Having mentioned MultiTrack DAW I have to mention FourTrack which is a great musical sketchpad or notepad for getting quick ideas together. As a 4 track recorder it is amazing. It has all the options and facilities you could want and copy/paste means that it plays nicely with lots of other apps too.
I use this a lot if I’m working on something fast or want to see how things will go together quickly. A really good app that won’t be coming off my iPhone any time soon.