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This month, the Oriana Consort opens its 25th season with a program including a miniature masterpiece that originated as a musical brain-teaser: Giuseppe Verdi’s “Ave Maria,” one of his “Quattro Pezzi Sacri.” In 1888, the Gazzetta musicale di Milano, a journal that regularly included musical puzzles for its readers to solve, published a curious scale invented by Bolognese musician Adolfo Crescenti: neither major nor minor, modal nor chromatic. The challenge: devise a convincing, contrapuntally-correct harmonization of it.

The following year, Verdi’s friend, librettist, and fellow composer Arrigo Boito showed him the scale and its published solutions. The “awkward scale,” as Verdi called it, piqued his interest; within a few weeks, he had fashioned his own solution, a setting of the “Ave Maria.” But, while Verdi eventually was convinced to publish it, the “Ave Maria” was omitted at the premiere of the “Pezzi Sacri.” It wasn’t “true music,” Verdi complained. “It’s a game.”

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That aspect intrigued one of Verdi’s countrymen. By the mid-1970s, the composer Luigi Nono was at an impasse. He had been a leading exponent of atonal modernism, and then, in a series of increasingly confrontational works, put that style in service of his radical Communist politics. But then Nono’s composition stalled. His breakthrough, the 1980 string quartet, “Fragmente-Stille, an Diatoma,” was an extreme turn: brief, quiet sonic aphorisms, separated by lengthy passages of silence. And the vocabulary was new, too — Nono derived his material from the same “scala enigmatica” Verdi adopted.

Nono’s concept was inspired by his friendship with Massimo Cacciari, an Italian philosopher and politician. Cacciari’s philosophy centered on the idea of “negative thought,” a critique of the traditional philosophical dialectic, the thesis-antithesis-synthesis cycle moving ever-closer to absolute truth. Cacciari rejected the possibility of dialectical synthesis, instead proposing a negative background to all discourse, a nothingness surrounding and delimiting irreconcilable philosophical and political language-games. (Negative thought sparked fierce if recondite debates that nevertheless had real implications for leftist Italian politics: In Cacciari’s formulation, traditional Marxist politics, predicated on dialectics, could never attain its revolutionary goal through bottom-up class struggle.)

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The invented scale’s frustration of conventional harmonic resolution and arbitrary nature became a musical analogue to Cacciari’s ideas. Nono’s quartet made Cacciari’s “negative thought” audible, a nothingness of silence surrounding self-contained modernist updates of the “game” that Verdi dismissed. But for Nono, the game was serious. Like Cacciari, Nono wished to clarify problems and possibilities, not least those of musical communication. Just to listen to music “is very difficult,” Nono wrote. “Perhaps one can change the rituals; perhaps it is possible to try to wake up the ear.” At the very least, Crescenti’s odd scale woke up Verdi’s, and Nono’s.

Oriana Consort’s “O Radiant Dawn.” At University Lutheran Church, Cambridge, Dec. 8; Church of Our Saviour, Brookline; Dec. 13; First Lutheran Church of Boston, Dec. 15. $15-$20; www.orianaconsort.org

Matthew Guerrieri can be reached at matthewguerrieri@gmail.com.