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First I have to say that I really like your ideas you have realized with your app. But at all I want to replace the original music app on the iPhone against yours.
But therefor I miss some features:
1. You should update play counts and last played date of the song
2. You should show the song name and artist on lock screen - I have seen other apps with this feature, so I think it's possible.
3. You should add the song covers to the lock screen - I have also seen THIS feature on other apps, so it wouldn't be a big deal, too.
4. Is there a way to optimize the performance while song switching? It takes about 2 seconds for changing a song - this is not ideal for continuous albums.

I would be glad to see the features 1 to 3 in your app, so I can replace the music app with this and recommend your app