On Thursday, early-music groups Blue Heron and Les Délices combine for a Cambridge concert that includes one of the medieval era’s most ingenious works. Guillaume de Machaut’s 14th-century “Ma fin est ma commencement” is one of the earliest examples of a crab canon: a canon in which one of the voices sings the theme in retrograde, or reverse. Machaut’s piece is particularly intricate — the text simultaneously narrates the music’s construction. “My end is my beginning and my beginning, my end,” the voices sing. “My third part moves in retrograde three times and thus ends.”
The work’s conceptual-art overtones have made it seem perennially modern, a favorite of the avant-garde. Milton Babbitt, that most thoroughgoing of musical modernists, paid homage with his 1978 clarinet solo, called “My Ends Are My Beginnings.” Babbitt’s borrowing of the title is, in part, characteristically punning. The middle of the work’s three sections elaborates a retrograde transformation of the music’s well of pitch material; that underlying scaffolding combines 12-tone rows by overlapping their final and initial pitches.
But the title also hints at renewal. The basic structure — a four-part, all-partition array, in theoretical terms — was both a summation of Babbitt’s research into the musical implications of partitions (dividing a row into smaller, interrelated motives) and a forward-looking breakthrough. The background array of “My Ends Are My Beginnings” would seed numerous subsequent works.
The symbolism can run even deeper — or higher. Scholar Michael Eisenberg noted how the construction and self-referential text of Machaut’s “Ma fin” echoes divine descriptions from Revelations (“I am Alpha and Omega”) and the Gospel of John (“the Word was with God, and the Word was God”). The 20th-century French composer Olivier Messiaen — who, in his vast, posthumously published “Traité de Rythme, de Couleur, et d’Ornithologie,” cited Machaut as the pioneer of such permutations — was of a similar mind, considering musical retrograde as a leap beyond human concepts of directional time, toward divine eternalities.
For all three composers, the technique of retrograde was a specific reconciling of a musical work’s inherent forward flow with its self-contained, objective identity — an idea that can extend well beyond music. T. S. Eliot, in “East Coker” (from the “Four Quartets”), likewise graduated from a rueful consideration of time’s passage to conclude that “Love is most nearly itself / When here and now cease to matter.” The poem ends with a familiar refrain: “In my end is my beginning.”
The Cambridge Society for Early Music presents Blue Heron and Les Délices in “ ‘A More Subtle Art’: the 14th-Century Avant-Garde,” Thursday at 7:30 p.m. at Christ Church, Cambridge. Tickets $25-$30. 617-489-2062, csem.org.
Matthew Guerrieri can be reached at firstname.lastname@example.org.