In their headlining set at Globalfest Sunday night at Webster Hall, Mucca Pazza played what had to be the most exciting, lavishly intense live show by any band in New York in recent months. With zombie apocalypse choreography and a raw, frequently macabre, punked-out brass band sound, the 28-member version of this Chicago circus rock monstrosity careened through a mix of instrumentals that drew equally on marching band music, the Balkans, horror surf and menacingly cinematic vamps. They used the big split-level space for all it was worth, marching their way in from the balcony, many of the instruments running through battery-powered amps built into the band members’ uniform hats, the players trailed by a ceaselessly energetic crew of cheerleaders who lept gleefully and hoisted each other high above the band when they weren’t flopping into horror-stricken Pompeiian poses. On a couple of occasions, the band split, the brass section scampering from the stage to the balcony and then engaging in a lively call-and-response with the reeds gathered on the sidelines below.

As seemingly chaotic as their antics are, in reality Mucca Pazza are an exceptionally tight, well-rehearsed unit, which an act this size has to be in order to pull off their shtick. The juxtaposition of a bunch of wholesome, athletic, Middle American-looking bunch of guys and girls leaping and grinning against a backdrop of ominous minor keys and monster movie chromatics blasting behind them is surreal to the extreme, and it’s far more disconcerting than it would be if, say, they dressed like dead monks or real apocalyptic zombies (do such things exist? This band makes you think they might). And as entertaining as they are to watch in their non-matching vintage marching band uniforms, ultimately it’s the music (their most recent album Safety Fifth and other releases are streaming online or available for free download at their site) that’s the most exciting part of their act. The surrealism extended to a couple of intros chanted in unison by the cheerleaders: “Embrace absurdity and all that comes with it, good or bad,” seemed to be the message.

One after the other, the songs maintained a creepy carnivalesque atmosphere. A couple seemed to be parodies of happy-go-lucky parade marches; a handful of others were minor-key surf songs turbocharged many times over with roaring brass arrangements. They looked to Serbia or thereabouts a couple of times for pulsing two-chord vamps to bludgeon the audience (or make the cheer squad look as if they’d been bludgeoned); a few of the other tunes had a less gloomy, more lively Mediterranean flavor (the band name is Italian for “crazy cow.”)

One of the best songs got a sobering intro when a member of the band reminded the crowd how brave it must be to go to the school bus stop carrrying a violin – and then the band’s violinist made his way furtively and actually very hauntingly into a wicked gypsy-fueled dance number. Later in the set, guitarist Jeff Thomas led them through a pounding hardcore punk number built on a menacing series of tritone chords, spurring another exodus from the stage by what seemed half the band. The drumline came to the front, the cheer crew and some of the horn players keeled over into mock grotesquerie, and the glockenspiel player and electric mandolinist fired off chillingly strange, ringing solos. Before Mucca Pazza marched in, the impressively large crowd who’d stuck around after five hours of three stages’ worth of gypsy music, brass band funk, latin rock and an early-evening performance by brilliant Iranian composer/spike fiddle player Kayhan Kalhor, were suddenly reinvigorated. Which they should have been: Mucca Pazza are a force of nature. To think that this band actually squeezed themseves into little Public Assembly in Williamsburg a few months ago is as impressive as it is funny. Where this act really ought to be is Broadway, in a big space where they can work their theatrics for all they’re worth.