Although iOS 7.1 doesn't contain a way to save emailed music files to your iPhone, you can share these attachments with certain apps designed for note taking or cloud storage, including Dropbox, Evernote and Box. These apps not only save the files so you can access them on your phone whenever you have an Internet connection, they sync the files to computers, tablets and other devices connected with your account. If don't want to use up your mobile data each time you play a music file, these apps can save music files on the iPhone for offline access.
Download Dropbox from the App Store. Use this app to sync and access files on your mobile devices and computers, including email attachments such as music files.
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Open the Dropbox app. If you haven't signed up for a free Dropbox account, tap "Create an Account" to set one up and log in. Otherwise, tap "Sign In" and log in with your existing credentials.
Open the email with the attachment in iPhone's Mail app. Tap the music file's icon within the body of the message. Tap the "Share" icon, which looks like a square with an arrow going through it, and select "Open in Dropbox."
Tap "Save" to save the music file to the root folder of your Dropbox account and to sync the file to any other devices connected to your Dropbox account. If you want to save the file for offline access on your iPhone, swipe across the music file's name in the app's file list and tap the star to mark it as a favorite.
Download Evernote from the App Store. WIth this note-taking app, you can save an email attachment to a note that you can access from different devices.
Open the Evernote app. Type your email address. If you have an existing account with the service, you are prompted for your password. Otherwise, create an account and sign in. A basic account with the service is free.
Use the iPhone Mail app to open the email. Tap the music file attachment icon followed by the "Share" icon and then select "Open in Evernote." This automatically creates a new note in the app and attaches the music file to the note.
Type a new title for the note. Use the artist and song title to make the note easy to find in the future. Tap "Save" to save the note with its music file attachment and to sync the note to other devices with Evernote. The note with the file is available offline on your iPhone by default.
Download the Box app from the App Store. Use this cloud storage app to share files on any device with access to the service.
Open the Box app. Tap "Log In" and enter your credentials if you're already signed up with the service. Otherwise, tap "Sign Up" and enter the requested information to make a free personal account. After you make a new account, check your email and click a confirmation link before you log in to Box on your device.
Use the Mail app on the iPhone to open the email with the music attachment. Tap the icon for the attachment in the message. Tap the "Share" icon and then select "Open in Box."
Tap "Upload" to save the file to your Box account. After the file is uploaded, swipe across its entry in the file list and tap the lightning bolt icon to save it on the iPhone for offline access.