I am forever finding new things to include in the classification, which means that this notation keeps changing. However, I will attempt to describe it as it is now, in hopes that tomorrow's version will not be too different.
In the string "fhNfrlRK" there are three main parts, which say that the fhNfrlRK has partial powers of the N, partial powers of the R, and all the powers of the K. In other words, the capital letters are the main landmarks.
Before each capital letter there might be some lower-case letters that modify the powers.
After the capital letter might be another modifier, a number. For example, "R4" is an R that can move only four squares. It should really be called "W4", which is an example of how the notation is often imperfect.
[Obsolete?] If the capital letter is repeated, it means the piece has a long-range move of unlimited length: for example, WW means the same thing as R. Perhaps I should now say "W7" instead of "WW", but what happens then when we extend the system to 12 by 12 boards?
Some of the capital letters are shortcuts. For example, R is a shortcut for WW or W7; K is a shortcut for WF, and Q is a shortcut for RB which is a shortcut for WWFF (or W7F7).
I would like to always have the capital letters appear in the same order, but I am not always careful enough.
mA is a piece that moves like an Alfil but cannot capture.
cA is Alfil capture without Alfil movement.
fA is Alfil forwards movement and capture.
bA is the Alfil in retreat.
D is Dabaaba, a jump to (0,2), two squares Rookwise.
rlD ("right+left") is the sideways movement of the Dabaaba.
W is Wazir, (0,1), one square Rookwise.
F is Ferz, (1,1), one square diagonally.
H is (0,3), three squares Rookwise.
G is (3,3), three squares diagonally.
L is (1,3), the "long Knight".
J is (2,3), a piece which is too big for the 8x8 board.
And here's a diagram to make it easy to remember:
G J L H L J G J A N D N A J L N F W F N L H D W . W D H L N F W F N L J A N D N A J G J L H L J G fG fJ fL fH fL fJ fG rJ fA fN fD fN fA lJ rL rN fF fW fF lN lL rH rD rW .. lW lD lH rL rN bF bW bF lN lL rJ bA bN bD bN bA lJ bG bJ bL bH bL bJ bG
b is backwards.
c is capture-but-not-move. "fcFfmW" is a Pawn (except for promotion).
f is forward. Sometimes ff is used to distinguish forward-forward from forward-half -- see the use of "ffN" in the section about the modifier "h".
g is "grasshopper". A grasshopper piece is a runner that must jump over exactly one other piece and land on the square just past that piece.
h is "half". for example, the ffN can go from e4 to d6 and f6, but nowhere else, while the fhN can go from e4 to c5, d6, f6, or g5. There was never any notation for a move that can go from e4 to c5 or g5 and nowhere else, but I think it would be "fsN" -- the sideways part of the forward motion of the Knight.
j is "jump-only". Of course, a jump-only D could also be described as a "gW2". I prefer "jD", however.
l is "left". I have no plans for any pieces that move one way to the left and another to the right. "rNlB" would be a funny piece to have, wouldn't it?
m is move-but-not-capture. "fcFfmW" is a Pawn (except for promotion).
n is non-jumping. An nD would be a Dabaaba that cannot get from b1 to b3 if b2 is occupied.
o is cylindrical. Cylindrical pieces do not stop at the edge of the board -- they think that if you go to the right from h1, the next square is a1.
p is cannon. Cannon pieces move like Rooks, Bishops, Queens, but require one intervening piece to move. Similar to grasshoppers, except that the piece jumped over can be anywhere on the path.
r is "right". See next entry ("rl").
rl is "right-left". As I write this document, I have decided that I should use "s" instead of "rl". You will still see "rl" in many places.
s is "sideways". See the entry for "f". "s" is short for "rl".
v is "vertical". Short for "fb". z is crooked; zF7 is a crooked Bishop.
My notation has no way to describe such a piece.
Not yet, anyway.