Music history reads like a cupboardful of opus numbers - discrete parcels of creativity which composers have methodically accumulated through their lives and filed for easy access - but in practice it's rarely so neat. No two composers will tell you the same story of how they work, but most would agree that they generate ideas in a continuum, and the process by which the ideas are siphoned off into separate pieces is neither inevitable nor certain. The very decision of what constitutes "a" piece is nothing more than that: a decision, which could have gone another way. And composers occasionally prefer to keep their options open, as is the case with Harrison Birtwistle's Pulse Shadows which premiered at the Queen Elizabeth Hall on Monday as part of the South Bank's Birtwistle retrospective.

Pulse Shadows is a major work of 65 minutes' duration, and the South Bank presented it with a degree of style - its own, freestanding concert slot, with lighting and a specially built set - to endorse the general expectation that it would be an Event. It was. But whether it was "a" work at all, as opposed to two works, or even 18 works, is debatable. Essentially the score is a sequence of nine string-quartet movements alternating with a sequence of nine song-settings for voice and mixed ensemble; and the ambiguous relationship between the sequences - which interlock and overlap but are otherwise separate entities - suggests a calculated tension on which the drama of the whole thing turns. In talking about it, Birtwistle says there can't be a relationship between the songs and the quartet movements, because their respective sequences are random: when it came to fixing a performance order for the premiere he just "shuffled the pack". But I'm not sure how much I believe that. In performance it certainly sounds as though there is some underlying commonality - an idea of provocation and response. And even though the language of the writing differs, the ensemble music comes close to a conventional accompaniment: pliant, supportive. The quartet music is more assertive, with a contrapuntal vigour rooted in the old English renaissance tradition of the consort of viols. Not that it sounds like Dowland, but the connection is there, and felt.

The most interesting thing about the quartet-writing, though (and it's worth saying that Birtwistle has no real track record in the genre, although quartets do feature in Secret Theatre and his In Memoriam Stravinsky), is that some of the movements come in the form of what he calls a "frieze". The analogy is with the sort of broken artefact you'd find at the Parthenon: a linear unfolding of ideas and images with sections obviously missing. And in structural terms it echoes the way Birtwistle reads the poems in the parallel song sequence. They are all by Paul Celan, the Romantic Expressionist poet whose evocative but unfathomable verse does indeed read like narratives with missing segments. Fragments of a hidden whole. Anyone familiar with Birtwistle's work will know his fascination with the dramatic possibilities of fragmentary statements, and Pulse Shadows is one of the most eloquent of all his essays in the subject. The writing is keen, economical, an antidote to the excess of recent scores like Panic, but with no rationing of ideas. It's all exposition, endlessly inventing new material, rather than developing what has already been established. Birtwistle likes to say that what interests him in theatre is where the characters are introduced, and that from then on, there's a risk of boredom. Pulse Shadows is nothing but the introduction of characters; and with such superb interpreters as the Arditti Quartet (the undoubted leaders in the field of avant-garde quartet performance), the mixed- instrument ensemble Capricorn, and the soprano Claron McFadden, it certainly wasn't boring. My one objection was that Ms McFadden's diction was too poor and the auditorium lighting too low to follow the words in any way - and, for once, the textural weight of Birtwistle's writing was light enough to suggest that he did want the words to register. But given the impenetrability of the poet, we may not have been missing so much there.

People who boo Birtwistle tend to like Malcolm Arnold, whose 75th birthday was observed, some months in advance, with a Barbican concert by the LSO last Sunday. Arnold is that relic of a former age, a tunesmith - you can whistle him - and tunes prompt what is probably the great hypocrisy of modern music: we all want them but we disallow them on the grounds of aural health, as though they were a cream-cake for the ear. The underlying problem is that to write the sort of tunes that register with average ears means writing diatonically - in a language which, however fondly we might feel for it, is not the language Of Our Time. Malcolm Arnold's tuneful scores accordingly sound older than they are, and they've been doing it for 50 years. But don't dismiss them just for that. They're usually well-written, with insider knowledge of the orchestra, and some (not all) are powerful works. No less a musicologist than Donald Mitchell is a champion; and in a perceptive essay from his recent collection Cradles of the New (Faber, pounds 35) he makes the point that Arnold's music inhabits a "state of innocent grace", the sanctuary of a lost world that his tunes symbolically look back to. Hearing again the 5th Symphony, superbly played on Sunday by the LSO under Richard Hickox, I agree - but with the reservation that the symbolism doesn't run particularly deep. The tunes are wonderful, and surface with a rare facility that only listeners with asbestos souls could honestly resist. But they don't sustain. They either decant into wry parodies of other composers (Holst, Britten, Walton) or they're overwhelmed by bluff English-vernacular banter blaring, punch- drunk, from the brass. The programme for the birthday concert made that all too obvious. The Tam O'Shanter Overture, the John Field Fantasy, the Sound Barrier Rhapsody were all light music out of its depth. Only the English Dances and the Symphony betrayed the genius that sometimes lives in Arnold's work - and even then it was a genius toying with the commonplace. Composers like Mahler, of course, get away with that. But Malcolm Arnold isn't Mahler, however hard his slow movements try to be.

For sheer musicianship, the event of my week was Alfred Brendel playing the last three Beethoven piano sonatas in a recital for the 30th anniversary of the Brighton Festival. It happened on-stage at Glyndebourne, where the new theatre doubles very effectively as a concert space, and said more about this fundamental repertory than words could pretend to. Now 65, Brendel has lived with this music for long enough to be able to address its stature without inflation, pretension, or any obvious sense of burden. The authority is thoughtful, not didactic, with amazing subtlety of tone. Asked for a definition of great playing, Brendel once said that the ideal was to be correct but bold: the correctness declaring how things ought to sound, the boldness revealing that what seemed impossible can, in fact, be true. Brendel's Beethoven is exactly that: impossibilities reveal themselves and are accommodated bar by bar. Great is a fair description.