"When the invitation came from the British Antarctic Survey," says Max (as he's universally known), "I thought at first it was a joke, because even six years ago, which is when I went, I was way beyond the age where people do this sort of thing."
But it was both serious and sensible. Looking for a composer to mark the 50th anniversary of Vaughan Williams's Sinfonia Antarctica with a new work that would bridge the gap between the arts and the sciences, the sponsors had hit on the perfect man for the job. As Max said on Desert Island Discs last week, he had been responding musically to the sounds of nature ever since walking up Helvellyn with his parents as a small boy. "The mist came down, and I heard in the distance the music I was going to write. That was the sound of the orchestral music I write now."
And when he came to settle on his Orkney island, "the soundscape of sea and gull noises, the wind in the heather" immediately found their way into his music: "I didn't consciously set out to mirror them, but when I was writing my first symphony those flute-calls came through - the seagulls I was hearing."
For Max, this congruence between nature and art is filtered through mathematics. On his desk, he always keeps a shell. "At present," he tells me, "it's an ammonite fossil, whose spiral directly reflects the Fibonacci mathematical series." That is a sequence of numbers where each is the sum of the two preceding it; the shell, Max says, is his justification for organising one of his latest quartets on a similar mathematical form.
"It gives you patterns of recurrence that sound absolutely right, yet are haphazard enough to sound improvised. You don't plan all this on paper, of course - you're not consciously working with numbers. But with notes and rhythms you are consciously working with proportions, and those reflect numbers."
The responses in his Antarctic diary, which is written in breathless wonder, are more visceral. After medical checks and basic training in survival techniques, he joined the crew of a research ship, living with them in cramped, hugger-mugger intimacy, making what sound like very dangerous forays across the ice, and noting his impressions in the diary:
"Disconcerting, in the infinite silence, to hear ice crack and split before the ship's bow, then roar along the keel to the stern in a tumultuous clatter of slabs and shards..."
"An elephant seal, a long way out. A Minke whale blows and flips. Penguins on distant ice honk. The seals demonstrate their considerable vocabulary, as gentle snorts, wheezes and warbles sound from all directions."
A snow avalanche pouring over the ship creates "the mightiest, gentlest, longest whisper ever". And, although there's no wind, "occasionally an astonishing sound whistles gently from the peaks, almost subliminal at first, but growing into an alto-flutish lament that resonates somewhere between your ears, then reveals its true origin when a high and complex counterpoint, suggesting ghostly Oriental flutes, and creates a sonorous wandering tone, softly pulsing across the whole ice shelf."
This "terrible, hostile wonderland" reminds the composer of the hidden artwork in medieval cathedrals, "created by sculptors to the greater glory of God". Of all this, says the humbled diarist, "any music I eventually write can only give the palest hint".
And he insists that what he's written is, despite its title, not a symphony. "It's a tone poem. And it's not a literal representation of my experience, because that wouldn't make musical sense. It's a distillation. All you can do is try to give the impression of what it was like." But a very vivid impression: the sounds of the ice-break and the avalanche permeate everything, and one movement ends in what he calls a musical junkyard, echoing the way Antarctica is littered with junk from earlier explorations. "I make references to several of my recent works, consigning them to an ice-bound junk-heap." Taking its place among his 200 other works, this is a musical monument that will endure.
The Antarctic invitation may have been a surprise, but it was as nothing compared to the job offer that came last year from Buckingham Palace. "I've never been more surprised in my life. I'm not a republican, but I have in the past expressed certain opinions about the Royal Family, saying it would be a very good thing if they showed more interest in the arts." The Queen, he adds, is now willing to go along with that.
When I point out that she never goes to concerts, he chuckles: "We're going to change that! She said to me categorically, `Philip and I are interested in music, and we've had this terrible press. We are not philistines.' And I can confirm that she is not." So what music does she like? "She has her opinions, and I'm not going to say what they are."
When first appointed as the palace's musical Master, he announced that his aim would be to raise the profile of serious new music, but now he qualifies that as taking "music in general' to a wide audience. "It's a direct challenge, and I will try to rise to it usefully."
