by Becky Magan

Although scholars disagree on which evolved first, mathematics or music, history shows that man was aware of the relationship between mathematics and music as early as 500BC when the Pythagoreans observed that the ratios of the lengths of vibrating strings used to produce musical notes followed a mathematical relationship. Leibniz wrote that music is "a hidden arithmetical exercise for the soul."

In order to fully understand the mathematics of music, it is essential to understand what sound is. Once the physics of sound is understood, then the mathematics of music can be explained for all types of musical scales. We will investigate the major and minor Pentatonic Scales, the Pythagorean Diatonic Scale, and the Equal Tempered Scale.