It is noon on an almost empty Piazza Maggiore in Bologna. A few visitors seek shade under the giant porticoes of the Paviglione. The Gothic basilica of San Petronius, designed to be larger than St Peter’s in Rome but curtailed at the last minute by a resentful pope, throws its vast shadow across the square. Tilting recklessly over russet roofs, Bologna’s 12th-century twin towers, the Asinelli and Garisenda, are outlined against a crystalline sky. The centre of the city in high summer is as eerily still, and as sharp a contrast of sunlight and silhouetted arches, as a de Chirico painting. But at my side, incessant as a mosquito, is the rhythmic beat of an iPod turned up too loud and the urgent tap-tap-tap as text is keyed into a mobile phone.

From pizza to Prada, there are many reasons why Italy should appeal to teenagers; for ours though, these turned out to be either superficial or soon palled. So our deal was this: our children would accompany us, not too sullenly, for a three-week trawl north-south through Italy’s historic towns, in exchange for which we supplied them at the start with state-of-the-art music players and cellphones, and at the end granted a final week of lazy luxury on a Mediterranean island.