Solothurn has a long-running fondness for the number eleven, and the Eleven-Hour Clock is the neatest little expression of that obsession. Its face has eleven hour markers instead of twelve, turning a normal city clock into a private joke shared with anyone who knows Solothurn's churches, fountains and guild history.
It is a quick stop, but a good one on a walk through the old town because it captures the city's personality better than a plaque could. See it as part of the larger pattern: Solothurn is formal and Baroque, but it also enjoys a small numerical eccentricity.