Musica Touch offers music education (ear training, music theory/note reading, counterpoint) and composition tools (play a tune on the screen piano and see it notated, write a lead sheet, prepare a chorale or quartet), let the app invent a musical idea). Each of the 45 activities is sold individually so you need buy only the parts that interest you. Free (non-saving) versions of several of the writing tools are included, plus a free beginning exercise in rhythm tapping (Easy Rhythms) and a simple exercise in pitch reading (Single Pitches). The free Songbook Sampler shows you a few of the singalong tunes found in the Songbook activity (great for kids). In the purchased activities music can be exported as a printable pdf, or as a MIDI file, or shared with a friend for hearing/viewing in Musica Touch.
Now with MIDI in/out capability for those would like to connect an external keyboard, Musica Touch can be used with iPads running iOS6, but we recommend iOS7 or later.

In-app purchases (descriptions of each available in app):

Writing activities:
Free Idea Generator (free, doesn't save/share files)
Idea Generator
Free Composition (free, doesn't save/share files)
Composition
Free Leadsheet (free, doesn't save/share files)
Leadsheet
Free Tune Notater (free, doesn't save/share files)
Tune Notater

Ear training activities:
One Bar Rhythms
Hearing Intervals
Hearing Triads
Hearing Sevenths
Hearing Progressions
Pitch Errors
Pitch Patterns
Rhythm Patterns
Pitch Dictation
Rhythm Dictation
Melodic Dictation
Complete Ear Training Set

Music Theory/Note Reading activities:
Easy Rhythms (free)
Single Pitches (free)
Songbook Sampler (free)
Songbook
Rhythm Reading
Pitch Reading
Melody Reading
Rhythm Band
Degrees
Playing Intervals
Playing Chords
Seeing Intervals
Seeing Chords
Complete Theory/Reading Set

Counterpoint activities:
1st Species 2 Parts
1st Species 3 Parts
1st Species 4 Parts
2nd Species 2 Parts
2nd Species 3 Parts
2nd Species 4 Parts
3rd Species 2 Parts
3rd Species 3 Parts
3rd Species 4 Parts
4th Species 2 Parts
4th Species 3 Parts
4th Species 4 Parts
5th Species 2 Parts
5th Species 3 Parts
5th Species 4 Parts
Palestrina 2 Parts
Palestrina 3 Parts
Palestrina 4 Parts
Complete Counterpoint Set

Complete Activities (all the above)