Q: I purchased an album of music and can play it on my computer but I cannot see it nor play it with my iphone. Other music purchased plays fine.

Hello there, omena2013.

The following Knowledge Base article provides some steps for troubleshooting your iPhone:

iOS: Understanding multitasking

http://support.apple.com/kb/HT4211

Particularly:

Additional Information

If an app doesn't respond to your input, or doesn't perform as expected, do the following, testing after each step:

1. Check for app updates.
2. Force the app to close.
3. Restart your device.
4. Update your iOS device.

Learn more about troubleshooting apps.

Additionally you can also follow the next article for downloading previously purchased content to your iPhone as well:

Downloading past purchases from the iTunes Store, App Store, and iBooks Store

http://support.apple.com/kb/ht2519

Music

1. Make sure you're signed in with the same Apple ID used for the original purchase.
2. Tap the Music app.
3. Find the song or album you want to download.
   
4. Tap the download icon next to the track or album title.
   
5. The song or album will begin downloading.

Thanks for reaching out to Apple Support Communities.

Cheers,

Pedro.