Corinne Bailey Rae dynamites her own musical past and embraces a larger historical one on her new album, “Black Rainbows.”

With her self-titled 2006 debut, Bailey Rae established herself as an agile, airy-voiced pop songwriter; it reached No. 1 in her home country, Britain. Her big hit single, “Put Your Records On,” cheerfully but unmistakably called for celebrating a Black heritage.

Bailey Rae hasn’t rushed her albums. Her second one, “The Sea” in 2010, dealt with her grief — at 29 — at the sudden death of her first husband, the saxophonist Jason Rae; the songs reflected on time, love and sorrow. For her 2016 album, “The Heart Speaks in Whispers,” she followed record-company advice to return to polished pop-soul love songs. By then she had married S.J. Brown, who has co-produced “Black Rainbows” with her.

On “Black Rainbows,” Bailey Rae boldly jettisons both pop structures and R&B smoothness to consider the scars and triumphs of Black culture. “We long to arc our arm through history,” she sings in “A Spell, a Prayer,” the album’s opening song. “To unpick every thread of pain.”

The songs on “Black Rainbows” flaunt extremes: noise and delicacy, longing and rage. In some, Bailey Rae reclaims her distant punk-rock past, when she was in a band called Helen. Others summon retro elegance, toy with electronics and move through multiple transformations. In the album’s genre-bending title song, Bailey Rae repeats the words “black rainbows” over a mechanical beat; her voice gets multiplied into a choir as a labyrinthine, jazz-fusion chord progression gradually unfurls, brimming with saxophone squeals.

The album has a conceptual framework. Most of its songs are inspired by artifacts Bailey Rae saw at the Stony Island Arts Bank in Chicago, a former bank building that now holds a huge repository of African and African-diaspora materials gathered by the artist Theaster Gates: art, books, magazines, music and what the arts bank calls “negrobilia,” everyday objects that perpetuated Black stereotypes. For Bailey Rae, the collection summoned thoughts about slavery, spirituality, beauty, survival, hope and freedom.

An ashtray in the shape of a Black child with an open mouth was a touchstone for “Erasure,” a pounding, screeching, distorted rocker about the exploitation of enslaved children; Bailey Rae blurts, “They took credit for your labor!” and “They put out lit cigarettes down your sweet throat!” Another, more ebullient rock stomp, “New York City Transit Queen” — with Bailey Rae overdubbed into a hand-clapping cheerleading squad — commemorates a cheesecake photograph of Audrey Smaltz, the Black teenager who was named Miss New York Transit in 1954.

That song is followed by a different take on Black beauty: “He Will Follow You With His Eyes.” Bailey recites what sounds like old advertising copy — “Soft hair that invites his caress/Attract! Arouse! Tantalize!” — over a nostalgic bolero. But partway through the track, she casts off the cosmetics, with an electronic warp to the production and a scornful bite in her voice, as she sings about flaunting, “My black hair kinking/My black skin gleaming.”

While Bailey Rae allows herself to shout on “Black Rainbows,” she doesn’t abandon the graceful nuance of her pop past. In the shimmering, billowing “Red Horse,” she envisions romance, marriage and family with a man who “came riding in/in the thunderstorm,” cooing, “You’re the one that I, I’ve been waiting for.”

Bailey Rae shared a Grammy Award — album of the year — as a vocalist on Herbie Hancock’s 2007 Joni Mitchell tribute, “River: The Joni Letters,” and she welcomes Mitchell’s influence with the leaping, asymmetrical melody lines and enigmatic imagery of “Peach Velvet Sky,” which has Brown on piano accompanying Bailey Rae in an unadorned duet.

“Black Rainbows” is one songwriter’s leap into artistic freedom, unconcerned with genre expectations or radio formats. It’s also one more sign that songwriters are strongest when they heed instincts rather than expectations.

Corinne Bailey Rae
“Black Rainbows”
(Thirty Tigers)