Will the real Prince please stand up? Oh, hang on, he already has.

It makes perfect sense – or, at least, as much sense as we’re ever likely to get from Prince – that his latest album project comes in two instalments, the first released in September and its sister suddenly dropped on us unawares. He is, after all, a man of two halves.

Even the most casual Prince-watcher will know that the 57-year-old has conflicted, permanently flip-flopping views on the internet. One minute he’s rhetorically asking Alexis Petridis to name one artist who got rich from the internet, the next he’s enthusiastically tweeting a song by Sunderland indie band Field Music (whose work would surely never have reached his ears without the web).

No one knows quite what to make of him right now – least of all his own fanbase. To say that HITNRUN has divided opinion would be an understatement. Phase One was widely panned by Prince nuts, though not by me (I considered it to be possibly his most satisfying album since Lovesexy, which is the Prince equivalent of calling a Bowie album “possibly his best since Scary Monsters”). With Phase Two, the loudest complaint is that anything up to nine of the tracks have been out there for years, if you knew where to look.

This much, at least, is undeniable. HITNRUN Phase Two, like Phase One, is initially available only via Tidal, the streaming portal launched by Jay Z in March amid much superstar hullabaloo as a more artist-friendly alternative to Spotify, but at least three of the tracks – Baltimore, Rock and roll Love Affair, Screwdriver – have already been very public indeed, all released as singles in the last three or four years. Others have previously been dropped as exclusives on Spotify, iTunes and Prince’s own 3rdEyeTunes site.

It would be completely wrong, however, to depict Phase Two as merely a grab-bag of odds and ends, recapping his greatest hits of the decade to date. That simply isn’t how Prince works. His modus operandi, as explained by Prince biographer Matt Thorne in his doorstep-sized tome, is much more methodical. He’ll record a handful of demos with a certain mood or theme which form the core of the album, then he’ll dig back into his legendary vault of thousands of unreleased songsfor others that match them, and finally he’ll write the three or four radio-friendly bangers for which the album becomes known.

His 39th, like its slightly older sibling, is no exception. The HITNRUN albums form a diptych of matching but opposing works. Taken together, they reflect the duality of Prince. Because, just as he loves/hates the internet, he loves/hates music technology. Phase One, unusually for someone not exactly famed for engaging with modern pop, made extensive use of Auto-Tune and some decidedly crunk beats (courtesy of co-producer Joshua Welton). Phase Two is entirely analogue, and far more organic in feel.

It’s also his horniest album for years. Literally: a 16-piece horn section, comprising Prince’s own NPG Hornz and Minneapolis’s Hornheads, are parping away all over most tracks. With his rock trio 3rdEyeGirl put on hold and his many-membered funk troupe, New Power Generation, brought back in, it’s inevitably a more maximalist affair than anything he’s done in a while.

The one thing the two HITNRUN records have in common is their fondness for referring to Prince’s past. Phase One kicked off with sampled snatches of his classic hits, and Phase Two is dotted with references, some more obvious than others.

Rock and Roll Love Affair, a barely veiled religious message wrapped up in a romance, is the most blatant, directly lifting the synth riff from Purple Rain’s Take Me With U, and even the way he phrases the line “That’s when the stars collide” consciously echoes “That’s when I saw her …” from Raspberry Beret. Extraloveable, a jubilantly shag-happy groover (“Remember whenever you need someone to take a shower with, call me up, please …”) originally written for his protegées Vanity 6 in 1982, begins with a split-second throwback: the stab of synth-horns at the start is clearly meant to make us think of 1981’s Controversy. And Stare even daydreams about the Dirty Mind/1999 era: “We used to go onstage in our underwear …”

The album begins with Baltimore, written in direct response to civil strife in America. Built around a guitar motif reminiscent of Thin Lizzy’s Sarah, it paraphrases Ice Cube (“Nobody got in nobody’s way / So I guess you could say it was a good day”), quotes Spinoza (“peace is more than the absence of war”), invokes the “No justice, no peace” chant, and names Michael Brown and Freddie Gray, African-Americans who died at the hands of the police. However, unlike the apocalyptic and similarly themed Hell You Talmbout by Prince’s friend Janelle Monáe, the atmosphere here is sunlit, Aquarian and idyllic. Baltimore could comfortably sit among the hippy-dippy positivism of 1985’s Around the World in a Day album.

Like Sign o’ the Times before it, however, this politicised prelude is deceptive. On the brassy second track, 2 Y 2 D (“too young to dare”), Prince is a randy old dog fantasising about a perfect young lust object who has a “head full of technology” but is “just enough old-school”. His lust leads him astray into one of his naffest lyrics in recent memory: “Internet beauty, everybody wanna hack her.”

However, on Look At Me, Look At U, an exquisite piece of night-time penthouse jazz-funk in a George Benson vein, it also leads him to a line that has your jaw hanging open, wondering whether it’s OK to laugh, as he salutes a beauty that “even Ray Charles can see, Stevie Wonder can too”.

Even more bizarre is the moment in When She Comes, an accordion-laden waltz-time ballad in which Prince refers to “a limoncello ballet, a psychedelic cabaret” – surely the only mention of Italian after-dinner liqueurs in his oeuvre to date. The poorest track is probably Screwdriver, a chugging pop-rocker that’s as subtle as a Dapper Laughs seduction gambit: “I’m your driver, you’re my screw.” The forgettable Groovy Potential, too, could perhaps have been left in the vault, cheesy title and all.

These weaknesses are more than made up for by Black Muse, an exhilaratingly, effortlessly free-and-easy Earth Wind & Fire-style gem that reminds you Prince is the most uncannily gifted musician alive. And, above all, by the penultimate track. The stunning six-minute Revelation comes on like a super-slow sex jam in the Smokey Robinson/Marvin Gaye Quiet Storm genre, although it’s initially uncertain whether he’s addressing his lover or Jehovah. In its closing monologue, however, all becomes clear: after making cryptic rhyming reference to English witchcraft and Hebrew, Greek, Roman and Pharaonic mythology, he concludes: “But the task at hand until we see the sun / Is to keep doing you, until you come … to Revelation.” Prince, in a nutshell: even when his head is in the clouds, his brains are in his underpants.

The album ends with Prince at his most divisive. Big City is a typical NPG party jam, in which the backing singers and horn section get to showcase their chops at great length, until the man himself steps up and yelps “Where’s my guitar?” Like the Sign o’ the Times song It’s Gonna Be a Beautiful Night, it’s exactly the kind of thing that some Prince lovers adore, and usually has me hailing a taxi.

Split fans, split albums, split personality. As anyone who remembers the trouser-endangering terpsichorean skills he displayed in his youth will already be aware, if there’s one thing Prince knows how to do, it’s splits.