Whole numbers and the scale

Pythagoras believed that whole number was the foundation of everything which can be known, and that included music. His investigation of stretched strings of equal tension revealed that the tones they produce when plucked are harmonious when their lengths are in the ratio of certain whole numbers. For example, a string twice the length of a C-string will sound a C and octave lower. Increasing the length of the string by other whole number ratios will produce the notes going down the familiar 8-note scale (as given by the white notes on a piano). Above are the ratios for the Pythagorean scale.

Ratios were not only used to define notes in this scale, but also to define those combinations of notes which are harmonious to the ear (known as ‘consonances’). These were used to construct chords and other scales.