A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord ("kanōn" law) straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason." However, "music, mathematics, and astronomy were inexorably linked in the monochord." As a pedagogical tool for demonstrating mathematical relationships between intervals, the monochord remained in use throughout the middle ages.