These are some for my favourite apps to help with piano playing and learning to read music. They are all available in the Apple iTunes App Store. (Some are also available on Android devices.)
Note Rush (£4.99)
Very good note learning program which enables you to play the notes on a piano or keyboard in response to those displayed on the screen.
Flashnote Derby (£4.99)
Another excellent note recognition app. Again you can play notes on a piano or keyboard in response to ones displayed. Get them right in order to pull ahead in the horse race!
This provides an excellent set of aids for those learning to read music and play it on a keyboard instrument. There are exercises for identifying notes, key signatures, intervals and chords. There are also several ear training aids.
This enables you to use the iPad as a real alternative to printed music. Any scores that are available in pdf format can be loaded into the iPad, and can then be used for study or performance. I have a huge range of classical piano scores stored on my machine, and can browse them at the piano quite satisfactorily. (I even have a foot pedal to turn the pages!)
Musictionary Music Dictionary (69p)
This is very useful for looking up obscure performance directions encountered in music scores. It includes the common Italian words, of course, but a lot of less common ones, and a range of terms in other languages.
Rhythm Sight Reading Trainer (£1.99)
This provides excellent practice at reading rhythm patterns in music, from the very simplest combinations of crotchet, minim and semibreve, up to quite complex syncopated structures. You tap the patterns in time with a metronome, and your performance is scored for timing accuracy.
Piano Notes Pro (£1.99)
This is a good alternative to Tenuto for gaining proficiency in note reading. The app presents a score with eight notes at a time, and an on-screen keyboard to play them on. Your performance is rated for both accuracy and speed.
Tempo Slowmo (Free)
This is a useful app for recording your performances, and playing them back for critical appraisal. You can play them back at slow speed if you are being ultra-critical.
This is Apple's music performance app. It's great fun for exploring a large range of instrumental sounds.
(NB The asterisk is part of the name). This is a general flash card app, not specifically for music study, but there is quite a range of music card sets available for download in its on-line library.