These days there’s a lot of talk about artists who “break down barriers” and defy stylistic conventions. But there’s nothing wrong with making music within the parameters of traditional styles. John Zorn’s jazz is good jazz, and his classical music – he calls it “notated” music – is good, too.

Mr. Zorn is about going to extremes – physically as well as artistically. He can be heard most frequently at Tonic, the Ludlow Street club that’s so far south it makes the Knitting Factory look like Midtown. Yet his compositions are also performed regularly at the Miller Theater, way up at 116th Street, as they were Friday night.

All three works on the program referenced the supernatural and the metaphysical. The first piece was “Mysterium,” conducted by Brad Lubman – a work with four movements in that many different languages (if you count the Latinate title). For me this was the highlight of the program: Mr. Zorn has made hundreds of albums, but one of the charms of seeing his music live is untangling the ways he creates his sound.

The first movement of “Orphee” uses an unusual sextet of flute, violin, harp, plus one player each on keyboards, percussion, and what Mr. Zorn refers to as “live” electronics. Flautist Tara Helen O’Connor did bird calls, while electronics replicated other sounds of nature. Meanwhile, percussionist William Winnant made hornlike noises and keyboardist Stephen Gosling used celeste and harpsichord to create pitches that sounded electronically generated even though they weren’t.

Other movements were equally stimulating. “Sortilidge” was a protracted duet between two bass clarinets (Michael Lowenstein, Tim Smith). “Frammenti del Sappho” used the voices of five female singers singing wordlessly (“There’s no point in using a text unless you’re going to do a Cole Porter thing,” Mr. Zorn said). And “Walpurgisnacht” was for string trio (two violins and cello). To me, “Mysterium” was a reminder that notated chamber music can be as exciting as the best small-group jazz.

The second work was “Gri-Gri,” whose title refers to a voodoo talisman. This was a solo piece for percussion, played by William Winnant on 13 tuned tom-toms. When I saw the battery of percussion on stage, I expected to hear something reminiscent of John Cage; instead, Mr. Zorn’s writing was some of his most straightforwardly melodic (even though, in this format, melody and rhythm are essentially the same thing). This was avantgarde music that could have been performed on “The Ed Sullivan Show.”

In a pre-concert discussion, the Miller Theater’s executive director, George Steel, asked Mr. Zorn, who is also a fine alto saxophonist, why he never integrates the saxophone into his “notated” pieces. Mr. Zorn responded, in language more colorful than his bright camouflage trousers, that when he writes in a classical style, he feels it impossible to improve upon the time-honored format of the string quartet.

Fittingly, he final piece was “Necronomicon,” a spooky and mysterious five-movement work for a traditional string quartet. He used contrast as a key element, playing up the distinctions between bowed and pizzicato playing, as well as between piano and forte dynamics. The first movement, “Conjurations,” had four strings that sounded like chanting and casting spells, and the fifth movement, “Asmodeus,” was filled with intense, demonic energy – almost like a string quartet playing rock ‘n’ roll or free jazz. Hells bells!

Perhaps this is the time for me to mention my opinion that Mr. Zorn’s music is fully deserving of being heard at Jazz at Lincoln Center – or even the Chamber Music society.