Definition
Das Musikalische Opfer (Musical Offering, BWV 1079) is a set of fugues and canons composed by J. S. Bach in 1747 on a theme — the Royal Theme — provided by King Frederick the Great of Prussia. It includes a six-voice ricercar, several canons including the famously self-referential Endlessly Rising Canon, and a trio sonata. The Endlessly Rising Canon modulates upward through six keys and returns to the starting key one octave higher — a strange loop in music.
Why it matters
How it works
Bach's strategy: take Frederick's theme and subject it to every contrapuntal device of his era — fugue, canon (at various intervals and inversions), retrograde, augmentation, modulation. The Endlessly Rising Canon achieves its closed loop by transposing up by a tone each time the canon repeats. After six repetitions you arrive at the starting key, one octave higher, having traversed the chromatic scale. The piece can in principle be played indefinitely; in practice performers play it through a few cycles.