Musical Ear Trainer

This app provides you with a set of customizable ear training exercises. You can train to recognize pitch, intervals, or types of chords, using either the built-in exercises, or custom exercises that you create. You can control things like the instrument sound, what types of intervals or chords to play, how to play them (ascending, descending, open, close, etc), and which area of the keyboard to use.  

With the free download, you can use a few basic exercises. To unlock the rest, purchase the full app (an in-app purchase).