Jazz singer makes varied song set her own; Claudia Acuña at The Jazz Kitchen

All together now: I’d like to teach the world to sing — like Claudia Acuña.

Well, no, not really. Individuality counts for a lot, especially in the wide world of jazz singing. So finding a personal style is almost a duty.

The Chilean-born singer has such a style. It involves a broad reach of repertoire, songs that don’t necessarily emerge from the jazz bag, songs that don’t seem to be pulled from any particular pigeonholes.

It reaches more than gesturally to the South: Astor Piazzolla’s “Vuelvo al Sur” (Return to the South) was movingly performed in her first set Wednesday night at the Jazz Kitchen. The show was part of Indy Jazz Fest.

Acuña interprets songs out of some deep place within. She doesn’t take a flamboyantly emotional approach: Her phrases never heave, hiccup or gasp to convey feeling.

Instead, they billow attractively, without strain, like a sail catching a good breeze. The tone stays unmannered and clear, as in the originals “Tulum” and “That’s What They Say.”

As focused as the show was on Acuña’s vocals, she worked collegially on the bandstand, supported by Jason Lindner, keyboards; Juancho Herrera, guitar; Mark Kelley, bass; and Yayo Serka, drums.

The arrangements often relied on ingenious rhythmic patterns, none more so than the set-ending “Every Time We Say Goodbye,” with Cole Porter’s melody floating over a churning groove. It offered a completely different perspective on a favorite standard, including a subtle shift in atmosphere when the lyrics contrast the beloved’s presence with his absence.

Inspired instrumental episodes tended to emerge in surprising places. “El Cigaritto,” an un-PC song from Acuña’s childhood about the joys of smoking, featured a lyrical guitar solo that was gradually transformed by the intensity of Kelley’s bass.

But the band’s chief marvel properly remained Acuña ‘s singing. To put one’s own stamp on music without affectation is rare among jazz vocalists, many of whom never stop primping. Acuña seems to have traded in her mirror for a window.