Tuttlingen

Tuttlingen calls itself the world centre of medical technology, and the claim is simply arithmetic: several hundred medical-device companies — from the venerable Aesculap to specialist workshops — cluster in this Danube town, which produces a commanding share of the planet's surgical instruments. If you have ever been operated on, the odds are excellent that something in the tray said Tuttlingen. The trade grew from cutlers and knife-grinders on the Danube; the town museum traces the leap from blades to scalpels.

The Danube itself performs the local miracle: a few kilometres upstream, in dry months, the river vanishes — the Donauversickerung, where the young Danube seeps entirely into the porous limestone, travels underground across the European watershed and resurfaces in the Aachtopf spring to feed Lake Constance and the Rhine. For days at a time, the great river of Vienna and Budapest simply is not there; Tuttlingen sits at the world's most distinguished disappearing act.

The town burned in 1803 and was rebuilt on a rational grid — locals call it the youngest old town in Germany — watched over by the ruined fortress Honberg on its hill. There, each July, the Honberg-Sommer pitches its great tent for two weeks of concerts, from jazz and world music to rock, one of the region's best-loved festivals. Below, the Danube promenade collects strollers and herons: precision by trade, vanishing river by nature, music on the hill by habit.