The most famous Austrian archduke is undoubtedly Franz Ferdinand, but the one with the most musical clout is Rudolph, a piano student of Beethoven as a teenager and a significant patron of the composer as he matured. To him we owe the creation of such major Beethovenian essays as the “Archduke Trio” (natch) and the mighty “Missa Solemnis.” But when he was a lad of 16, Rudolph inspired one of the most problematic works of the Bonn master.

The “Triple” Concerto, for violin, cello, piano, and orchestra, which was featured on Wednesday evening by the New York Philharmonic, was conceived by its composer as a vehicle for his young aristocratic pupil to perform in public. Rudolph wasn’t ready to solo in a full-fledged piano concerto, so Beethoven hid him in a trio of soloists that hark back to the era of the Classical sinfonia concertante. In order for the three instruments to be heard over the accompanying instrumental ensemble, the cello part needed to be a bit more challenging, concentrating on its higher register to distinguish its sonorities from the assembled throng. As a result, the solo passagework is disproportionately weighted toward the cello.

Beethoven envisioned the archduke teaming with two professionals for the inaugural concert. But the work was a miserable failure, given its premiere at a concert that commenced at 6 a.m.and in which the noble pupil did not even participate. Like the “Choral Fantasy” and the ballet music to “The Creatures of Prometheus,” the triple concerto continues to haunt the fringes of the repertoire, dragged out during anniversary years for the sake of encyclopedic completeness.

One of the work’s many problems is casting. If the cellist is featured, then how do the other solo parts avoid irrelevance?

One method is to secure the services of the greatest cellist in the world, so that the other soloists can hold their heads high as supporting players. The Philharmonic did exactly that by hiring Yo-Yo Ma for these concerts, leaving the relatively unknown Jonathan Gandelsman (violin) and Joel Fan (piano) with great stories to relate to their future grandchildren.

Mr. Ma and the Philharmonic’s guest conductor, David Zinman, will be alternating the Beethoven with the Brahms “Double” Concerto this weekend. The works are similar in that Brahms also employs the higher register of the cello to ensure that his soloist is not drowned out at key points. The Beethoven, however, is the much weaker piece.

In the Allegro, Mr. Ma was nothing short of brilliant, digging deeply into his bag of controlled intensity to produce a bitingly high tone with an arresting timbre. Grouping him with young artists produced an interesting contrast. While he explored the richness of generous vibrato, Mr. Gandelsman declaimed much more straightforwardly.Thus the melody, which is consistently bifurcated in this movement – apparently so that Rudolph never had to intone alone for too many measures – was offered in differing styles within the same statement. This juxtaposition highlighted Mr. Ma’s infectious brio, which extended to his facial expressions.

The Largo is the only movement that allows its melody to breathe in an extended, lyrical manner, and Mr. Ma made the most of his one opportunity for rhapsodic communication. Mr. Fan played at a much higher level than the archduke could have. But this short movement serves only as an interlude and introduction to the Rondo alla polacca, a jaunty dance with its rhythms slightly askew. All three soloists seemed energized by this unusual meter and produced a lively concertante to the Philharmonic’s tutti. The orchestra, meanwhile, performed everything very well.

The piano part in the “Triple” is elementary enough that when a version of the piece for just the three instruments was fashioned, the entire orchestral accompaniment was converted to the keyboard to be played in conjunction with the original solo passages. The same malleability allowed Bela Bartok to adapt one of his pieces, the “Rhapsody for Violin and Piano,” into at least four iterations, one of which, for cello and orchestra, was also on this evening’s menu.

Mr. Zinman never seemed to have the measure of this piece, and the ensemble was unfocused throughout. Even the addition of Laurence Kaptain and his cimbalom could not summon up the proper Hungarian flavor. Mr. Ma appeared to be encountering it for the very first time, staring intently at the printed music in front of him – he had needed none in the Beethoven – and uttering various unwelcome squeaks and squawks. But he is a quick study. I daresay that he will be much better Friday night and Saturday night.