The story behind Mahler's Tenth Symphony, the composer's last work, suggests that the piece would be as vehement as Shostakovich or as sorrowful as late Brahms. Mahler died before he finished it, and midway through composing, he was heartbroken to learn of his wife’s infidelities. The manuscript is strewn with “ach, ach, ach” in the composer’s hand, and such anguished comments as “O God why hast thou forsaken me?” Yet the work itself balances its tormented, despairing passages with elaborations of the Viennese waltz and the Ländler, an Austrian folk dance, and ends with music of incomparable beauty and serenity.

Of the symphony’s five movements, Mahler completed only two, the first and third. The rest of the work is in short score, a four-stave, glorified string quartet voicing of the piece with much of the harmony and counterpoint but only occasional indications of instrumentation. Several musicologists have tried to complete the Tenth; Deryck Cooke’s version has won the widest acceptance. Cooke insisted that his was only a “performing version” of the draft, not a completion. Mahler, a compulsive reviser, would have reworked the material and brought forth thousands of unknowable details. Yet, Cooke argued, the work is still worth performing as it stands. “Mahler’s actual music, even in its unperfected and unelaborated state, has such significance, strength, and beauty, that it dwarfs into insignificance the momentary uncertainties” about missing instrumentation and counterpoint.

The result is similar to a classical sculpture reconstructed using shards and cement. The shape is definitely Mahler’s, and the Viennese Schwung, even though the unfinished movements lack some of the complex textures and unexpected twists that characterize his earlier works.

With the Tenth Symphony, Mahler came closest to anticipating the revolutions of twentieth-century modernism. The first movement opens with a meandering, barely tonal melody in the violas, and later climaxes in one of the most famous passages in all his music: a wrenching, agonized chorale for brass, followed by a grindingly dissonant nine-note chord. The second movement’s frantic changes of meter in almost every measure anticipate Stravinsky’s Rite of Spring. The terse third movement, “Purgatorio”, has a rustling, quiet perpetual motion interjected several times by the full orchestra. A harsh brass dissonance opens the fourth movement, over which Mahler wrote: “The devil dances with me.” The movement alternates between violent despair and wistful waltz-like passages. It ends with a heavy crack on a muffled drum. “Only you know what it means,” Mahler wrote here; Alma disclosed that it recalled a fireman’s funeral procession which they both witnessed in tears. The fifth movement begins with a funeral march punctuated by the drum. Out of this, a soaring flute melody provides a glimmer of hope. The ensuing main section brings back the agitation of the Purgatorio, ending in a return of the nine-note dissonance. In its wake, an ethereal, hymn-like passage for the strings concludes the work.

As with all Mahler, in the right hands it is glorious, in the wrong, it’s a mess. The 36-year-old English conductor Daniel Harding has made a specialty of the Tenth, having chosen it for his debut recording with the Vienna Philharmonic. He is a top-to-toe conductor, shaping and pulling the space with his entire body to shape the sound. Whatever his technique, Harding emphasized the lyrical elements of the score while doing full justice to its more intense passages. He proved particularly adept at the crucial task of realizing and dramatizing Mahler’s kaleidoscopic shifts of mood and timbre. Another strength was in his sensitivity to transitions and the silences between and within phrases; as Mahler said, “Not all the music is in the notes.” This was especially evident at the very end, when Harding let the resonance linger, somehow cutting off premature applause with his back.

With other conductors, the New York Philharmonic can deliver noisy, choppy Mahler performances. But here, they delivered the warmth and blend the piece needed. The timbres of the different instruments wove their way in and out of prominence, striding forward or lending depth as called for. Of note were the first horn, Philip Myers, with a series of demanding solos, and principal flute Robert Langevin, who sang on the flute melody.

In an excellent performance such as this, the supposedly problematic issue of the Tenth’s authenticity fades away. For people who fear Mahler, or listeners who have not found their way into his expansive sonic world, the Tenth Symphony may actually be a fine point of entry.