NEW YORK (NYT NEWS SERVICE).- What constitutes virtuosity?

It’s a commonplace, yet problematic, word in classical music. It generally refers to a performer’s technical prowess, the ability to dazzle with a sheer display of technique. But what’s the threshold for virtuosity, and how do you even isolate it from depth and insight?

Two studies were recently on offer in New York. On Friday, Yuja Wang played a program at Carnegie Hall that boldly mixed works spanning nearly three centuries. Then, on Tuesday at Alice Tully Hall, Daniil Trifonov performed, for him, a rare outing into Bach.

These immensely gifted young artists have not only different musical orientations and personalities, but also different kinds of virtuosity. Wang is, perhaps, more overtly brilliant, though she is capable of probing musical sensitivity. Trifonov is the thinking-person’s idea of a virtuoso — a serious-minded, modest-seeming musician with uncannily formidable technique.

Where they’re similar, however, is in how they both took their audiences on unusual musical journeys that challenged the meaning of virtuosity.

Wang, by juxtaposing 13 wildly contrasting works, invited us to hear resonances and connections in the music that go deeper than eras and styles. Some of the pieces were subdued and reflective, like the graceful Galuppi Andante with which she began. Yet she brought a pensive approach to everything she played, even to long stretches Scriabin’s teeming, fervid, single-movement Fourth and Fifth Piano Sonatas. I wouldn’t have thought it possible to draw such delicacy and Chopinesque nuances from the hellbent Fifth as she did. But she could also dispatch the piece’s leaping chords, bursts of breathless runs with cool command.

In Ravel’s “Une barque sur l’océan,” Wang’s playing was undulant and rippling. Berg’s early Piano Sonata — a harmonically elusive, almost expressionist work — sounded here like something Brahms might have composed had he lived another decade. During one stretch, she found common ground between two of Brahms’ searching intermezzos and a few of Chopin’s mercurial, lilting mazurkas.

In a program note and recorded message played before the concert, Wang explained that she would not perform the works in the order originally listed; instead, she would give the recital “its own life” by responding to how she felt in the moment and playing whatever piece struck her. This raised some difficult questions that have stayed with me, and it seemed to leave many audience members shuffling through their programs trying to figure out what they were hearing — especially with less-familiar fare by Berg, Monpou and Scriabin.

Wang was inviting audiences to just “enjoy the ride,” as she wrote. Do you have to know the name of a piece in order to enjoy it? That’s a profound question. Maybe not in the moment, but certainly soon after. Yet no clarification ever came during the concert. And, as usual, Wang did not announce her encores, which included a crackling account of Prokofiev’s driving Toccata in D minor.

Trifonov has seldom played Bach’s music in public, so he considered his program at Tully a new and challenging venture. He began and ended with transcriptions of Bach: Brahms’ ingeniously detailed and dramatic transcription for left-hand alone of the great Chaconne from the Partita No. 2 in D minor for solo violin; and Myra Hess’ beguiling, flowing transcription of “Jesu, Joy of Man’s Desiring.”

The main offering, though, was “The Art of Fugue,” which was left incomplete at Bach’s death. It includes 14 elaborate fugues, about an hour’s worth of the most riveting, complex and astonishing contrapuntal music ever written. I have never been so impressed by Trifonov’s virtuosity — the most musically comprehensive kind, which is what it took for him to play this work so magnificently.

In a way, “The Art of Fugue” is another transcription, since Bach scored it on multiple staves (one per part) and never specified what instrument, or instruments, he had in mind. A pianist has to figure out how to execute some lines that crisscross awkwardly. But Trifonov had the music sounding as if Bach had conceived for the modern piano.

Looking like a somber, scruffy monk in training, Trifonov played with a focus and concentration that radiated throughout the hall. The performances abounded in scintillating grace, wondrous shadings, even touches of impetuousness — all the qualities that distinguish his Chopin, Liszt and Schumann. Yet no romantic excess or affect intruded upon the integrity and directness of his music-making. And his voicing of the strands of counterpoint was uncannily clear. Suddenly, in the midst of subdued, flowing streams of notes, a midrange statement of a theme would sing out with clarion sound and subtle lyricism.

For encores, he played charming, buoyant and playful works by three of Bach’s sons: Johann Christian, Wilhelm Friedemann and Carl Philipp Emanuel. True to form, he did not announce what the pieces were, leaving the audience to just listen.

I bet, however, that people in the audience would have loved to know what they were hearing.

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