When the New York City Ballet’s production of “George Balanchine’s ‘The Nutcracker’ ” opens today, the dancing onstage will offer fairy-tale delight. But what is equally important — and often overlooked — is what’s going on in the orchestra pit. Tchaikovsky’s music for “The Nutcracker” is both overplayed and underappreciated. The composer extracted eight numbers from the score and incorporated them into “The Nutcracker Suite”; the most famous of those portions are often abusively employed in television commercials, movies, and, worse yet, cell phone ringtones. As a result, it is not unusual for the well-exposed ear to perceive this music as juvenile, even trite.

But listening to the complete score can counter that. The annual return of the ballet is an occasion to give its magnificent orchestral work fresh attention. It allows us to put the overly familiar compositions of “The Nutcracker Suite” within their proper context, to appreciate the composer’s innovations, and to hear it all anew.

Tchaikovsky’s score is a musical narration of the plot, which is somewhat slender, even though it was derived from reputable literary sources: E.T.A. Hoffmann’s fairy tale “The Nutcracker and the King of the Mice” and a French version of it by Alexander Dumas père. The ballet scenario, prepared by the legendary choreographer Marius Petipa together with Tchaikovsky, streamlines the plot considerably. Nearly all the action takes place in Act I: a family Christmas party, followed by an imagined battle between mice and toy soldiers, after which the Nutcracker Prince leads Marie (or Clara, as she is named in some productions) to the land of the sweets. In Act II, the Sugar Plum Fairy presides over what is essentially a plotless act consisting of pure dances and divertissement.

The work’s magic begins with a “miniature overture,” which is in sonata form but without the expected central development section. As with so many pieces in “The Nutcracker,” Tchaikovsky’s imaginative orchestration is central to the musical effects. Here, the distinctive element is the absence of instruments that play in lower registers. Thus, the overture does without cellos and basses. The result is an unusually bright sound that, combined with the crisply sparkling thematic material, neatly suggests that “The Nutcracker” is a piece about children, yet in a sophisticated way. Another choice moment comes when the girls at the party lull their dolls to sleep with a soft lullaby played by flute over a gently rocking accompaniment. They are interrupted by a boisterous clash as the little boys at the party charge them with toy guns and horns. The lullaby returns, and so do the boys again, but the interruption then leads to the Grossvater dance, an old German tune that Schumann immortalized in his piano works “Papillons” and “Carnaval”; it is danced by all the guests, both children and adults. After the Grossvater dance, the lullaby is heard a final time. It is one of the tenderest and quietist moments in the score.

No slight to the dancers, but perhaps the most dazzling visual moment of Balanchine’s “Nutcracker” comes when the family Christmas tree grows to an enormous, exaggerated proportion. During this ideal combination of music and stagecraft, Tchaikovsky’s melody is simple: two phrases, each consisting of four notes ascending stepwise, with two falling notes added to the second phrase. It is, in fact, a reworked version of a tune originally intended as a violin solo in his earlier ballet, “The Sleeping Beauty,” but later cut. The melody is repeated again and again at ever-higher pitch levels, with a steady crescendo that is achieved both through greater volume and an expanding array of instruments. The process is then repeated not once but twice, perfectly conveying the mystery and wonder of the tree’s miraculous growth. It ends with a triumphant clash of cymbals and blaring of horns that never fail to elicit a round of applause. The most substantial dance movement of Act I comes at the end, with the Waltz of the Snowflakes. First, a flutter of seemingly random notes, each of which is embellished by double grace notes to suggest falling snow, comes from the flutes. Then the notes, as so embellished, are arranged in a descending pattern to form the waltz’s first theme. Again, the richness of Tchaikovsky’s orchestration is arresting, but the most striking aspect of the waltz involves not instruments but offstage women’s voices (performed in the Balanchine production on tape) that present a lilting, contrasting theme suggestive of the wind. The technique is similar to Verdi’s offstage humming chorus in “Rigoletto,” but Tchaikovsky’s soothing melody suggests a heavenly choir.

In Act II, the various national dances of the divertissement section are all distinctive and engaging. Though the exuberant, hyper-energetic Russian dance is widely recognized, the Chinese dance is especially ingenious. What’s striking is the wide gulf between the piccolo’s melody-carrying solo and the bassoon’s insistent two-note pattern octaves below; plucked strings create contrast by responding with a light, bouncing motif. Throughout the score, the flutes are kept busy, but never more so than in the Dance of the Reed Pipes, in which three flutes play the melody in close harmony.

The most novel effect of all comes during the Dance of the Sugar Plum Fairy. In this piece, Tchaikovsky employed what was at the time a new instrument. On a trip to Paris, he discovered the celesta, which he described as “midway between a tiny piano and a glockenspiel, with a divinely wonderful sound.” Tchaikovsky made arrangements to have a celesta shipped to St. Petersburg, but he instructed a colleague that it should be shown to no one, for he feared that Rimsky-Korsakov or Glazunov would learn of it and use it for unusual effects before he could. It is not just the instrumental timbre that is key to the Dance of the Sugar Plum Fairy, but also the gently mysterious staccato harmonies Tchaikovsky devised to show it off.

After more than 50 years, Balanchine’s production remains essentially unchanged, although new sets designed to take advantage of the new facilities were constructed when New York City Ballet moved from City Center to the New York State Theater in the 1960s. But one thing will be different this year. When the orchestra brings to life Tchaikovsky’s score, it will be playing from new orchestral parts. The old ones had been so worn out that they were close to disintegrating. Few other classical works face this enviable problem.