Synth One FREE

Described as “the first ever professional opensource iOS synth”, Synth One was developed by a pool of more than 100 developers and sound designers (many of them serious players, working with the likes of Kanye, Tycho and Rihanna), who all gave their time for free. The app itself is completely free, too, with nary an ad to be seen, but the specifications are impressive nonetheless: a five-oscillator analogue/FM hybrid with analogue-emulating filters, a 16-step sequencer, an arpeggiator, envelopes and LFOs, and a multitap delay effect.

It sounds great, and being open-source, anyone is free to mess about with its code to make their own instruments based on it.