My iPad was going kaput (screen becoming non-responsive after almost two years) and I got a replacement from the Apple Store just this past week (benefits of that extended warranty), so I’m in the process of re-installing apps. Rather than just reproduce what I had before, I’m doing this one by one, to get reacquainted and to be more selective. So far, what my memory and experience are telling me are central to my use of the iPad are as follows. My backlog is quite sizable, and I’ll be pulling more from it, but this is the core for now:
AUM - Audio Mixer
Audiobus 3
AudioShare
MIDI Wrench
Loopy HD
STROM
Koala
Samplr
Ripplemaker
Audulus
Synth One
Nature-Oscillator
Update: I’ve now added these from my backlog, as I rebuild my iPad rig:
Borderlands Granular
Replicant 2
ReSlice
Update 2: Added these from my backlog, as well:
Cubasis 2
Autony (still working on this one)
Also, as a side note, if you are learning to play guitar, the app Chord! (that’s the one with an exclamation point) is an excellent chord database.