It would be easy to view Mr. Pärt’s compositional arc as unique to his personal vision, but it was also in line with an international exodus from serialism that began in the mid-’60s, looking inward and backward. He pored over the writings of the early church, and immersed himself in medieval chant and Renaissance polyphony. The sparse, gothic music for which he is known emerged out of that period of study. Today, “Für Alina” and its complement “Spiegel im Spiegel” — ubiquitous from film soundtracks and as accompaniment for modern dancers — represent études in Minimalist technique that point toward more promising developments.

Tintinnabuli comes to fruition in Mr. Pärt’s masterful choral works, including the 1997 “Kanon Pokajanen.” But it is music that also presents a conundrum for the secular listener, one who might seek out the spirituality of classical music at large rather than that of the Orthodox church.

These works are rhetorically charged, their most effective musical moments matched to the message of their sacred creeds. Mr. Pärt once wrote of the “Kanon Pokajanen”: “I tried to use language as a point of departure. I wanted the word to be able to find its own sound, to draw its own melodic line. Somewhat to my surprise, the resulting music is entirely immersed in the particular character of Church Slavonic, a language used exclusively in ecclesiastical texts.” The exactitude with which Mr. Pärt sets the text is consistent with Orthodox theology, which stresses the reciprocity between beauty and truth.

Historical distance has tempered the explicit Lutheran message of Bach’s cantatas or the Roman Catholicism of Palestrina’s Masses. Disregarding the scriptural details of Mr. Pärt’s music, though, might mean ignoring an aspect integral to a living composer, even if he is vague about it.

The perspective also follows a trajectory of thinking about Mr. Pärt that dates back to the 1984 album “Tabula Rasa,” which started his collaboration with the ECM label and its producer Manfred Eicher. The elegantly wrought abstract spirituality of those records has helped position Mr. Pärt as a composer for all faiths. The global classical music market has mediated — or perhaps tamed — his religion, opening up the iconography of the Orthodox church to a broader mysticism.

It is that tension that the Arvo Pärt Project will explore. “Some of the classic things that are observed about Pärt, and even expressed by him, are these utterly universal human realities, like the interplay between suffering and consolation,” Dr. Bouteneff said. “That’s the whole logic of tintinnabuli as well, that you have the melody voice, which is the human straying, and the triad voice, which represents the divine stability and consolation.”

But there are narrower implications for Orthodoxy that Dr. Bouteneff said he hopes the project will address. “What has our liturgical tradition done with that dynamic? And how might that feed into what Pärt is doing?” he asked.

This dichotomy is particularly evident in Mr. Pärt’s 2009 “Adam’s Lament,” his most recent large-scale work and the centerpiece of the Carnegie concert. In a program note, Mr. Pärt described Adam as a “collective term which comprises humankind in its entirety and each individual person alike, irrespective of time, epochs, social strata and confession.”