John Zorn, wearing an alto sax around his neck, is staring at Jackson Pollock's Autumn Rhythm (No. 30) as if unaware that we're all staring at him. Sixty or so people – some cross-legged on the floor, some standing, all reverentially quiet – fill the Metropolitan Museum of Art's Gallery 921. Next to Zorn is a Rothko and a Marca-Relli, as well as Milford Graves, the free jazz pioneer, who is busy creating a tornado of tom rolls and cymbal crashes from his psychedelically painted drum kit.

After studying Pollock's beige, black and white swirls for a few minutes, Zorn turns to the crowd and begins to sketch a mysterious, serpentine melody with his sax. The agitation mounts, the drums begin to roil. Zorn stands on one leg like a flamingo, pressing the sax mouth against his thigh, producing a muted, fluttering effect, before racing up the scale to a particularly pained note – high, quivering. Then came the squeals, the bleats, the blaring zoo noises that sound like abstract expressionism looks.

"In the beginning, when I started playing with John, there were lots of mouths open," says Graves after the set. "They thought they knew John. Don't judge what someone can do until you see them in two environments."

To understand just what John Zorn can do, you'd need to see him in more than just two environments. Having produced, composed and performed on hundreds of albums in genres too numerous to name, you'd need an army of musicians performing for a solid month to have a workable understanding of the breadth of Zorn's oeuvre.

That was exactly the aim of Zorn@60: A series of events taking place all across the city over the month of September to celebrate the birthday of New York's most eclectic, idiosyncratic composer. There was a night of improvised music at the Japan Society with academy-award-winning pianist Ryuichi Sakamoto; a festival showcasing Zorn's film scores; a concert featuring six compositions for string quartets; and the debut of a new piece written for two female vocalists, to be performed beneath James Turrell's luminous installation in the rotunda of the Guggenheim.

But rarely are sound and setting so perfectly paired as the event on September 28th, when a roving band of musicians perform Zorn's music in the city's most revered institution of art. Zorn, easily identifiable in his orange shirt, baggy camo pants and dangling tzitzit, was omnipresent: introducing acts, nodding appreciatively in the crowd as would a fan, pursued from one gallery to the next by a coterie of clipboard-carrying organisers who spoke into headset mics and marshalled the shapeless crowds that followed in his wake.

He stands amid tall, thin, eroticised totems in the Melanesia Room. "To me, this is the spirit room," he says. "You should know that there are ghosts in here, hence the music. Especially that one." He points to an Ambrym Slit Gong – a massive hollowed-out breadfruit tree trunk, into which had been carved a visage with menacing red eyes, a sneering mouth and stunted, reptilian arms. "Look: You can see it reverberating."

In this room of spirits, percussionist William Winant performs Gri-Gri on an array of tuned drums, including one with a circumference of roughly three feet, over the surface of which he slides his thump to produce eerie whale-like moans. Beneath a gold chandelier in the American Wing, an ensemble comprised of Chris Otto (violin), Dave Fulmer (viola) and Jay Campbell (cello) performs All Hallows' Eve, a piece filled with long periods of silence, followed by plucked strings and high frequency violin whistles, climaxing with a fusillade of frantic, ascending notes.

At the Temple of Dendur, Mike Patton – vocalist for Faith No More, Mr. Bungle, Tomahawk, and about a dozen other supremely strange bands – performs Litany IV (For Heliogabalus), inspired by a particularly cruel Roman emperor who was rumoured to have suffocated unwitting dinner guests beneath hundreds of pounds of rose petals that fell from trap doors in the ceiling and who was, in Zorn's words, "killed, cut apart, and flushed down the toilet before he was twenty." (A perfunctory internet search confirms the Emperor's grim fate.) Zorn warns the crowd that the piece was "kind of extreme," but it is still a shock when Patton begins violently stuttering, producing sounds something like a drum machine being dunked in water. Shrieks, gargles, heavy breathing, puking sounds, a few full-bellied screams and a hawked loogie – a five-minute, wordless exorcism, shorn of melody. One would have thought it was random if Patton couldn't be seen flipping between pages of sheet music.

The evening ends in the Arms and Armour Court. Up on the balcony, overlooking the old crests and crude instruments of death, is the Appleton Organ – a stunning contraption of mahogany and pipes sheathed in gold leaf. Where we are sitting – on the floor, near four armoured horses –Zorn can't be seen. And then, unannounced, the hall is filled with an unsettling dissonance that brings to mind a haunted house, with creepy, maniacal laughter emanating from an unknown source up in the wings, out of view. The low, forbidding hum strives for consonance for five minutes until, at last, it resolves in a shimmering, triumphant major chord. We stay in the moment for a while, the sound golden as the organ pipes. And then it is over. Zorn stands and walks to the edge of the balcony, raises his arms and regards the rapturous applause as would some kind of emperor.