"These are brokenhearted love songs," Leslie Feist called out at her show at the Academy of Music on Tuesday night. "Can you relate?"

Feist, who performs under her surname, was only a song into her set, but it wasn't too early for her to proclaim that song, "The Bad in Each Other," as the evening's thesis statement. "For however long we play," she said, "it's the same old stuff" (only she didn't actually say stuff).

In truth, Feist substantially undersold the breadth of her songwriting, but even accepting her premise that her oeuvre is simply composed of variations on a theme, the range of variation was striking. "How Come You Never Go There" was a relatively straightforward lament about lopsided commitment, while "The Circle Married the Line" worked its geometric metaphor to oblique ends.

The song selection was weighted heavily toward Feist's 2011 album, Metals, and pointedly skipped "1234," which brought her fame by way of an iPod commercial in 2007. That song pegged her as something of an easy-listening artist, to be referenced in the same breath as a pumpkin spice latte. The turbulent Metals goes a long way toward dismantling that reputation, and on stage, she went further still, demonstrating an urgency lacking from the more polite recorded versions.

More than anything, Feist's two hours on the Academy's stage were testament to her prodigious skills as an arranger, orchestrating sparse, smartly deployed instrumentation and intricate, mobile vocal harmonies. In addition to a three-man backing band who contributed bass, drums, and keyboards — as well as the sounds of a custom contraption composed of two violins clamped to a table — she was joined by the female vocal trio Mountain Man. Sometimes, they simply added a smooth surface to Feist's abrupt vocal leaps, filling in gaps and sanding down sharp edges. But more often, they functioned as an additional instrument, or instruments, evoking the a cappella orchestras of Björk or her Canadian countrywoman Mary Margaret O'Hara.

The audience played its part as well. Inspired by the looped birdcalls of opener Timber Timbre, which built atmospheric tableaux that evoked the sweep of spaghetti Westerns and the eeriness of Gothic drama, the crowd turned the high-pitched whistles of between-song encouragement into a fluttering, twittering chorus that plainly delighted the evening's headliner. "This place is beautiful," Feist said, likening the Academy to Royal Albert Hall, "and you all are making it more beautiful by not being precious about it."

At several points, Feist played choir director, singing instructions to the crowd. As a prelude to "The Circle Married the Line," she split the Academy into three tiers, handing each audience segment a piece of a major triad. (The high C she assigned to a man in the third row she caught using his iPad between songs.) Shaped by chromatic accents and resonant open fifths, the harmonies were rarely so middle-of-the-road, but even when the songs found a place of relative calm, Feist would splinter it with her jagged guitar playing, her arms jerking away from the strings as if pulled from the rafters by an unseen puppeteer. But of course, she was the one pulling the strings.