The strings on the opening track of “The Greatest,” Cat Power’s seventh and most vivid album, will break your little heart in two. A molasses-soaked violin, cello and viola waltz us into an album that bears more resemblance to Van Morrison’s blissful “Tupelo Honey” than to Cat Power’s devastatingly austere early records. These songs of solitude are tenderly wrapped in the majestic velvet shawl of Leroy and Teenie Hodges, core members of the Reverend Al Green’s early-70s band. And thanks to their ceaselessly slinky instrumentation, these songs make for a gallant and ecstatically poignant record.

Last summer, Chan Marshall (known as Cat Power, as if her birth-name weren’t perfect) went to Memphis to record with a brand new band, recruiting some of the city’s legendary musicians. In 1969, the big-haired, bigger-voiced Dusty Springfield did the same thing: Although “Dusty in Memphis” is a pop landmark, decades later it amounts to a white-girl cover album of blue-eyed soul.

“The Greatest”, on the other hand, has an aura all its own — distinct from the desolation of earlier Cat Power albums (“Myra Lee”, “Moon Pix”), and distinct from the Hi/Stax Records sound she’s using as a springboard. By weaving together the two, she’s created songs that are instantly compelling.

The album is too shifty to label, and the only name that might sound remotely right is “indie-soul,” which has a repulsive ring to it. No two songs sound alike: The band lunges from the devout buoyancy of “Living Proof,” to the Texas swagger of “Empty Shell,” then to the subtle misery of “Where Is My Love.”

Yet the songs hold together the whole way through: intoxicated strings swell underneath sparkling guitars, gleeful brass marches next to southern-fried organs, and Ms. Marshall’s deep-throated moans slide into high-register harmonies. This artful coherence extends to an untitled bonus track, a whispered afterthought of lovelorn misery.

But nothing can compare to the jaw-dropping radiance of the title track at the other end of the album. I don’t remember the last time a song with so little (three chords, no chorus, drummer-boy percussion, guitar, piano and strings) did so very much to me. If your knees don’t go weak when she begs, “Secure the ground/ for the later parade,” you should play “The Greatest” again. And again.

The songs that follow are uneven by comparison, which is hardly their fault. The exultant “Living Proof” slickly marries seductive come-ons (“Will you terrorize this/ With your perfect lips”) with unmistakably messianic imagery (“I am your answer, I am living”). But the Hodges brothers soak the song in such rapturous, gospel-inspired instrumentation that it’s tough to worry about the irony.

“Lived in Bars” struts with druggy footsteps, building up momentum as smoky saxophones and muted trumpets lift the song into the album’s most memorable chorus. (Honorable mention goes to “Empty Shell,” a half-silly honky-tonk that bridges Bob Dylan’s 1969 “Nashville Skyline” and 1976 “Desire.”)

Besides a furious closing track — “Love & Communication,” driven by the only distorted electric guitar in sight — the second half of “The Greatest” slows down dramatically. Its songs are impeccably delicate and enduringly memorable, with the exception of a coarse letdown, “The Moon,” which sounds like an age-old leftover.

While the two-minute “Islands” is a crowd pleaser, thanks to its greasy pedal steel guitar, the staggering “Hate” is morbidly dark. It is twice as long, yet adorned with only Chan Marshall’s bitter guitar and downy voice. The late-60s delight of the Memphis musicians is abandoned for grungy solitude, yet the song is somehow as soulful as anything on the album.

And “The Greatest” has its fair share of soul. Despite occasional dreariness, it’s also stuffed with instrumental riches, thanks especially to the inspired guitar work of Mabon “Teenie” Hodges — whom we should all bow to and thank for his role in crafting Al Green’s “Here I Am (Come and Get Me).”

Maybe one day we should be doing the same for Cat Power.