I'm making this post on all the colored chip forums that work with the strange apparati.
The Password is based off the first 3 characters of your name and the zone's number.
The first thing you want to do is decided which zone, the zones value is the starting value of the alphabet's number values. So, if you go to Wadi A = 00, but the Maze A = 07.
Now, once you have that get the first 3 letters of your name, and find the numeric value of them. Let's use ABE as an example. For Wadi, A = 00, B = 01, and E = 04. But, for the Maze, A = 07, B = 08 and E = 11. These are the first 6 numbers of the password.
To get the last 2 you need to take the value of your letters, and add them, i.e. ABE @ Wadi = 00+01+04 = 05, and ABE @ Maze = 07+08+11 = 26.
So, for the Password of ABE in Wadi you need 00010405. While ABE at Maze is 07081126.
I hope this makes sense to most of you. And here is the listing of the zone values.
For anyone looking to use the Strange Apparatuses, this is a list of locations and colors. Given is the location, the color of the chip necessary, the position on the map where you enter the hidden area, difficulty rating (1-10), and maps necessary to reach the Apparatus. All of the maps used are from http://www.speakeasy.org/~sticks/ffxi/treasure/ It's got maps of every zone - very useful.
Dangurf Wadi - Red - (F-11) - Difficulty: 2 <Beware; there is a small hole right before the cermet door, no real problem, but you have to go out of your way.>