I went through quite a number of iOS apps and have retained the following for further consideration.
My criteria are for shortlisting the apps are, in order of importance:
1) Free, preferably;
2) Must generate music procedurally;
3) Must save out to midi or wave file;
4) Must not have restrictions on use of output content (the music).
Cycler3D Free - not an easy interface to learn; still figuring out what to do inside this generator.
Poly Synthesizer with low delay - nice alternative interface to making sounds
Midi Tool - still figuring out what to do inside this.
MidiPads Lite - still figuring out what to do inside this.
iRockPlayer - still figuring out what to do inside this.
Ministepz - matrix-based boom-chik boom-chik drumkit groove creator
Arix-303 - matrix-based retro-synth groove creator
Sound Zen - matrix-based groove creator
2billionsongs - keeps crashing at this time !
TrueChords - for when I pretend to play the guitar again
HexaSound - I actually played a duet with a family member using their own installed version ! Unusual interface, easy to get used to. A sweet app !
Sweet Midi - I needed a virtual midi device on my iPad.
TEFView - works using TEF format files, shows scores.
Utakaell - Midi playback (among other formats)
PatternMusic - not an easy interface to learn; I am still figuring out what to do with this generator.
BeatWave - matrix-based sound generator; needs a bit of patience to figure out what sounds are assigned to which matrix cell.
Bucephalus - nice crunchy rock guitar sounds; randomly-generated based on physics and gravity. Learning slope.
Musync - generates sounds from collisions of graphical components on screen; physics based; I am still figuring out how I can use this.