As it happens, "useful" was Benjamin Britten's favourite word for what he wanted his music to be, and as Britten helped the young Maxwell Davies to get a publisher, the echo is appropriate. "But I could come a cropper. I've not done it yet." True - we still await fruit from this particular tree. When shall we see it? "Quite soon, but the Buckingham Palace press office will want to make their own announcement."
Then Max hints at what he may do for the 60th anniversary of the Second World War armistice: "I've been to Kneller Hall [the Royal Military School of Music], and thoroughly enjoyed what I found there. Military-band music has its own rules and regulations, it exists in its own enclosed musical world. It's a bit of history which has crystallised, but it's still producing lively pieces. I didn't know how those marches are constructed, V C I didn't know about their melodies and countermelodies, but I'm now a bit richer for knowing them." He thinks that his delight at seeing an amateur production of The Gondoliers when he was four - which first spurred him to improvise - has some echo in this enclosed musical world, and in his "completely childlike reaction" to its ebullient charm.
Yet this is a man who carried a banner on the great London march against the invasion of Iraq in 2003. How does he relate to the political establishment, as opposed to the royal one? "That's a very good question, because the royal establishment stands independently of the political one - and Iraq has widened the gulf between them. For me, the invasion and occupation was a personal disaster: I can't vote for any of the three main parties now. The Liberal Democrats didn't support the war, but they went along with the Army, and when the British Army is doing something as stupid, brutal and illegal as that, you have to qualify it, whatever your desire to support our boys. You just don't go along with it. I voted twice for Blair, and one just feels very dirty having done that. One can't trust those people now."
But doesn't his official position mean that he has to deal with them? "Of course I have to deal with them - politely, in the course of this job. I shall try to use them for whatever one can get out of them, in terms of culture. But, you know, they are tarnished people, and they certainly do not represent me on any level whatever."
And when they are re-elected, and America invades Iran? "Then I will go on protesting. And if they say that you can't take that position and still be Master of the Queen's Music, so be it!" For the first time in centuries, this honorary post is starting to look significant.
And, in musical terms, Max has already launched his attack. The second movement of his Third Naxos Quartet (to be released in April) goes under a title that must be read ironically: "In Nomine" (in the name of). "I started writing a purely abstract piece," he explains, "but Iraq intruded. The first movement became an extraordinary parody of a military march, which becomes progressively more grotesque and bitter. The `In Nomine' movement is definitely not `in nomine' - it's definitely `not in our name'."
Meanwhile, the spooky hymn ending the third movement - marked "stucchevole" (cloying, nauseating) - has a sulphurous political subtext: "It's all tied up with the way a group of Italians were killed in Iraq. I happened to be in Rome watching [Prime Minister Silvio] Berlusconi being very pious and sentimental about it on television, but I was also watching him in reality from my window - and there were far fewer people in the crowd than television was giving the impression of." This work has a burning Bartokian intensity - anger is a creative spur for Max - and though the political message needs words to spell it out, it would still have haunting power without them.
Meanwhile, Max continues to wage war on another front. He's long campaigned for an improvement in music education - or at least a halt in its headlong decline - and though he discerns faint signs of a governmental change of heart, he promises fireworks in his forthcoming Royal Philharmonic Society oration.
Music education, he once told me, "might have been designed to inhibit children from expressing themselves through music. It's horrendous to go into a school and see kids all by themselves with electronic keyboards and headphones, in total isolation." Moreover, he added, there's a vital element lacking in music made by electronic means: "You need to feel the physical vibration, under your fingers, coming out of the instrument, as you do through your own body when you sing."
His Strathclyde concertos, written expressly to provoke musical creation in junior amateurs, have blazed a trail in Scottish schools. The amateur fiddlers on his Orcadian island are currently learning new pieces he's written for them.
After 30 years of domicile, how Scottish - or Orcadian - does he feel? "Well, it's my home, but I've still got those roots in Lancashire. But, though Scotland unfortunately can't control its military affairs, and though in the arts the Scottish Parliament has been an unqualified disaster, politically I feel more in tune with Scotland than England."
