We think of music as one of the arts, but music is also the science of sound and harmony. In fact, the ancient Greeks thought music belonged solely to the realm of mathematics, with its emphasis on number relationships, ratios and proportions.
A Greek philosopher named Pythagoras first invented the musical scale. He discovered that different musical notes could be produced by the same piece of stretched-out string, simply by placing a bridge across it. This divided the string into two related parts, very similar to the mathematical act of giving the ratio of two numbers. Plucking the string with no bridge gives you the "fundamental" musical note. Cutting the string exactly in half -- a ratio of 1:2 -- means that each half will play a note exactly one octave above the fundamental note.
Pythagoras found he could divide the string into many different note combinations -- not all of them pleasing to the ear. The string must be divided into a simple ratio to produce a harmonious tone. For instance, if one side of the string has three-fifths of the length and the other has two-fifths, the result is a "perfect fifth," said to be the most pleasing to the human ear.
The best-known ratio is called the "golden mean," later dubbed the "divine proportion." If you've read the bestselling novel The Da Vinci Code, you know this occurs whenever a line (or string) is divided in two so that the ratio of the small part to the large part is the same as the ratio of the large part to the whole. The golden ratio can be seen in paintings, architecture, and music. For instance, certain key passages in the "Hallelujah Chorus" from Handel's Messiah follow the golden mean.
The Greek notion of musical ratios extended to their view of the universe. They believed the earth was at the center of the solar system, with the sun and other planets rotating around it in fixed circular orbits. These orbits were separated by intervals corresponding to musical chords. The planetary motion in these orbits gave rise to a divine "music of the spheres."