PBX Alternate Number Ring
Alternate number ring is a feature where a particular line is assigned more than one extension number so that if one of the numbers is dialed, one ring (such as a ring - pause - ring) occurs when one of the extension numbers is dialed, and a different ring (such as ring-ring - pause - ring-ring) if the other extension number is dialed.

Comments
333Also known as Distinctive Ring
Alternate Ring is a feature of Call Sign which is an option from BT in the UK. Allows 2 numbers to be assigned to a single POTS line, each number gives a different ring. One number gives the usual ring-ring - pause - ring-ring UK ringing tone, the other gives ring - pause - ring rather like a north american ring.
Zaptel can be configured to discriminate incoming Alternate Rings:
http://www.voip-info.org/wiki/index.php?page=Asterisk+ZAP+channels
Alternate Rings can also be configured outgoing.