Clairvoyance
Clairvoyance allows you to map an area of the dungeon around you, similar to magic mapping but somewhat limited. Where magic mapping reveals the whole level, if it can be mapped, Clairvoyance will only reveal a square approximately 15x15 around you. Like magic mapping, the map will remain unlit and will not reveal secret doors, traps or objects. Importantly however, Clairvoyance will reveal the map surrounding you on levels that will not be mapped by magic mapping, such as the Valley of the Dead.
If you have Clairvoyance as an intrinsic or extrinsic, the effect of mapping the area around you is not constant but will only occur randomly, often taking dozens of turns before executing and revealing the area around you, once.
Gaining Clairvoyance
Intrinsic
You can only ever get intrinsic Clairvoyance temporarily, for a random length of between 500 and 999 turns, by donating between xplevel*200 and xplevel*400 to an aligned priest.
Extrinsic
Clairvoyance can only be obtained as an extrinsic by wearing a cornuthaum as a wizard, or by carrying the Amulet of Yendor.
Single use
You can get a single application of Clairvoyance by casting the level 3 Divination spell, Clairvoyance.