David Bowie, “Blackstar” (ISO/Columbia)

Instability and ambiguity are the only constants on this strange, daring, ultimately rewarding album Bowie released last Friday on his 69th birthday — two days before his unexpected death. It’s at once emotive and cryptic, structured and spontaneous and, above all, willful, refusing to cater to the expectations of radio stations or fans. The closest thing it offers as an explanation of its message is the title of its finale: “I Can’t Give Everything Away.”

Bowie’s 2013 album, “The Next Day,” ended a silence of 10 years between studio albums; it revisited his chunky 1970s guitar-band rock with a mood darkened by bitter awareness of mortality. “Blackstar” veers elsewhere. Bowie’s 2014 anthology “Nothing Has Changed” included a new song, “Sue (Or in a Season of Crime),” recorded with the Maria Schneider Orchestra, a modern-jazz big band. The quartet led by the saxophonist Donny McCaslin, a mainstay of Schneider’s orchestra, is Bowie’s studio band on “Blackstar,” and it jams its way into rock, funk and electronics from a jazz perspective. The group complicates the harmonies and fills the interstices of the songs with improvisation, often with McCaslin’s saxophone chasing Bowie’s voice.

Each song on “Blackstar” is restless and mercurial. The 10-minute title track opens the album with wavering guitar and flute tones that refuse to settle on a single key. Mark Guiliana’s drumbeat, when it arrives, is a matter of sputtering off-beats and silences, while Bowie intones lyrics about “the day of execution.” Midway through, the song moves through an improvised limbo and coalesces into a different tune: a march with lyrics about a messianic “blackstar” who also declares “I’m not a popstar.” Eventually the two halves of the song merge, with the opening verses over the march beat, darkening the tone even further. The video clip shows candlelit rituals and, near the end, bloody crucifixions.

Thoughts of death hover throughout “Blackstar.” In “Lazarus,” a slowly gathering dirge with jolts from Bowie on electric guitar, the narrator is “in heaven” with “scars that can’t be seen,” looking back on a profligate life. A remake of “Sue (Or in a Season of Crime),” with a hurtling rock beat and Ben Monder’s keening guitar replacing Schneider’s impressionistic big-band horn arrangement, leaves unclear whether it is a farewell or a murder confession.

Throughout “Blackstar,” Bowie stays more cantankerous than contemplative. “Tis a Pity She Was a Whore” slams out a boom-bap hip-hop beat while Bowie’s voice leaps through an odd-angled melody amid a swarm of overdubbed saxophones. He delivers “Girl Loves Me” in an odd, yodeling cackle, with lyrics that, for reasons unknown, often slip into the Russian-rooted slang Nadsat, from “A Clockwork Orange.”

This album’s last two songs, “Dollar Days” and “I Can’t Give Everything Away,” circle back toward a familiar Bowie approach: the richly melodic, slow-building mid-tempo rocker. “Dollar Days” even allows itself some lush strings. But Bowie isn’t suddenly going cozy. In “Dollar Days,” he croons, “I’m dying to/Push their backs against the grain/And fool them all again and again.” He may be briefly dropping his mask; he may be trying on a new one. Either way, he’s not letting himself or his listeners take things easy.

JON PARELES, New York Times