The tart, bluesy quaver in Andra Day’s voice has a long heritage. It bends the well-tempered notes of the European scale into idiosyncratic microtones and mocks any inflexible rhythm. It reaches back through Jazmine Sullivan, Amy Winehouse, Erykah Badu, Esther Phillips, Dinah Washington, Ella Fitzgerald, Bessie Smith and, of course, Billie Holiday.

Day won a Golden Globe portraying Holiday in the 2021 film “The United States vs. Billie Holiday,” and recorded a full album of Holiday’s repertoire. She also learned deeply from her bittersweet amalgam of vulnerability and flintiness.

Throughout the history of American music, blues, jazz and soul singers have used the jazzy quaver for the subtlest nuances of emotion: for tension, playfulness, defiance, flirtatiousness, ache or just blithe ornamentation. Day deploys it all those ways on “Cassandra (Cherith),” her second album of her own songs.

Her first, “Cheers to the Fall,” was released in 2015. It displayed her agility and power in dramatic, retro- flavored tracks, and it featured a resolute ballad, “Rise Up,” that became an anthem of Black Lives Matter protests in 2020.

Day followed “Cheers to the Fall” with a Christmas EP in 2016 that included a duet with Stevie Wonder. Since then, she has released soundtrack songs and singles and recorded some guest appearances. But “Cassandra (Cherith)” makes clear that Day has been stockpiling material; she is a writer and producer, alongside many collaborators, on all of its 16 songs.

Day’s 2015 debut album had a reverberant, widescreen, retro sound. By contrast, “Cassandra (Cherith)” favors focused close-ups; it heightens details, making Day’s voice more exposed and even more daring. Throughout the album, her delivery feels questing and improvisatory. She’s so sure of her melodies that she can embellish them at any moment, stretching or rushing or wriggling them as the impulse strikes.

She breezes across styles and eras. From a base in neo-soul, with hip-hop beats underpinning sinuous R&B melodies, Day also touches on Motown, jazz, bossa nova, piano rock and orchestral pop. But the most important sound on Day’s album is her voice. It’s precise but uninhibited, sometimes carefree and sometimes fiercely intimate.

Cassandra is Day’s full first name (she was born Cassandra Monique Batie); Cherith is derived from the Hebrew word for “to cut away.” But many of the new album’s songs are about lingering romantic and emotional entanglements, about how difficult it is to cut away or make a clean break. By the end of the album’s sequence, Day has found some serenity, but only after navigating an emotional labyrinth: from a reluctant, backsliding separation through a thorny new start to, eventually, self-acceptance.

In “Probably,” Day sings about wondering whether to set the record straight about a breakup with someone she still loves: “Probably tell the world that I hated you/ But you know more than anyone that’s far from true.” Her hopping, gliding vocal lines treat blunt piano chords like roadblocks that she’s determined to get around, or above.

Day compares a mutually wounding relationship to drug-gang rivalries in “Narcos (H.C.D.).” Even though she observes, “Your same old tricks and my same mistakes will make things worse,” she admits, “I don’t like things to end.” The beat is obstinately slow, with a creeping bass line, while Day’s voice moves in fits and starts, almost arguing with herself. In the old-school soul ballad “Bottom of the Bottle,” she realizes “You’re bad for me/ I know ’cause I’m bad for you,” but she gives in to temptation, with gauzy backup vocal harmonies easing the way.

She does, eventually, pry herself away from the old romance, only to face different pitfalls. In “Nervous,” a minor-key shuffle, she recognizes that a new partner might be intimidated by her success — but she sings about it in a nonchalant high register, showing it’s not her problem. And in “More,” a waltz with a string section fluttering behind her, she warily accepts a partner — “Promise not to break me if I choose you” — on the way to a euphoric crescendo that has her exulting, “You are what I waited for.” The album’s closing songs, “Still” and “Still Part 2,” use gospel chords to underline hard-won inner peace.

Throughout “Cassandra (Cherith),” Day uses her virtuosity for transparency, exploring the conflicts that come with complicated private desires and public ambitions. Can she handle it all? Her voice says she can.