Prince probably never expected these recordings to be made public. The album feels like eavesdropping, as Prince the songwriter delves into nuances and Prince the pianist cuts loose. He’s exploring and playing around, not constructing taut commercial tracks. Yet the album also turns out to be a compendium, or at least a thumbnail, of Prince’s boundless musicality and of his lifelong themes: romance, solitude, sensuality, salvation, sin, yearning and ecstasy. He shifts musical styles and vocal personae at whim — melancholy, playful, devout, flirtatious — yet it’s all Prince.

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The album includes familiar songs (a brief excerpt from “Purple Rain”), B-sides (“17 Days,” which was the B-side of the single “When Doves Cry” in its band version), album tracks (“Strange Relationship,” “International Lover”), covers (Joni Mitchell’s “A Case of You,” the gospel standard “Mary Don’t You Weep”), and previously unreleased songs and sketches (“Wednesday,” “Cold Coffee & Cocaine” and “Why the Butterflies.”)

Image “Piano & a Microphone 1983” is the first release from Prince’s storied archive of music. Credit...

Nearly all of the lyrics are, in some way, about longing. Prince sings about post-breakup loneliness in “17 Days,” offers a slow-motion come-on in “International Lover” and depicts a love-hate seesaw in “Strange Relationship.” He performs “International Lover,” which had already been released on “1999,” as a suspenseful, impulsive constellation of sounds and silences, chords and clusters and single notes answering his falsetto vocal; the lyrics jettison the airplane metaphors of the studio version for single entendres.

Prince plays “Strange Relationship,” which he would rework for eventual release on “Sign ‘o’ the Times” in 1987, as a jazzy rhythm workshop, a two-minute experiment in percussive chords and vocals that devolve into grunts. He even reshapes “Mary Don’t You Weep” — a spiritual that, as he must have known, Aretha Franklin turned into a catharsis on her gospel album “Amazing Grace” — from a profession of faith into a bluesy warning that “Your man ain’t coming home.”