I wasn't sure whether to put this here, or in the 'Open Source Alternative' category - I'm sure you'll all tell me if I'm wrong
LMMS stands for Linux MultiMedia Studio. Which is actually a missnomer as it is cross platform, Windows & Linux. The latest version is 0.4 so you can see it is very new.. The version available from debian testing is 0.3.2 and that is what I quickly loaded into my ordinary office machine (I don't mess with the DAW).
It appears to be a very complete package, having a built-in soft synth that sounds remarkably like Zyn. and even seems to have many of the same controls
There is a built-in chord selector and arpeggiator (somewhere - I didn't find it!)
It also supports both LADSPA and VST plugins (I noticed that the debian version installed wine), and it also supports sample libraries.
There seems to be support for both tracker style operation as well as piano-roll sequencer, but I haven't been able to get a drum pattern running in the tracker yet. It might help if I was to read the {ahem} fine manual
I haven't had time to do more than just make a quick few sounds and a recording of 'Three Blind Mice', but I'd say a lot of thought has gone into the general design and layout. It would probably be well worth watching.
Finally, It says it's free, but I can't find out what license it is under.