Resolution

The error will most commonly occur while syncing music. This issue can be resolved by following these steps:

Select the iPhone or iPod touch in iTunes under Devices.
Click the Music tab and under the Sync music option, choose Selected playlists.
Deselect the Voice Memos playlist.
Click Apply and then click Sync.
If the above steps do not resolve the issue, check the device and the iTunes library for duplicate voice memos. If you find any duplicate voice memos, delete the duplicates and then sync.

If those steps do not resolve the issue, then follow these steps:

Select the iPhone or iPod touch in iTunes under Devices.
Click the Music tab and deselect the Sync Music option.
Click Apply and then click Sync.
After the sync is complete, reselect the Sync Music option.
Click Apply and then click Sync.
If the Error 13019 occurs while syncing content other than music (applications, podcasts, and so on), then perform the same steps above but uncheck the content that stops syncing with Error 13019.

If the steps above do not resolve the issue, attempt to sync an empty iTunes music library to the device while logged in as a new admin user. Follow these steps to create a new admin user:

Windows Vista and Windows XP

From the Start menu, choose Control Panel.
Open User Accounts.
Select Create a new account and follow the instructions to complete the account setup process.
Once the new account is created, choose Log Off from the Start menu.
Log in to the newly created user account.
Mac OS X

From the Apple menu, choose System Preferences.
Choose View > Accounts.
Click the "+" (you may need to authenticate to be able to click this).
Give the new user a name and short name and enter a password.
Select the checkbox for "Allow user to administer this computer". This makes the user an admin user.
Click Create Account.
Log out and then log in to the new account