Infinite Looper from Secret Base Design is a MIDI looping app for iOS. A spokesperson had this to say about it...
"Easily create loops using any of the six internal SoundFont instruments, or with IAA compatible synths - you can loop MIDI segments to make complete music productions. Infinite Looper features a traditional piano-style keyboard, ten pages of programmable pads, and an innovative loop sequencer to build complete songs. Arrangements can be exported as standard MIDI files, which can be used in full-featured desktop DAWs."
Pricing and Availability:
$9.99 at the app store.
More information:
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