“After all,” said Daniel Barenboim, half jokingly, “where else can you see a group of Arabs wishing with all their hearts that an Israeli won’t mess up at an important moment?” There was a slightly nervous ripple of laughter from his listeners.

The Israeli in question was a young trumpeter; the well-wishing Arabs were his fellow musicians in Barenboim’s West-Eastern Divan Orchestra, which brings together young players from both sides of the Middle Eastern conflict. The tricky trumpet bit comes in Tchai-kovsky’s Fifth Symphony, through which Barenboim had just conducted his young charges, to a standing ovation, at London’s Barbican Centre earlier this month. And even though he was talking informally at a reception afterwards, the pianist-conductor was careful to be even-handed. When it came to that fiendish clarinet bit in the Beethoven Piano Concerto No.3, Barenboim added - he had conducted from the keyboard, his own playing taut and electrifying, but his commanding eyes never leaving his “children” - the Arab wind-player could feel the same: the powerful support of Israeli colleagues clustered around him, locked together to succeed or fail in what they were all striving for. The making of music. The creation of harmony.

That was a simile so corny that it had to be got out of the way early on. Barenboim’s co-creator in the orchestra project, the Palestinian writer Edward Said, who died last year, would probably have rolled his eyes. As his widow Miriam said in an address before the concert, Said felt the orchestra was one of the greatest achievements of his life. But he was a realist, too; he famously said: “It doesn’t pretend to be building bridges and all that hokey stuff.” Yet, he’d added, “there it is - a paradigm of coherent and intelligent living together.”

The orchestra was born six years ago with a meeting between the Israeli musician and the Palestinian writer, who both dreamt of such a “paradigm”. Its first base was Weimar, Goethe’s town, and its cumbersome name comes from the poet’s West-Ostlicher Divan, a synthesis of Islamic and European poetry. Its home these days is Seville, where musicians aged 13 to 26 congregate each July for a summer school and rehearsals before their concert dates - last year they made their debut at the Proms, to critical as well as political acclaim; this year they have visited Barcelona, London and Berlin.

There are equal numbers of Jews and Arabs in the orchestra, the latter including Egyptians, Syrians, Lebanese and Arabs of Israeli nationality. No Palestinians? It seems a disappointment, until we realise how few Palestinians could have had the chance for this sort of musical education. There is just one, a 14-year-old girl from Ramallah, pretty and tongue-tied, whose skill on the violin is a result of teachers making half-secret forays into the camps. A month ago in Seville, the Barenboim-Said Foundation launched its “musical kindergarten” programme, devoted to just such musical education.

At the Barbican it was a hot and emotional night: a benefit for the orchestra in memory of Edward Said. As the great music crashed around and Barenboim coaxed and bullied his luscious, string-rich tones out of this pack of brilliant children, as if through sheer willpower, it would have been easy to feel that this, surely, could cure the ills of the world.

But the cold realities were there. This orchestra cannot perform in Jerusalem, for fear of disruption, or worse, from one set of extremists or another. This orchestra has never performed in any of the countries from which its members are drawn. Last year there was a single, heavily guarded, performance in Rabat in Morocco - the only one to date in an Arab city. Security for these youngsters, as they make their way to and from their homes, is such a problem that on occasion the Spanish government has even provided diplomatic passports. And - most chillingly of all - the concert programme contains no names. Even if I knew the full name of the pretty Ramallah violinist, I could not tell it to you here.

Is it, then, possible for art to break through such formidable barriers of hatred and incomprehension? Did that night, and nights like it, with their ecstatic ovations, do anything more than make a lot of well-meaning liberals feel good about themselves? Is this just a pretty pink plaster lovingly placed over a terminal cancer?

There is no answer to such questions, except hope. On one of his darkest days in Auschwitz, Primo Levi survived by summoning Dante’s clarion call to the human spirit: “You were not born to live like brutes.” There are times when even a cynical atheist can dare to believe that heroism can exist in a bad world.

There are several brave heroes in this story: Edward Said is one; Daniel Barenboim, whose celebrity may be as provocative as it is protective, is certainly another. Then there are these young musician-fighters, who strap on their talent and go into crowded public places and make it explode, a blast whose reverberations echo in our hearts and heads for a long time. They are the real counter-terrorists.