Vincenzo Galilei

Galilei promoted equal temperament. In his exploration of tuning and keys, he composed 24 groups of dances, "clearly related to 12 major and 12 minor keys" (1584). Some of Galilei's most important theoretical contributions involve the treatment of dissonance: he had a largely modern conception, allowing passing dissonance "if the voices flow smoothly" as well as on-the-beat dissonance, such as suspensions, which he called "essential dissonance". This describes Baroque practice, especially as he defines rules for resolution of suspensions by a preliminary leap away from, followed by a return to, the expected note of resolution. Vincenzo Galilei was one of the pioneers in the systematic study of acoustics, mainly in his research (assisted by his son Galileo) in the mathematical formula of stretched strings. Galileo told his biographer that Vincenzo introduced him to the idea of systematic testing and measurement through their Pisa house basement, which was strung with lengths of lute string materials, each of different lengths, with different weights attached. Galilei made discoveries in acoustics, particularly involving the physics of vibrating strings and columns of air. He discovered that while the ratio of an interval is proportional to string lengths—for example, a perfect fifth has the proportions of 3:2—it varied with the square root of the tension applied (and the cube root of concave volumes of air). Weights suspended from strings of equal length need to be in a ratio of 9:4 to produce the 3:2 perfect fifth. This work was taken further by Marin Mersenne, who formulated the current law of vibrating strings. Mersenne was only three years old when Vincenzo died, but he would later maintain a regular link to Galileo (and many other scientists). He treated Galileo as a prized member of his scientific network. He communicated Galileo's ideas for a pendulum clock to Christiaan Huygens (who improved on it). Despite being a priest, Mersenne defended Galileo when he came under attack by the church in 1633, but he also questioned Galileo's claims and disputed the accuracy of some of Galileo's findings. He conducted his own duplicate experiments, which improved on their accuracy.