Everyone loves a good mystery. We are captivated both by an unsolved riddle and the brilliant sleuthing that leads to its solution. If Sherlock Holmes seemed to know more than he should have – the country of origin of the tobacco in a heap of cigar ashes, or the trials of Dr. Watson’s late brother based solely on the pocket watch he wore – the explanation was elementary. Holmes simply engaged in a higher level of observation and clear-headed reasoning than the rest of us.

In the world of classical music, the closest thing we have to Holmes is pianist and scholar Robert Levin, whose latest adventure – the completion of Mozart’s fragmentary Mass in C minor, K. 427 – involved, along with vast academic research, the hunting down of documents in such disparate places as Augsburg, Vienna, Coburg, Krakow, and Berlin; the discovery of a missing Mass section among the sketches of an unfinished comic opera called “The Goose in Cairo”; and forensic analyses of music manuscript papers and inks used at different points in the composer’s life.

The denouement will take place this Saturday night at 8 p.m. at Carnegie Hall (the institution that commissioned the completion) – a performance of the newly completed Mass, featuring conductor Helmuth Rilling, the Orchestra of St. Luke’s, sopranos Juliane Banse and Marlis Petersen, tenor James Taylor, bass baritone Nathan Berg, and the Carnegie Hall Festival Chorus. Mr. Rilling will direct a weeklong choral workshop at Carnegie Hall leading up to the concert, and Mr. Levin will give a preconcert lecture at 7 p.m.

Mr. Levin’s compositional task was to imagine what might have been. Yet the circumstances surrounding Mozart’s original version and its performance in Salzburg’s St. Peter’s Abbey Church in October 1783 are themselves matters of conjecture. From a letter Wolfgang Mozart wrote to his father, the composition has been tied to a vow he had made to vis it Salzburg. That trip had been delayed. “The score of half a Mass, which lies here, still in the best of hopes, may serve as proof, however, of the reality of my vow,” the younger Mozart reported. His wife, Constanze, later spoke of that vow in connection with the birth of their first child, about whom Mozart “had been particularly anxious.”

The work is seen by some as Mozart’s attempt to heal the rifts that had developed with his father and sister, as well as a gift for Constanze, who was in fact the featured soloist in its performance. The new Mass was musically virtuosic and enormous in scale; it clearly violated the wishes of both Emperor Joseph II and the archbishop of the church, who had called for the simplification of church singing, the elimination of solo singing and fugues, and a time limit of 45 minutes.

“It resembles nothing so much as the Bach B Minor Mass,” Mr. Levin told me. “Having showy vocalism praising God is nothing new, and whether it had anything to do with what the emperor wanted was irrelevant, because Mozart wasn’t writing it for the emperor. He was writing it for himself and for his family. It represented, as very few of his pieces do, art for art’s sake, and faith for faith’s sake.” Yet it remained unfinished. The composer is thought to have filled out its missing sections with material from his earlier masses.

Why didn’t Mozart complete the work? “Just about every piece Mozart conceived for his wife remained unfinished,” Mr. Levin pointed out. “Freud would have a field day with that.” But there were more proximate reasons. “Mozart and Constanze took off for Salzburg in July,” he said. “Their new baby died in Vienna on August 19. When I listen to the Et incarnatusest section – some of the most tender music Mozart ever wrote – and realize that the text speaks of being ‘made into flesh by the holy spirit,’ it occurs to me that the death of his son might have made the completion of the Mass just too difficult to contemplate.”

Records of the original work are scattered and often problematic. Most of the autograph score was notated on Viennese 12-stave paper, which could not accommodate all of the instrumental parts, so Mozart created overflow scores for all the choral movements that used a full orchestra. Yet not all movements are fully scored. Many sections of the Mass are missing. And Constanze threw away 90% of the remaining sketches.

Mozart’s sister Nannerl, however, bequeathed the originals of the individual performance parts (now lost) to the Church of the Holy Cross in Augsburg, Germany, and some time before 1808 its choirmaster assembled a score. But this score only adds to the mystery: It contains, for instance, only a single four-part chorus, where Mozart must have had a second chorus as well. Our view of the material is further complicated by the fact that, several years after the Mass in C minor was presented in Salzburg, Mozart used its music again in a cantata, “Davidde penitente,” K. 469.

Others before Mr. Levin have completed the Mass in C minor by extracting material from additional works by Mozart (and, in one case, by using material that was incorrectly thought to be by Mozart). The question, according to Mr. Levin, is: “What kind of quarry do you use to supply the missing elements?”

A version by Philip Wilby used much of the “Davidde penitentee.” “I do, too,” explained Mr. Levin, “but the question is, what movements might those arias be used for, and what is the justification for their use? I may have thought a bit more torturously than many about the liturgical appropriateness of certain music to certain texts.” Mr. Levin said he looked at every piece of sketch material from 1782 and 1783 but also looked to the surrounding years, “as far as 1781 and as far forward as 1785,” the year of “Davidde penitente.”

“In 1783, Mozart was working on only two things of any significance that are vocal or choral,” he said. “One is the abortive opera ‘The Goose of Cairo,’ which he was writing in Salzburg; the other is the C minor Mass. There is a large fascicle that contains the fragment of ‘The Goose of Cairo,’ and on one of its last pages there is a sketch to the text ‘Dona nobis pacem.’ Everybody has agreed that that sketch surely had to be for the Mass. It is printed in the back of the New Mozart Edition score of the Mass.”

Yet this section was not used in the completions of the Mass done by Alois Schmitt, Ernst Lewicki, H. Robbins Landon, or Richard Maunder; Mr. Wilby used it as a brief prelude. “He is the one person who has taken its existence into practical account,” Mr. Levin said. “There is also an eight-part double fugue sketch in D minor, with flags on the eighth notes, showing that Mozart intended this to be a text setting (he’d use beams if it were for instruments). The odds are awfully high that it is for the Mass.”

Mr. Levin found seven different paper types used in Mozart’s materials, and many different shades of ink, each of which has a chronological implication. He visited every city in which sketches or scores could be found and used all of them (as well as his thorough knowledge of Mozart’s practices) to construct the five missing “Credo” movements and to fill in all the other gaps. “It won’t guarantee that the result is of any particular quality,” Mr. Levin said modestly. “But it will assure a maximum awareness of information that might be enlightening.”

Who will judge whether the outcome is a success? “Whether the challenge has been met in an acceptable way will not require the opinion of experts,” said Mr. Levin. “Every member of the audience in Carnegie Hall on January 15 will have a legitimate view of that.”

Robert Levin’s Mass in C Minor, K. 427, will be performed at Isaac Stern Auditorium on January 15 at 8 p.m. (57th Street at Seventh Avenue, 212-247-7800).