You can only export audio files from GarageBand on IOS, share them to email or to iTunes.
But if you have iCloud, you can share your GarageBand project to iCloud. Then it will be synced to your other devices and you can open it in GarageBand on your Mac.
I have never used Logic, so I am not sure, if Logic will be able to open GarageBand projects and if this will be useful for you. At least opening in GarageBand on your Mac should enable you to print the score of your midi track.
I can only tell you for IOS 6 - I hope you have the same version, or it will work in IOS 5.1 the same:
- In GarageBand, go to the "My Songs" View, then click the "Edit" button.
- You songs will start to wiggle. Select the one you want to share to iCloud.
- Click the "+" button to duplicate it (for backup).
- Then select the copy and press the "cloud" icon to upload the song to the cloud. It should now show the cloud icon.
- The next time you sync your iPad with the mac the song should be available in iTunes in the shared documents section.
If the cloud-button is not available in GarageBand, check in the "Settings" app, if you have enabled "Documents & Data" in the iCloud settings. You will also need to enable "Documents & Data" in the iCloud settings of the System Preferences on your mac.
Also you can share the GarageBand Project to iTunes, then it will also be synced to your Mac, see thsi section of the GarageBand manual:
If you do not see your song on the shared documents section on your mac, see the following discussion:
- Open Garageband on your iOS device and select the My Songs display
- Long hold on the song to export (songs wiggle), then tap the sharing icon top left, use Share Song Via iTunes as GarageBand
- Click Done when finished
- Connect device to iTunes
- Select the device in the left-hand column, then the Apps tab, scroll down to File Sharing area, within that scroll down to GarageBand
- Copy the project to a folder on your computer
- Open the project in GarageBand and export your data from there.