mr. Tepfer, 38, who also excels in classical music and has an undergraduate degree in astrophysics as well as sophisticated technology skills, wrote a computer program. He recorded himself playing Bach’s “Goldberg” Variations, beautifully, on a Yamaha Disklavier, a full grand piano with a high-tech player piano function; his program then played back each variation, but flipped.
Without getting too theoretical, counterpoint refers to music written in multiple parts, or lines, that overlap and intertwine. Sometimes Bach — as well as other counterpoint masters — played around with inversions of lines. For example, a melodic strand where the notes basically ascend in a specific pattern would be turned upside-down, so that the altered line basically descends — a mirror-like reflection.
The results, Mr. Tepfer writes on his website, are like looking at Bach “through a prism”; the music “feels like a new piece.”
Yet at the same time, it sounds eerily familiar, starting with the upside-down Aria — the theme developed over Bach’s 30 variations. The slowly ascending notes in the lower staff of Bach’s original, which outline a G major triad, become, in the upside-down version, a graceful falling figure in the top line. The gently embellished original melody, with its turns and trills, becomes an animated lower line. And the crucial bass pattern, which begins with four descending notes and provides the foundation for the entire piece, now becomes the topmost voice, starting with four rising notes. The music, which Bach wrote in G major, now sounds vaguely like it’s in G minor, though the harmonies are elusive and disorienting.
Bach’s first variation is defined by its jocular rhythmic swing: Hearty strands of 16th notes unfold atop a dancing bass line, until the parts switch roles — and keep on switching. In Mr. Tepfer’s upside-down version, the sway, contours and character still come through.
In that case, Mr. Tepfer indulged in “complete messing around” with Bach, as he put it in a recent phone interview. But with #BachUpsideDown he is, he said, “leaving the info pristine,” and just creating its mirror. To do so, however, while leaving the spacing between the notes — the intervals — the same, involved an arcane process that has been called negative harmony.
This gets very complicated. But the theoretical manipulations the conversion entailed are not likely to matter to most listeners, who will instinctively hear the upside-down versions as having an unorthodox yet weirdly familiar allure. And somehow, the rigor of Bach’s writing — its rhythmic and contrapuntal intricacies — comes through vividly. The new minor-mode cast to the overall sound is disorienting. I’d say wonderfully so.
Take the breathless Variation No. 5, which in Bach’s original is, Mr. Tepfer said, a “stunning combination of virtuosity, keyboard gymnastics and drama.” Turned upside-down, it sounds like a demonic pianist is playing some wild-eyed, impish piece written by Prokofiev in a fit of Neo-Baroque madness.
In Variation No. 7, the Baroque dance character of Bach’s music, with its clipped ornaments and jagged dotted-note rhythms, is almost more pronounced in the upside-down version, though the harmonic realm of the piece now seems curiously spacey. In its new version, Bach’s Variation No. 10, a short fugue, may be the strongest example of the “prism” effect Mr. Tepfer described. You feel you’ve heard this music before. Yet the counterpoint seems to roam all over the place and the harmonic language is vaguely like Hindemith in his Neo-Classical vein.
Variation No. 13 is Mr. Tepfer’s favorite of the 15 he has completed so far. Bach’s original is the first contemplative variation in the series, at once sad and innocent. The inversion works “shockingly well,” Mr. Tepfer writes in his notes, with the melody now in the bass and the two supporting voices in the treble. It sounds like a “more ominous” version of the original, he writes — but “just as poignant.”
This isn’t the first time Mr. Tepfer has combined his music-making with his programming expertise. On his latest jazz album, “Natural Machines,” he improvises on standards like “All the Things You Are” while a computer hooked up to the Disklavier he’s playing reacts in the moment and supplies contrapuntal additions.
#BachUpsideDown involved intense work of a new kind, he said, which is why he only finished half of Bach’s 30 variations: “I needed a break,” he added. “I’m about to start again.”
The videos he has created include manuscript pages for the inverted variations that can be printed out easily. Some pianist colleagues have been learning them and sending him videos of their own. Mr. Tepfer has only just begun reading through the upside-down versions himself.
“They’re not harder to play than the originals,” he said — though, he added, “the originals are hard!”