arpeggiators

Arpeggiators provides synth players with an easy way of playing complex synth parts via simple chords. A good intro can be found at the Dawson's blog. Many MIDI controllers come with basic Arpeggiators built in.

Linux tools dedicated to them include qmidiarp and arpage. LMMS also has powerful support. There is also a 2 part 2010 Linux Journal article covering this topic.