Institutions under the management of a head schoolmaster, and open to lay pupils as well as those destined for the Church, developed in the 8th century from the episcopal schools founded a century or two earlier, by bishops who conducted them chiefly for clerics and were themselves the teachers. Chrodegang, Bishop of Metz (742-766), is the reputed founder of such schools. They flourished in France, Germany, England, and Spain, especially from the 11th or 12th century; and continued to be, with modifications, the public schools of western Europe down to the 18th century. In the medieval lower school, reading, writing, psalmody, and Christian Doctrine were taught. In the higher school, to the trivium, including grammar, rhetoric, and dialectics, might be added the quadrivium, or arithmetic, geometry, astronomy, and music, with Scripture and theology. In cities and towns where there was no cathedral there were similar canonicate schools under the local canons. Well-known schools existed at York, Canterbury, and Chartres.