Sooner or later, war is likely to erupt in any major Christopher Rouse work, and in his new

Organ Concerto

, it happens right on time and with an intriguing sense of purpose.

This co-commission by the Philadelphia Orchestra, National Symphony Orchestra, and Los Angeles Philharmonic had its world premiere this week at the Kimmel Center. The Friday performance under music director Yannick Nézet-Séguin revealed some of the composer's most satisfying music, but not for typical reasons. It started triple forte - not unexpected for this master of orchestral extremes - though what followed in the first movement left me wanting more.

The second slow movement, however, found an unexpectedly fascinating middle ground with a downright lyrical opening - a soliloquy of sorts - with organist Paul Jacobs accompanied by warm, cozy strings. Almost inevitably, the lower brass intervened ominously. An organ-timpani duet was so indescribably itself, you want to hold onto it and demand, "What exactly are you saying?" The passage returned, like an atonal, upside-down marching song, one that clearly seems to know where it's going but wants to leave you speculating.

Then, in the third movement, orchestra and organ moved into all-out mayhem, of which Rouse is also the master. It's a piece that puts its ideas first and organ display second, which is ultimately more convincing than the program's opener, Samuel Barber's Toccata festiva, which has a lot of exhilarating moments, but which shows the composer pushing himself to into ultraextroverted music that he could write but that wasn't where he lived.

The all-organ program celebrated the 10th anniversary of the Fred J. Cooper Memorial Organ, with the Saint-Saëns Symphony No. 3 in the second half, a piece Nézet-Séguin has recorded twice (in 2006 and 2014), but not with the best features of Friday's Philadelphia Orchestra outing.

The piece itself can seem about as deep as a bottlecap, though Nézet-Séguin gave the slow introduction a great sense of mystery. The first allegro moderato section can seem to putter to a close, but the orchestra's wind soloists gave their two-note motifs an eloquent gravity I'd never previously heard. Elsewhere, the performance was a romp with masterfully built climaxes and meticulous orchestral balances.

Both in Saint-Saëns and Rouse, organist Jacobs delivered subtle shifts in sound that had an infallible sense of rightness with the music at hand. He also let it rip with a crisp, fast, high-virtuosity encore, Widor's "Toccata" from his Symphony No. 5. The audience was suitably wowed.

Additional performance: 8 p.m. Saturday at the Kimmel Center, Broad and Spruce Streets. Tickets: $40-$147. Information: 215-893-1999 or www.philorch.org.