Comments/Ratings for a Single Item

Still, Falcon have some moves, this pieces can't fulfil. If one of
adjecent squares is occuppied, this pieces loses 2 destination squares,
while Falcon is still able to move anywhere he can with free paths.

Thanks for featuring Falcon/Bison, Charles.  ChessboardMath6 has many different "Falcons" arriving at same
Falcon/Bison squares just beyond the Knight:
http://www.chessvariants.org/index/listcomments.php?subjectid=ChessboardMath6.  They include: (1) Osprey, (2) Bison, (3) Fourriere Falcon.  There is only one Orthodox Falcon and all others to exclusive (1,3) plus (2,3) are heterodox including Bison. There is only one Orthodox Rook and all others to its (0,n) are heterodox, including Ramayana Buddha and limited Sissa. (follow-up elsewhere emphasizes standard f.i.d.e. 64-square form is flawed without 4 basics F,R,N,B, not simplemindedly three only)

 Chess variants often rename piece-types acknowledging origination: 17th-century Centaur and Champion have score of names by now.  Beyond mere naming, given piece-type is technically even legitimately "new" if it has different pathway(s) than earlier one to all-same arrival squares.  Past Gnu (1,2 plus 1,3) in travel length, the better oblique piece-types are multi-path and usually least-path. Except a very few of these fixed-length sliders -- Scorpion, Dragon, Phoenix -- none of them have names yet, with potentially thousands needed.  It is understandable Man & Beasts has to begin with oblique leapers and their compounds all far from ideal in play. For example Beastmaster's awkward leapers in Zillions would far better interact under rules of blocking and blockability.

The pieces on the middle level and the middle filestack, save for their intersection, are of course standard Xiang Qi pieces, albeit ones able to leave that level or filestack and reach the rest of the board. Of the pieces on the long diagonals of ranks the Guards are Man and beast 01 Viceroys (as acknowledged) and the Eunuchs Man and Beast 06 Stepping Eunuchs, while the Battering rams, Fireworks, and Mules are Brooks, Acannons, and Stepping Nsextons from Man and Beast 12 - the B, A, and N stand for Bishop, Arrow, and Ninja. Interestingly I originally termed the Nsexton a Mule myself until I decided to substitute something more suitable for extrapolation - to Uelf for a Camel analogue, Lfencer for a Zebra one, et cetera (U being for Underscore and L fr Lecturer).

The promoted Hirelings are essentially Fwazirs (F for Ferz) without the backward step. The plain Wazir with no backward step I term a Superpoint, but that will clearly not do for a different piece. Perhaps it should be considered a Super- verion of a notional Cpoint (C for Cross), and so termed a Supercpoint.

The piece at the centre of the end ranks is essentially a royally-restricted version of the compound of the Wazir and Fwazir, and the promoted Lieutenant the compound of Superpoint and Supercpoint. This hints at the possibility of other compounds such as Rook+Brook, Cannon+Acannon, and Knight+Nsexton - alongside the Baron (Ferz+Viceroy) and Elk (Elephant+Eunuch). Any ideas about a naming pattern for these pieces?

The names Battering ram, Firework, Hireling and Mule are not currently in Man and Beast, but Ram on its own is Horn+Point, the forward form of he Besieger, in Man and Beast 01 and Fire- as a prefix indicates the direction of Man and Beast 10's Firegeneral, which is Rumbaba+Heir. Lieutenant I use for Sexton+Lecturer in Man and Beast 05.

The best that I can devise is that at the turning point it might go through a radial but not bounce off one. Here are some examples on the FIDE board: Valid Prince-Knight Monster moves include a1-a2-b4, going through the a2-b1 and a2-g8 diagonals; a1-b1-d2, going through the a2-b1 and b1-h7 diagonals; and a1-b2-c4 and a1-b2-d3, both going through rank 2 and file b. They do not include a1-a2-c3, as it bounces off the a2-g8 diagonal; a1-b1-c3, as it bounces off the b1-h7 diagonal; a1-b2-a4, as it bounces off file b; or a1-b2-d1, as it bounces off rank 2. Does this seem a satisfactory and sufficiently rigorous definition?

Have anybody ever noticed that cannon (in some sense) is also some kind of
piece, wich starts move as one, and continues as another?
True rider of grasshoper's move would make several hops over several
pieces in same direction, while cannon starts as grasshoper (orthogonal, in
case of cassic cannon) and continue as rook.

(1) The Korean Cannon can also make an orthognal Grasshopper move without a Rook move following it, whereas the Mao cannot make a Wazir step without then making a Ferz step and so its octagonal analogue cannot make a Wazir or Ferz step without then making a Knight leap. Another way to look at the Korean Cannon is that it makes an orthogonal Cntragrasshopper move preceded by an optional Rook move.

(2) The Chinese Cannon is something more complicated, a divergent piece that can make a noncapturing move only as a Rook but a capturing one only as a Korean Cannon.

> Have anybody ever noticed that cannon (in some sense) is also some kind
of piece, wich starts move as one, and continues as another?

Fairy-Max implements all its pieces this way: they always have a primary
and a secondary move, and on pieces that don't need that, these two are
simply taken the same. Primary moves kan be marked as 'hopping', in which
case the transition to the secondary phase takes place when it lands on an
obstacle with its primary move. Otherwise the transition to the secondary
phase is spontaneous, and can be configured to occur with a delay, i.e.
after making a specified number of steps of the primary move. This to
implement limited-range sliders, which first make a number of slider steps,
before reverting to a leaper for the final step.

In general all 'move rights' can change in the transition; not only the
'rider' right that allows repeating the step (if not blocked), but also
capture and non-capture rights. So a Cannon is defined as a hopper with a
Wazir step and rider rights, with primary non-capture and secondary capture
rights.

A difference with the interpretation given below is that in the Fairy-Max
description the transition takes place when the hopper is on the platform
square, not just behind it (Grasshopper) or before it (Contragrasshopper).
So the Grasshopper itself is in fact considered a transition piece, which
loses its rider rights in the transition, but gains capture + non-capture
rights, which it didn't have before.

Where exactly the transition takes place would only be noticeable if the
direction (actually board step) would differ between primary and secondary
step. A Mao is indeed implemented as a primary Wazir without rights and a
secondary Ferz with capture + non-capture rights, the transition taking
place spontaneously after the first Wazir step. Hoppers that alter
direction would be bifurcators.

The extension of Betza notation I proposed also uses 'chaining' of
different, independently specified phases, where the number of phases is
not limited to two (as it is in Fairy-Max). As there is also a notation
there for "indefinite repetition" of a phase, it would be possible to
define "multi-hoppers", like the mentioned Grasshopper-rider.

There are other pieces complementing these, and I have gone for non-board names for these. For Oxranker+Bittefiler I suggest the long-unused Ibex, and for Curatranker+Albatfiler Almoner, meaning a giver of charity often for religious motives. I am not sure about Bishop+Carpenter. i wondered about Nutter, a slang term for a mad person, in reference to the Bishop as Fool, but wondered whether some people might consider this an offensive piece name. If anyone can suggest something better, ideally connected with squirrels in some way (it tansforms the Squirrel's Elephant component from proto-Bishop to modern Bishop) for this piece I would be grateful.