At first, Jack White's first solo album seems to be a straightforward affair. He once claimed "I've got three fathers: my biological dad, God and Bob Dylan," and here, it seems, is his Blood on the Tracks. On the cover, the recently divorced White broods with a vulture on his shoulder. Inside, there are songs about collapsing relationships. These are sometimes depicted via lyrics that are clever and moving: "When someone tells you they can't live without you, they ain't lying," sings White on Missing Pieces. "They'll take pieces of you and walk away." They are sometimes depicted via lyrics that are completely hysterical in every sense of the phrase: "Your momma was a bastard, had your bastard face all over the scene," howls Trash Tongue Talker. "I got some words for your ass, you better find someone up the street." And they are occasionally depicted via lyrics that suggest Jack White might be the most infuriating person imaginable to get into a domestic with. "I know you're mad at me, but if you're thinking like that, I think you'll see you're mad at you, too," he offers, presumably before exiting the room to avoid the heavy items being thrown by someone who's had enough of this passive-aggressive bullshit to last a lifetime.

If the songs aren't about relationships collapsing, they're about Jack White swearing himself off women. And who can blame him? If the songs that aren't about relationships collapsing or Jack White swearing himself off women are to be believed, the fairer sex are basically responsible for every evil in the world, up to and including causing lifeboats to deflate with their high-heeled shoes. Even the internet troll depicted over a clattering drum pattern in Freedom at 21 is a glamorous femme fatale, which has to be one of the more extreme recent examples of artistic licence, at least until such time as someone who looks like Rita Hayworth in Gilda gets hauled before a magistrates court for tweeting abuse to a Premier League footballer.

Not since techno auteur Mike "μ-Ziq" Paradinas released an album called Duntisbourne Abbots Soulmate Devastation Technique has a record appeared to signpost its roots so clearly in a failed marriage. Or perhaps not. The woman you might suppose to be at the root of all this, his ex-wife Karen Elson, turns up all over the album singing backing vocals. Either Elson is a superhumanly tolerant musical collaborator in the vein of Rita Marley, who on Exodus lent her talents to a series of songs about how amazing her husband Bob's mistress was, or White is back to his old "this-is-my-big-sister" trick of playing with public perceptions of his personal life in a weird and unsettling way.

In fact, presenting something deeply weird as entirely straightforward may be the whole point of Blunderbuss. Leaving aside the lyrics, the most striking thing is the way White uses his melodic skills to mask some off-the-wall musical ideas, next to which the fidgety prog-rock riffs that open the album and the irresistible vaudevillian arrangement of Hip (Eponymous) Poor Boy are relatively straightforward. Elsewhere, the listener is treated to structures so wildly episodic that the closing Take Me with You sounds like three different songs – including a 70s stadium-rock anthem and a piece of library music – lashed together, the donning of funny accents ("I'm noivuss," he sings on a cover of Little Willie John's I'm Shakin') and several bursts of falsetto vocals so ridiculous that the Darkness's Justin Hawkins might advise him to tone it down a bit.

White does it so skilfully you don't notice how profoundly odd most of Blunderbuss is until the third or fourth play, at which point you listen to, say, On and On and On and boggle not just at the way he continually shifts the song's mood, but the sheer improbability of the moods he chooses to shift to: from portentous to ghostly to corny to intimate in less than four minutes.

The red herring of the White Stripesish single Sixteen Saltines aside, Blunderbuss is a 45-minute double-take, one long "hang on a minute". But then so, you could argue, is Jack White's career. "People around me … want me the same," he laments on On and On and On, which seems wide of the mark. If people mourned the White Stripes' passing, it might have less to do with a passion for the familiar than a sense that the strange, contradictory, unfathomable figure White cut as half of that duo was more interesting than the straightforward powerpop or 70s blues-rock musician he appears to be in the Raconteurs or the Dead Weather. Those people should be suitably bucked to learn that Blunderbuss is White at his most strange, contradictory and unfathomable, and therefore at his best.