Vincenzo Galilei was born in Florence. He made his living as a lutenist, composer, theorist, singer, and teacher. Around 1560 he settled in Pisa, where Galileo Galilei was born in 1564, the oldest of six or seven children. During this period Galilei also studied for some time in Venice under the theorist Gioseffo Zarlino, with whom he later had a dispute about music theory. In the early 1570s Galilei and his family settled in Florence. His prowess as a musician and theorist attracted a number of powerful patrons, and he often spent time at their residences. e.g., in 1578-79 with Duke Albrecht of Bavaria in Munich.

Vincenzo Galilei published a number of books of musical scores for the lute and several books on musical theory. What is important about Galilei for our purposes is that he combined the practice and theory of music. Since antiquity, the theory of music had consisted of a mathematical discussion of harmony, in other words what are the mathematical ratios of the lengths of strings producing consonances, and how does one divide the octave? It had always been thought that not only was the ratio of lengths of two strings sounding an octave 2:1, but that so also was the ratio of the tensions of strings of equal lengths tuned an octave apart. Galilei showed that this is not the case: the ratio of tensions is 4:1. He found that ratio by hanging weights from strings. Here was an experiment that produced numbers and bore directly on the age-old theoretical discussions.

Stillman Drake argued that Galilei performed these experiments in 1588, when his son Galileo was living at home and giving private lessons in mathematics. The implication here is that young Galileo actually helped in the experiments. Be that as it may, Galileo received from his Florentine environment in general and from his father in particular the tendency to combine practical considerations with theory and to try to answer theoretical questions by experiment.