http://ffxi.allakhazam.com/forum.html?forum=10&mid=112537484627344598&num=29

A=00 B=01 C=02 D=03 E=04 F=05 G=06 H=07 I=08 J=09
K=10 L=11 M=12 N=13 O=14 P=15 Q=16 R=17 S=18 T=19
U=20 V=21 W=22 X=23 Y=24 Z=25

Fire = 00
Earth = 01
Water = 02
Wind = 03
Ice = 04
Thunder = 05
Light = 06
Darkness = 07

Password = (First Letter + Machine Element) (Second Letter + Machine Element) (Third Letter + Machine Element) (Sum of three letters + (Machine Element * 4))

IE: (all using A L Y)

Fire:
(00 + 0) (11 + 0) (24 + 0) (35 + (0 * 4)) = 00112435
Earth:
(00 + 1) (11 + 1) (24 + 1) (35 + (1 * 4)) = 01122539