The famous story says Count Keyserlingk, a sleepless Russian diplomat in Saxony, asked Bach for keyboard music that his 14-year-old servant Johann Gottlieb Goldberg could play through the night, and rewarded him with a golden goblet holding 100 louis d’or. This episode explains why historians doubt that tale, from the 60-year gap before Forkel’s 1802 biography to the absence of any dedication on a title page Bach paid to have engraved on copper and published himself in Nuremberg.

The episode then opens up the architecture: an opening sarabande aria, 30 variations built on its bass line and harmonic progression rather than its melody, and a return of the aria. It walks through the strict rule of three, where every third variation is a canon at a progressively wider interval from the unison to the ninth, followed by a genre piece and a hand-crossing arabesque, and follows the emotional arc from the French overture at Variation 16 to the chromatic Black Pearl of Variation 25 and the quodlibet finale built on folk songs about cabbage and turnips.

• Why a bass-line foundation gives a composer more freedom than traditional melody variations
• The 1974 discovery in Strasbourg of Bach’s own printed copy with 14 handwritten canons in an appendix
• How B-A-C-H adds up to 14 and why the Haussmann portrait shows the 13th canon
• The two-manual harpsichord specified on the title page and the traffic jam pianists face on a single keyboard
• Adaptations for string trio, jazz ensemble, synthesizer and saxophone quartet, plus a 1971 New York City Ballet production