## Music & Mathematics

Up to the Middle Ages, *music* was considered a part of mathematics. It was taught as the principle of *number in time*, along with arithmetic – *number in abstract*, geometry – *number in space*, and astronomy – *number in space and time*.

In ancient Greece, Pythagoreans were the firsts to investigate the expression of musical intervals in terms of numerical ratios, laying the foundation for *music theory*. Still today, these ratios are used to make musical instruments and compose music. Famous scientist Kepler even posited a mathematical theory using such musical notions – intervals and harmonies – to describe the movements of the six planets known at the time.

Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse relate to the measurement of time and frequency, offering ready analogies in geometry.

Modern digital technologies opened the door to new methods of sound design and music composition. *Additive synthesis* for instance describes the building up of complex tones and waveforms from simpler elements such as *sine waves*.

And various sonification techniques, which convey data and information converted into acoustic signals, are now used in electronic music production.

Given the many stunning mathematical properties inherent to music, one can say that *listening to music is experiencing mathematics*, numbers, and patterns, that we embody by dancing, or intuitively beating time.