So why has he sold his flat in Edinburgh? A rueful sigh: that goes back, he says, to when his record company Collins was taken over, and all its classical music ditched. "But in my contract I had the right to buy back the masters, which I did. I couldn't afford it, so I had to borrow money and sell my Edinburgh flat. I'm still paying the bank back, and living as cheaply as I can." He's put recordings of 50 of his works up for sale on his website (www.maxopus.com) at pounds 6 a throw, and more are going on every month. It's been worth it, he insists, even if he never gets his money back. "I was determined that after all that trouble by the orchestras and engineers, these recordings wouldn't just disappear down the plughole."
As Maxwell Davies talks about his life - punctuated by barks from his dog Judy - one gets the feeling that he's reached a contented plateau. He looks back on the 1969 fire that consumed not only his Dorset cottage but also his organ, his beloved cat, and half the manuscript of his opera Taverner, and thinks it taught him a valuable lesson. "It made me very aware that you don't own anything, you only rent it for a time. It changed my whole attitude towards personal possessions. And it demonstrated human vulnerability."
He may be full of fight over the big issues of the day, and his hostility towards British opera-directors is as implacable as ever, but he now seems comfortably at one with his youthful self, and he's healed age-old rifts with two fellow composers from his glory days in the Sixties. Alexander Goehr - who took against Max for reasons that have never been elucidated - is now the dedicatee of his just-finished Sixth Naxos Quartet, and one of the works Max is currently playing for pleasure is Goehr's new sonata.
With Harrison Birtwistle, who was Max's closest confederate in that tightly- knit Mancunian group that included the pianist John Ogdon, the rift was both deeper and (on Birtwistle's side) far more acrimonious. This is thought to have begun out of Birtwistle's jealousy at Max's early success, and was certainly fuelled by Birtwistle's puritanical contempt for Max's more populist exploits (like writing a soundtrack for Ken Russell's The Boy Friend, starring Christopher Gable and Twiggy). Last year, a newspaper lured the two composers into a joint shot and tried to photograph them shaking hands, but to no avail. "He wasn't having any of it," Max says. "I was fine, but he wasn't. But we met again shortly after in Geneva, and he was fine. So now we're friends again."
Given a lifetime of composing that has carried him into seemingly incompatible modes, one might have thought that Max would now look askance at certain works. But no: "They're all part of the same huge family." Moreover, he's as attached now as he was as a student in Rome to the plainsong that has always informed his work, and to the Liber Usualis that contains the regulation chants. "I like to look up the plainsong of the day," he explains, "not because I'm religious, but out of curiosity."
Then he offers an interesting apercu. "I like the idea that these things have filtered through composers' imaginations for centuries. A bit like icons, which people have been using to focus their thoughts on things that are self-transcendent. It gets an aura around it, a glow." But what can something as simple as plainsong do for a composer whose work is so routinely complex? "It gives you a root, a very plain, rock-solid base, from which you can build upwards. I enjoy working with it. Pity I'm not a Catholic!"
When I ask what else he plays for pleasure, the list comes out in a rush: "Mozart, Haydn, and Beethoven sonatas. Schoenberg's piano pieces. I've also got a small pipe organ, and on that I play early music of all kinds. And there's a clavichord on which I play Bach inventions and preludes and fugues."
He never revises: he's much too keen to get on with the work in hand, around which he gears his daily regime. "I'm up at seven - 5.30am in summer - then make tea, think about the day's food, then take the dog for a walk. When I come back, Colin - who I live with - will be up and starting his work as a builder. Then, after half an hour on the phone to my manager, I'll sit down and start writing music." Yes, full circle - and very happy with it.
Peter Maxwell Davies conducts his `Antarctic Symphony' at the Royal Festival Hall, London SE1 on 30 April (0870 401 8181). Peter Maxwell Davies: a Musician of Our Time runs at the South Bank Centre from 17 to 30 April. `Naxos Quartets Three and Four' is released on Naxos in AprilReuse content