Rhythmist

Rhythmist™ resembles one of the rhythm training activities found in Musica Touch™ for the iPad - also some of those in Practica Musica - but it's more gamelike and of course is intended for the iPhone.
Rhythmist creates melody examples and asks you to tap their rhythms correctly. You don't have to read the pitches; just the rhythm - but you will hear the correct pitches of the melody, plus chord accompaniment to make it more interesting. The free download includes the first 10 random melodies of 4 measures each; you can get many thousands more with an in-app purchase. You can even earn some free melodies by getting a series of these "right" on your first try.
Tapping is done on a pair of keys like piano keys - having two makes the tapping easier because you can alternate fingers. You can keep trying a melody until you get it right and earn a gold star. You can slow down or speed up the tempo if you want to. Each time you fill in the gold star for a melody your score goes up a point and you move on to the next one.
If you get expert at the Level 1 melodies, try Level 2. If you think you're really getting good try the melodies of Level 3. If you want to get competitive your scores can be posted to the Game Center; otherwise just try to meet the challenges yourself: can you get 5 melodies in a row correct on the first try? Can you get 10 of them without hearing them first? Can you get through the first 100?
If you've paid for the extra melodies any of them can be shared as music files readable by Musica Touch for the iPad and Ars Nova's desktop Songworks software, or as midi files or printable pdf files.