The Man Who Knew Too Much Music

Although many names of musicians are recorded in ancient sources, none played a more important role in the development of Greek musical thought than the mathematician and philosopher Pythagoras of Samos.  According to legend, Pythagoras, by divine guidance, discovered the mathematical rationale of musical consonance from the weights of hammers used by smiths.  The connections between the two seemingly disparate subjects of mathematics and music become obvious when studying Pythagoras' concept of the harmony of the spheres.  Pythagoras believed that all relations could be reduced to number relations, making observations in music, mathematics and astronomy.  Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments.  
In fact Pythagoras made remarkable contributions to the mathematical theory of music.  He was a fine musician, playing the lyre, and he used music as a means to help those who were ill.  He is credited with discovering that the interval of an octave is rooted in the ratio 2:1, that of the fifth in 3:2, that of the fourth in 4:3, and that of the whole tone in 9:8.  Followers of Pythagoras applied these ratios to lengths of a string on an instrument called a canon, or monochord, and thereby were able to determine mathematically the intonation of an entire musical system. The Pythagoreans saw these ratios as governing forces in the cosmos as well as in sounds, and Plato's Timaeus describes the soul of the world as structured according to these same musical ratios.   For the Pythagoreans, as well as for Plato, music consequently became a branch of mathematics as well as an art; this tradition of musical thought flourished throughout antiquity in such theorists as Nicomachus of Gerasa and Ptolemy and was transmitted into the Middle Ages by Boethius. The mathematics and intonation of the Pythagorean tradition consequently became a crucial influence in the development of music in medieval Europe.  Today, these simple rules can be applied in any physics class – all you require is a half-filled beer bottle and a non-smoker.  Here is a test composed by the McGuireans: have a non-smoker blow into the bottle; observe the sound; drink some of the beer; and blow again.  If your professor isn’t Dr. McGuire, substitute beer with tea. 

Information on Pythagoras taken from Pre-Socratic Philosophers @ http://ancienthistory.miningco.com/education/
ancienthistory/library/bl/blpyth_astronomy.htm.