Everyone knows and loves the music of the First Viennese School — you know, the big guys: Mozart, Haydn, Beethoven, and Schubert. Fewer people are familiar with — and a select few love — the 20th-century Second Viennese School: Arnold Schoenberg and his star pupils, Alban Berg and Anton Webern.

Not yet as familiar even as those worthies is today’s Third Viennese School, whose most successful representative is HK Gruber. The 12-tone element in his music, an obvious legacy from the Schoenberg school, is only one side of the highly personal language he has forged. At first blush, Gruber’s use of tonality might seem to align him with the movement that has been dubbed “the New Simplicity.” But tonal structures and popular idioms coexist with serial ones in his music in a totality that, for all the apparent simplicity of some of its parts, is very far from simple-minded.

A former member of the Vienna Boys Choir, HK has among his ancestors Franz Xaver Gruber, the inoffensive 19th-century church organist who wrote “Silent Night,” and who would doubtless be shocked at the wild musical exploits of his descendant. Though no longer active as a bass-player, today’s Gruber still triples as composer, conductor, and chansonnier. In the last-named capacity, he has traveled the world heading several hundred performances of “Frankenstein!!,” his 1976/77 “pan-demonium for baritone-chansonnier and orchestra,” sometimes singing it in German, and at other times, with his deliciously accented English, sounding even more exuberantly and indelibly Austrian.

It was with his composer and conductor hats on that Gruber made his Seattle Symphony debut on Thursday. His 1983 percussion concerto, “Rough Music,” intersperses delicate lines on tuned instruments with explosions of rhythmic and dynamic high jinks, entertaining yet fraught with desperately serious undertones. In his most violent passages, creating a sense of chaos that is yet held under magisterial control, Gruber sounds like a more sophisticated and technically proficient Charles Ives. And wielding the meticulously clear beat of a thoroughly experienced conductor, he drew from the obviously energized orchestra a deft and atmospheric setting around principal percussionist Michael A. Werner’s spectacular account of the solo part.

Gruber proved equally adept in evoking the vernacular American rhythmic zest of the symphonic suite from Bernstein’s film score for “On the Waterfront,” framed by evocatively lonely solos from principal horn Jeffrey Fair, and the Russo-French romanticism of Stravinsky’s “Firebird” suite, played in its 1919 version. The program had opened with “A Jazz Symphony,” by George Antheil (1900-1959), self-styled “bad boy of music,” and in his way no less a maverick than Gruber himself. It’s a diverting trifle, which sounds fresh and individual even in the somewhat toned-down orchestration and texture of the 1955 revision we heard on this occasion.

Coming straight after last week’s Mozart and Bruckner under Gerard Schwarz, the equally thrilling performances of 20th-century music that Gruber fashioned served to emphasize the Seattle Symphony’s broad stylistic range, as well as a technical excellence that deserves to be more widely recognized internationally.

Bernard Jacobson: bernardijacobson@comcast.net