SIR Paul McCartney has a dark side. It isn't one that need trouble the divorce lawyersortheredtops,butit's emphatically and unmistakably there. A sublime melodist he might be, but as Memory Almost Full - his umpteenth solo album since the break-up of The Beatles - bears out in every other track, thereissomethingstrangeabout McCartney'ssongcraft,anedgy approach to harmony that gives even the feeblest ditty a sting of ambiguity.

This has to do with something more thanMcCartney'sstrangebutnow unbreakable habit of singing in keys too high for his voice, giving all those classic songs that about-to-be-hoarse schoolboy strain. What's immediately striking about Memory Almost Full is the relative simplicity of the harmonic language.Inthepast,McCartney could, if he had been minded, sit back and smile knowingly when the rock presscastigatedhimforapparent lapses like The Frog Chorus and Mary Had A Little Lamb, the latter of which attractedJohnLennon'sscorn.For in each of these and in much of the non-Wings McCartney canon there is a fascinating (to the muso, at least) and deeply affecting (to the rest of us) distortion of the usual harmonic logic.

This was already happening in his Beatles days. The final chorus "yeah" of She Loves You is complex enough to keep a musicologist busy for hours. In his book The Unknown Paul McCartney, IanPeelexposedanotherintriguing aspect of the Macca story. While it was generally assumed that Lennon was the Beatle most interested in the avant-garde - when asked, George retorted "'aven't gard a clue, wack"; Ringo probably wasn't asked - it was in fact McCartney, usually seen as the hand behind the lighter and prettier stuff, who really showed an interest in and understanding ofcuttingedgeandexperimental music in the 1960s. It was McCartney who was listening to Stockhausen, turning up at the obscurest galleries to observe the latest shortwave radio virtuoso or "silent" composer, and it was McCartney who was dabbling in avant-garde work of his own. The real identity of Percy "Thrills" Thrillington has been an open secret for a long time, but McCartney's interest in going off-reservation and working in determinedly non-commercial contexts still almost never gets an airing.

There is a possible reason for this. No fault of Peel's but his book did leave open the interpretation that McCartney had once dabbled in obscurity the way Cecil Parkinson once dabbled in Communism; that this was all in the past. The striking thing about McCartney is that he is incapable of leaving that edgy, tonally skewed approach to songwritingbehindhim.Itcoloursalmost everything in the back catalogue and even tinges the sublime pop artifice of Band On The Run, a classic of Revolver andAbbeyRoaddimensionsbuta recordwithawholespectrumof unexpected overtones and subliminal awkwardness. I listen to it maybe once ayearandalwayswiththesame unease.

The voice no longer strains so much and has aged, seemingly rather suddenly, though there's a trap waiting for unwary critics here since some at least ofMemoryAlmostFullwasmade before the completion of his 2005 albumChaosAndCreationInThe Backyard,whichproducerNigel Godrich tweaked and pitch-shifted into something that almost sounded like a brilliant Macca tribute act; so quintessentially "Paul" it sounded fake. The new record is, for all its manifold faults and a similar spirit of generic retread,therealthing.It'stinged throughout with thoughts of mortality - Linda's, John and George's, his own, possibly Heather's as well - and that is a subject McCartney has always been uneasyaboutevenacknowledging.

Thetabloidsgotaperfect,bone-shaped story out of McCartney's seemingly offhand reaction - "It's a drag" - to the murder in New York of the man with whom he will be twinned in eternity as one of the greatest songwritingimaginationsever.Precisely how do you react to a shouted question from a reporter about a once-dear friend and joined-at-the-hipcollaboratorwho'd just been blasted by dum-dum bullets? More than usual, McCartney retreated into his shell and into that curiously elegiac and pastoral fantasy world he likes to inhabit when things get tough.

Here, he takes it on full-face. Feet In The Clouds seems to be about John and George. 'Til I Die isn't exactly Leonard Cohen, but it's the first time McCartney has been willing to admit there is a skull beneath the (deceptively youthful) skin. He's still not at ease in that skin and takes the worst photograph of any major music star, thanks to a self-conscious inability to suppress the thumbs-up or just stand still and smile. Given how often he must have faced a camera and given that Linda had one in her hand for most of the first years of their marriage, he never really got it. This time he's either squinting across an overturned armchair - and someone, so it might as well be me, will inevitably suggest a referencetopast"domestics"-or clutching the non-collar of a neo- Beatles jacket and pouting in a way that makes his mouth look old, old, old.

And yet, the songwriting is as young andasintenseas anything he's done since the overlooked 1993 classic Ram, previously the highpoint of the post-Beatles, non-Wings oeuvre.There'ssomerubbish thrown in (at least, rubbish if you want it to deliver up any meaning). Mr Bellamy has an Erik Satie-like oddity. Only Mama Knows sounds like pastiche ELO. Ever Present Past is a light and skittish thing, but it's significant that a song about failing memory is also a song in whichbasicrulesofharmonyare quietly and subtly "forgotten".What'sgoingoninthataccompaniment? Nothing more unsettling than an old man who pretends not to be able to do itanymoreandthendoesitwith consummate ease.

No-one was expecting Blood On The Tracks or even Blood On The Carpet. Theonelessontobetakenfrom McCartney's career to date is that you don't look for public airing of griefs and grievances. This is a man who's happy to show the world his model farm and train set and to "express his emotions" through them like a traumatised child, all the while knowing that his real psychic dramas are worked out in the structure of those remarkable songs.

That said, the new album is unmistakably a tribute to the only certain love of his life after music. Memory Almost Full has a nicely contemporary sound. The McCartney hard drive has perhaps been driven as far as it's able to go. We are all chock-a-block with retro culture, our iPods and downloads part of a vast Alexandrian library of sound in which The Beatles occupy an absolutely central place. But there's something else in that title. There are computer programmes that will do it for you, but it's nice to think that one night,doodlingwithapencil, McCartneyrecognisedbyaccident that Memory Almost Full is also an anagram of "For my soulmate - LLM".

He's never themed an album, or given it a title before the tracks are laid down, so it's nice to think that in this finished, very personal, possibly last and very moving record there's an unconscious - only the song Gratitude makes it explicit - last farewell to the womanwhosharedhishighsandlow,the obloquy and the embarrassments, and who added her thin, straining voice to someofthosebizarreharmonies: Linda Louise McCartney.