As we announced last Friday, the Monday series A Guide to the Galleries will feature each of the eighteen different galleries in Galileo’s World over the course of two weeks (two successive posts in the series). The purpose of this series is to help draw educators into the breadth of the world in which Galileo lived to facilitate the creation of educational resources.
Welcome to the Music of the Spheres. To enter the world of Galileo is to enter a world in which astronomy, mathematics, and music were considered inherent to the structure of the world. Since the time of the ancient Greeks, the predominant thought among the educated was that mathematics and music were intimately connected. For instance, in the 4th century BCE the mathematician Pythagoras demonstrated a mathematical ratio between the length of a string and its pitch using an ancient musical instrument, the monochord.1 It is no coincidence, then, that the late Roman philosopher, Capella, incorporated music alongside astronomy, geometry, and arithmetic in the stages of the liberal arts education known as the “quadrivium,” which came after the basic “trivium” of grammar, logic, and rhetoric. Thus, a fully educated person in the tradition of the liberal arts would learn music, alongside math and astronomy, as part of the fullest expression of one’s education. During the Italian Renaissance, beginning in the fourteenth century, the revival of ancient traditions brought with it a renewed interest in the study of the liberal arts.
Johannes Kepler, a contemporary of Galileo, demonstrated the close connections between music and astronomy in his Harmonices Mundi, a 1619 work in which Kepler, among other things, composed the elliptical movement of the planets with musical notation. His rationale for doing so developed from his observation that the ratio of the planets’ movement matched the ratios between notes in various musical harmonies. An expression of aspects of seventeenth century astronomy, Kepler’s Harmonices Mundi provides us with a picture into a world in which astronomy, mathematics, and music operated according to similar principles.
Before finding Galileo himself, then, we find the world in which Galileo lived. A world which did not display a sharp divide between the sciences and arts. A world in which both the planets and music operated according to fundamental mathematical principles. As one enters into this world it is conceivable to ask,
“What would it have been like to be a mathematician in an era in which music and astronomy were sister sciences?”
Galileo, a trained mathematician, certainly would have known. But it was due to more than his educational background. His father, Vincenzo Galilei, was an acclaimed musician, composer, and influential figure in the sixteenth century musical revolution of the Italian Renaissance. What might it have been like for Galileo to develop as a mathematician in such a world? We will give you a brief look at this next week in our second post on the Music of the Spheres gallery.
For educators who have a lesson plan that would help K-12 students understand the connections between music, mathematics, and astronomy, join in the development at the “Music of the Spheres” gallery in the Educator Workplace.
1 Torben Rees, ‘Monochord: an ancient musical and scientific instrument’, Explore Whipple Collections, Whipple Museum of the History of Science, University of Cambridge, 2009 [http://www.hps.cam.ac.uk/whipple/explore/acoustics/monochord/, accessed 04 August 2014]