 Galileo made original contributions to the science of motion through an innovative combination of experiment and mathematics . More typical of science at the time were the qualitative studies of William Gilbert , on magnetism and electricity . Galileo 's father , Vincenzo Galilei , a lutenist and music theorist , had performed experiments establishing perhaps the oldest known non @-@ linear relation in physics : for a stretched string , the pitch varies as the square root of the tension . These observations lay within the framework of the Pythagorean tradition of music , well @-@ known to instrument makers , which included the fact that subdividing a string by a whole number produces a harmonious scale . Thus , a limited amount of mathematics had long related music and physical science , and young Galileo could see his own father 's observations expand on that tradition . 
