Though they play Baroque music, the ensemble L’Arpeggiata is more like a jazz band than a traditional orchestra. Anchored by a continuo (rhythm section?) led by artistic director and theorbist Christina Pluhar, they are joined by various other instrumentalists, singers, and even dancers, fitting each of their projects. Using improvisation and felicitous combinations of traditions, they explore various forgotten repertoires from the Neapolitan tarantella to, on Thursday evening at Carnegie’s Zankel Hall, the Baroque mystery play.

Despite long program notes on the inspirations of ritual dramas performed during Holy Week, the conception is entirely Pluhar’s. Her most inspired stroke was mixing sacred Baroque music with Corsican folk material. The latter was sung by the all-male vocal quartet Ensemble Barbara Furtuna, and alternated with more classical Baroque material and Italian folk material. It may sound like a grab bag, and the structure was loose, but the result was a stunning mix of old and new.

The program opened with an long drum solo by percussionist David Mayoral, leading directly to an a cappella number by Ensemble Barbara Furtuna sung in close harmony. Next was a violin solo by Heinrich Biber, and then a lullaby by Tarquinion Merula, “Hor ch’è tempo di dormire.” The alternating pattern was maintained through the evening.

For this non-Catholic, following the narration of the Passion was difficult, but the emotional trajectory from astonishment to anger to consolation was clear. First linked by the passion play theme, other connections began to appear between the diverse material. The harmony of Corsican music is not Bach, with a more modal language and a tuning that is far from equal-tempered, but it found a counterpart in the seconda prattica Italian Baroque. Each number ran into the next to form an unlikely whole, some even featuring modern dancer Anna Dego, adding to the sense of the performance as a theatrical event.

It certainly wasn’t a conventional concert, but what should one call it? The experience was more than the sum of its parts. The parts were best when genres mixed, such as when Ensemble Barbara Furtuna joined the instrumentalists in “Maria,” which included a jazzy cornetto solo by Doron Sherwin. But except at the very start of the program, the spirit of improvisation seems to have left this project: while little of what was performed can be found exactly in a score, the mood was set, and indeed the playing was very similar that found on the group’s CD version of this project, Via crucis. Some more spontaneity may have been welcome.

Soprano Racquel Andueza sang the more traditionally Baroque numbers with angelic clarity and had a fine rapport with the audience; however, her power was limited by monochromatic vocal color and lack of dynamic range. While idiomatic and accompanied by an inventive and varied continuo realization by Pluhar, her renditions of the lament-like “Queste pungenti spine” by Benedetto Ferrari failed to make a major emotional statement. However, her spirited rendition of Monteverdi’s “Laudate Dominum” (certainly the best-known piece on the program) brought the concert to a joyful close. More immediately striking was the vocalist Lucilla Galeazzi, whose raw and throaty renditions of various traditional Italian songs had intensity and drama.

The instrumental contributions of L’Arpeggiata were distinguished, especially their continuo work: the interplay between Pluhar’s theorbo and the rest of the ensemble of lute, guitar, and (most of all) the unusual psaltery, which is something like a hammered dulcimer, produced a wide palette of plucked accompaniment. The instruments are, of course, historically informed, as was Veronika Skuplike’s excellent violin playing.

L’Arpeggiata is a product of the historical performance movement, but at a moment when fewer and fewer musicians and scholars are concerned with the “authenticity wars.” The past, in this view, is not something to be replicated but rather a source and inspiration for modern musicians to make something exciting and new. Traditional Corsican music can stand alongside Baroque music because it sounds good, without concern for a historical justification for this juxtaposition. We are fortunate that musicians as intelligent and creative as Christina Pluhar have the freedom to rummage in so many musical closets.