Pythagoras (c. 570-c. 495 BCE) is best known for his theorem that says that in the right-angles triangle the area of the square of the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
But Pythagoras took a scientific interesting in music, too. He believed that musical notes had mathematical properties. Although he went down some dead ends, his theories eventually came to describe the properties of strings used in musical instruments. Pythagoras was fascinated by an apparent congruency between music and math.
The answer lies in the ratio of the length of a free string to where it is stopped (say, with a finger). For example, if a string tuned to middle C is stopped exactly halfway along its length, the two equal segments of the string will vibrate at exactly one octave above middle C.