Here is another cool music making app for your iPhone, iPad or iPod Touch - Arctic Keys Virtual Analog Synthesizer. This is an instrument that emulates hardware synthesizers, which create sounds via oscillators. This one has two LFOs (low frequency oscillators) and the same kinds of controls you would expect from an analog synthesizer to create your own sounds by endless tweaking, including arpeggiator, 16x4 step sequencer, pitch and mod wheels.
You can save your performances as 16-bit 44.1KHz wav files or as MIDI files. And as with most iOS music apps, you then share it via one of several methods.
The app costs $4.99 in the Apple app store. For a complete description of the specs and features, see the article here: http://www.idesignsound.com/arctic-keys-virtual-analog-synthesizer-ipad/