**Vincenzo Galilei
**

Vincenzo, in his study of pitch and string tension, produced perhaps the first non-linear mathematical description of a natural phenomenon known to history.[1] This was an extension of a Pythagorean tradition, but went beyond it. Many scholars credit him with directing the activity of his son away from pure, abstract mathematics and towards experimentation using mathematical quantitative description of the results – a direction which was of utmost importance for the history of physics, and natural science in general.

He was born around 1520 in Santa Maria a Monte (Tuscany), and began studying the lute at an early age. Sometime before 1562 he moved to Pisa, where he married into a noble family. In 1564 Galileo was born, the first of his either six or seven children; another son, Michelagnolo, born in 1575, who also became an accomplished lutenist and composer.

Vincenzo was a skilled player of the lute, and early in life attracted the attention of powerful, well-connected patrons. In 1563 he met Gioseffo Zarlino, the most important music theorist of the sixteenth century, in Venice, and began studying with him. Somewhat later he became interested in the attempts to revive ancient Greek music and drama, by way of his association with the Florentine Camerata (a group of poets, musicians and intellectuals led by Count Giovanni de' Bardi) as well as his contacts with Girolamo Mei, the foremost scholar of the time of ancient Greek music. Sometime in the 1570s his interests in music theory, as well as his composition, began to move in this direction. 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.

In addition, towards the end of his life he made some substantial 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). In the case of strings tuned in a perfect fifth, weights suspended from them needed to be in a ratio of 9:4 to produce the 3:2 perfect fifth.

The use of recitative in opera is widely attributed to Galilei, since he was one of the inventors of monody, the musical style closest to recitative.

Galilei composed two books of madrigals, as well as music for lute, and a considerable quantity of music for voice and lute; this latter category is considered to be his most important contribution as it anticipated in many ways the style of the early Baroque.

Many scholars credit him with directing the activity of his son away from pure, abstract mathematics and towards experimentation using mathematical quantitative description of the results – a direction which was of utmost importance for the history of science.