“This is our first and last performance in these beautiful acoustics,” said baritone Gordon Jones before Britain’s Hilliard Ensemble sang its encore, Peter Erskine’s “Romeo and Juliet,” in Duke Chapel on Tuesday night. It was the sole piece of American music on a program that spanned 12th-century France and 21st-century Estonia, all knitted together in the traditions of sacred or courtly polyphony.

The chance to hear these four male singers, unaccompanied and relying only on the heavenly natural reverb of the vaulted chapel for amplification, would have been special in any case. It was especially so because Hilliard Ensemble is set to retire this year, scheduled to perform its final concert in London this December.

For four decades, the Hilliard has basically owned its lane—vocal chamber music from the medieval and Renaissance periods, as well as contemporary works in early music styles—against stiff competition from the likes of The Tallis Scholars and, more recently, Anonymous 4. The reasons for their eminence were evident in this sublime Duke Performances concert, which also served as the kickoff for the Triangle-wide HIP (short for “historically informed performance) Music Festival.

Singing without vibrato in full, rounded voices, the Hilliard displayed an effortless-seeming mastery of group timing and dynamics, of color and pitch and phrasing. The ensemble has enjoyed a long and celebrated recording career for the German label ECM and has ventured beyond a capella music in its collaborations with Norwegian saxophonist Jan Garbarek. But as transcendent as its discs can be (I’m particularly fond of 2008’s Audivi Vocem), the ensemble has to be heard and felt live to be believed.

The program ranged through time and space, beginning in the Renaissance with chansons and plainsong from England and Italy and France, some anonymous and some written by renowned names such as William Cornysh and Josquin des Prez. Then it leapt into modernity with a selection of madrigals by Gavin Bryars—settings of elegant love poems by Blake Morrison.

The Hilliard plunged back to the dawn of polyphony with the 12th-century innovator Pérotin, and it was remarkable to imagine what the mysterious composer would make of the world in which his music is still, miraculously, being performed. Some arrangements of traditional Armenian sacred songs followed. They were bookended by two works from close Hilliard collaborator Arvo Pärt, whose And one of the Pharisees punctuated all the polyphony with its stately homophonic lines.

Throughout the concert, the Hilliard’s voices blended beautifully, relying on the precise execution of layered rhythmic patterns for expression. Still, no amount of modesty could keep the unearthly voice of countertenor David James from standing out, especially in the solos provided by Pärt. Whenever the long, braided lines of melody resolved in unison chords, I invariably got the chills, as though hearing the long-delayed answer to a question I hadn’t known I’d asked.

The strange syllables rolled slowly over and turned through each other, full of meaning whether sung in English or Latin or French, so that ancient sacred works and modern romantic ones alike blended into one seamless mass. To contemporary Western listeners, polyphonic music goes by a commoner name—generally, we know it simply as “music”—and the Hilliard boiled it down to its most fundamental elements of harmony and rhythm, unadorned with frills and production techniques, which heightened and refreshed it.

The influence of this music still resounds, however quietly, through much that is modern: Fans of the indie voice-looper Julianna Barwick, who performs at the Carrack Modern Art on Valentine’s Day, would recognize her music’s origins in the Hilliard’s selections. This was a potent dose of the real deal, a holy experience even for the secular.