The Arduino has limited memory and processing speed, which makes real-time sound synthesis difficult. Usually people send MIDI from an Arduino to a capable output device of some kind. However the Mozzi library attempts to bring some synthesis chops to the Arduino itself.
“Mozzi brings your Arduino to life by allowing it to produce much more complex and interesting growls, sweeps and chorusing atmospherics. These sounds can be quickly and easily constructed from familiar synthesis units like oscillators, delays, filters and envelopes.
You can use Mozzi to generate algorithmic music for an installation or performance, or make interactive sonifications of sensors, on a small, modular and super cheap Arduino, without the need for additional shields, message passing or external synths.”