A lusty horn and a Roman carnival

When Richard Watkins plays a note it has a lovely authority. I can't quite put it into words - it's something to do with the very rounded quality of the sound he makes, which I love." Sir Peter Maxwell Davies is waxing lyrical. He is positively enraptured by the playing of Watkins, who will give the premiere of the full-blooded new Maxwell Davies Horn Concerto next Tuesday at the Barbican.

"I wanted to create music to exploit Richard's particular lyrical qualities: above all his singing and the extraordinary 'presence' of each note he plays: that's why I've composed a concerto which 'breathes' in one, long connected argument, right through to the final cadenza and coda. The solo writing is extremely virtuoso, not least in exploring the horn's full range, from deepest bass range to the most exposed high sostenuto. It presents challenges of embouchure and of sheer stamina which I should think are fairly unprecedented."

Many people might run a mile at the prospect of having to tackle one of Maxwell Davies's "rather virtuosic" sections - a habit he formed in his student days writing for John Ogdon and Elgar Howarth - but Richard Watkins has been there before. A former player with Davies's legendary chamber ensemble The Fires of London, he is now first horn of the Philharmonia. It was for Watkins that Maxwell Davies wrote his solo horn piece, Sea Eagle, now something of a repertoire classic.

"It was rather like when Britten wrote his Serenade for Tenor, Horn and Strings," says Watkins. "People said then that only Dennis Brain would have the technique to manage it. Yet only last time round, I noticed Sea Eagle was one of the set pieces for the Munich international horn competition. There's a lyricism to the new concerto that seems to be a sort of natural progression from Max's Fifth and Sixth symphonies, both of which I've played, with the Philharmonia and RPO respectively. It's certainly all about exploring the range and colours of the instrument. There's definitely a virtuosic element - not just trills but tremolandos, which are quite an unusual effect on the Franch horn. Obviously it would be very draining to play continually high, so those moments tend to be points where the music reaches an emotional or dramatic peak.

"It starts with a very striking gesture, and parts are quite taxing, including the cadenza: mechanically Max certainly does stretch the player to the limits, but I think in a very positive way. And in the last section there's a light fleet-footedness that I think really works."

Roma, Amor Labyrinthos, Tuesday's other substantial new piece, harks back to Maxwell Davies's time as a student in Rome, and is dedicated to the doyen of living Italian composers and teachers, the 95-year-old Goffredo Petrassi. Maxwell Davies says that "he was the one teacher who really took me seriously, and was interested enough to go into the fine detail of what I'd written, to go through it with a fine toothcomb and ask searching questions. Sometimes a lesson would last six hours."

It's a massive new work, scored in three movements for a huge orchestra, including quadruple woodwinds - notably contra bassoon and contrabass clarinet - four trumpets and two tubas. Thematically it draws, like many of Maxwell Davies's works, on plainsong - here, tellingly, the Dies Irae and Sanctus of the Mass of the Dead, which harks back to Maxwell Davies's second work for Petrassi, the St Michael Sonata for 17 wind instruments.

The first part deals with the underside of Rome: the layers of nastiness, the "cruelty, bloodiness and corruption" of the historic city, encompassing Imperial Rome, the Papacy and Inquisition and the Fascist era: "It definitely has the sound of jackboots in it, a kind of mechanical marching that permeates a lot of it. It also parodies Carl Orff - never my favourite composer, a lot of his writing gets pretty overblown, so it seemed apt here, when I want to emphasise the ringing hollowness and empty rhetoric implicit in some of the Republican and Imperial architecture, as well as the Mussolini-era monuments. The second movement is about Rome's hidden mysterious beauties. I've entitled it, in Greek, Ploutos Aphanes (literally hidden wealth) - I wanted the association with Pluto, the idea of the city at night as a kind of Hades full of riches, something dark and mysterious - I was thinking of James Joyce's Dublin in the Circe chapter of Ulysses. It's a nocturne, if you like."

There are, references to street bagpipes, and itinterant mandoline, brass bands and military music, folksy or kitsch or fusty restaurant music and church music. And the slow movement, ends with an extraordinary mock-folk tune, a vivid memory Davies has of walking back to his student pad not far from the Vatican and hearing "in a rarely open small church, I think San Giorgio in Velabro near the Tiber, elderly townswomen in black shawls singing with an openness and purity and innocence I found moving and inspiring".

Roma's last movement is entitled "Manet in Aevum", and refers - amid the city noises and snarls of congested traffic (how Ives or Debussy or Respighi would have loved all that: "I was very conscious of someone having been here before, though I feel what I've done is very different, it tries to be more searching on every level - it's more than a pretty picture postcard, and a lot angrier") - to Rome's eternity.

Here Maxwell Davies returns to the image of St Michael "weigher and judge of souls", high on the Castel San Angelo, and often - almost obsessively, he says, - epitomised in his music by passages of high trumpet over sustained strings, before the bells of the entire city - first one small tinkle and then the entire vast array, dominated by St Peter's Basilica - ring out in a great Mussorgskian blaze of celebration.

Sir Peter Maxwell Davies will conduct the Royal Philharmonic in his 'Mavis in Las Vegas' and the premieres of his Horn Concerto and 'Roma, Amor, Labyrinthus' at the Barbican, London on Tuesday, 2 May. Box office: 020-7638 8891