A free app for iPhone, by NCH Software.
WavePad is the best tool to make music in your iOS device. You can record, mix, cut, copy, paste and do much more with it.
With it you can record audio from the mic or from your computer, mix and edit it, cut some parts and add effects, and save it to a file or directly to the device. It supports many audio formats like mp3, m4a, wav, wma, wv, etc.
And you can record your voice and use it in the recording. You can also add effects like echo, amplify, and noise reduction.
It’s very easy to use and very intuitive.