The new piano concerto by the Swedish composerAnders Hillborgis vivacious, funny, heroic, eloquent, plain-spoken, thoughtful and wholly irresistible.

It serves, in other words, as a musical portrait of pianistEmanuel Ax, who joined the San Francisco Symphony and Music Director Esa-Pekka Salonen in Davies Symphony Hall Thursday, Oct. 12, to give the piece its triumphant world premiere.

Composers often talk about what it means to write with a particular performer in mind, but this 25-minute charmer, commissioned by the Symphony, takes the notion to a whole new level. It plays to all the qualities that make Ax one of the finest, and most underrated, pianists of our time — his tact, his seemingly effortless dexterity and the unnerving clarity of his artistic vision.

At the same time, the concerto opens up a world of beauty and entertainment for any listeners who may not be familiar with Ax’s artistry. There are no in-jokes for Axophiles (at least, none that I detected) and no daunting mysteries to be solved. This is a work in which constructive ingenuity and the pleasure principle walk arm in arm.

所以即使有一种不可避免的r的感觉ightness about Ax’s presence for this occasion, it isn’t as though other keyboard virtuosos couldn’t add the piece to their repertoire. They’d just have to approach it in an appropriately Axian state of mind.

What does that mean? It means taking joy in the technical challenges of Hillborg’s writing, which are considerable, and spreading that joy to the audience. It means infusing even the most athletic passages with lyrical grace, and sharing the vein of wit and wonder that runs through the entire score.

Hillborg has doffed his cap to his Muse by giving the piece, which is formally his Piano Concerto No. 2, the subtitle “The MAX Concerto.” “Max” is short for “Manny Ax,” and the all-caps styling, the composer says in a program note, reflects “the exuberance and geniality of this outstanding pianist.”

There’s really no arguing with that assessment. The piece is in a single movement played without pause, but within that stretch of music there are no fewer than nine distinct sections, each with its own character and dimension.

The price of that scheme is an occasional formal blurriness, a suspicion that even with its large-scale repetitions the score remains fundamentally a bit of a grab bag. But the recompense is a sense of profusion, as one musical thought after another bounces over the footlights.

The piece opens with rippling keyboard figures out of Beethoven’s “Emperor” Concerto, as if to acknowledge the piano concerto’s illustrious past. It includes a couple of delectable sections labeled “Toy Piano,” in which sparse, high-pitched patterns cast a crystalline spell with a fusion of Maurice Ravel and Steve Reich.

“Hard Piano” summons up a stretch of brusque, pounding keyboard chords, while “Mists” allows the orchestra to come to the fore in a series of eerily evocative string harmonies. Naturally, there is a cadenza for the soloist, a chance to take the spotlight alone and plunge into torrents of dense, dramatic finger-busting.

Perhaps the most striking aspect of “The MAX Concerto” is its easy but uncompromised accessibility. At a time when audiences remain wary of contemporary music — slow to unlearn the lessons of past generations whose tastes were treated by too many composers with snobbish contempt — Hillborg (whose“Rap Notes”helped open the Symphony season) writes with a generous, expressive touch. You can’t help but love the results.

The premiere alone would have been reward enough for an evening, but Salonen and the orchestra flanked it with superb performances of familiar music by Brahms and Beethoven. Brahms' “Haydn” Variations led off in a rendition that was by turns stately and warm.

Better still, the second half of the concert was devoted to one of the most thrillingly dynamic accounts of Beethoven’s Second Symphony I’ve ever heard live. This is a prickly, overcaffeinated score — the main theme of the finale is the auditory equivalent of a swift jab in the ribs — and Salonen and the orchestra decided to lean into that character with unabashed force.

The tempos were swift and aggressive, the phrasing hard-edged. It was glorious. Salonen bounded onto the stage afterward for the curtain call, his face wreathed in a smile and with an almost breathless air of accomplishment. He knew exactly what he’d just pulled off.

Reach Joshua Kosman:jkosman@sfchronicle.com