The Chess Variant Pages

Algebraic-Numerical Chess Notation

In this article Algebraic-Numerical Chess Notation, I will develop a new chess notation based on the algebraic notation and the numerical board invented by the arabs (10th century AD, for recording pieces tours and chess games). Today, it is the algebraic chess notation which is adopted by the orthodox chess Federation, where the pieces moves are identified by the departure and arrival squares, where each square of the 8x8 chessboard is represented by the coordinates (x,y), x=a,b,c,d,e,f,g,h and y=1,2,3,4,5,6,7,8. Example: 1. d2-d4 Ng8 - f6 means that the White pawn moves from the square d2 to d4 and the black Knight moves fom the square g8 to f6. Where the pieces are denominated by the letters R=Rook, N=Knight, B=Bishop, Q=Queen, K=King and P=Pawn. (see board (1)). Now, instead of using the coordinate (x,y) for for the pieces moves, I will use the following notation to represent the pieces move:

   Au-v

   where   A designates the the piece name and
           u, v identify the squares of the 8x8
           chessboards in terms of numbers and not
           in terms of (x,y) where x=a,b,c,d,e,f,g,h
           and y =1,2,3,4,5,6,7,8.

Thus using the previous numerical chessboard with pieces arrangements (see board(1)) we can write the moves Ng1- f3 by N7-22.

 

57 R

 

58 N

 

59 B

 

60 Q

 

61 K

 

62 B

 

63 N

 

64 R

 

49 P

 

50 P

 

51 P

 

52 P

 

53 P

 

54 P

 

55 P

 

56 P

 

41

 

42

 

43

 

44

 

45

 

46

 

47

 

48

 

33

 

34

 

35

 

36

 

37

 

38

 

39

 

40

 

25

 

26

 

27

 

28

 

29

 

30

 

31

 

32

 

17

 

18

 

19

 

20

 

21

 

22

 

23

 

24

 

9 P

 

10 P

 

11 P

 

12 P

 

13 P

 

14 P

 

15 P

 

16 P

 

1 R

 

2 N

 

3 B

 

4 Q

 

5 K

 

6 B

 

7 N

 

8 R

Board (1)

Now let's consider the following LASKER-CAPABLANCA chess game and rewrite it in this new notation. In the algebraic notation it is:

1 e4 e5  2. Nf3 Nc6  3 Bb5  a6  4 Bxc6  dxc6  5 d4  exd4
6 Qxd4  Qxd4  7 Nxd4  Bd6  8 Nc3  Ne7  9 0-0  0-0
10 f4  Re8  11 Nb3  f6  12 f5  b6  13 Bf4  Bb7  14 Bxd6  cxd6
15 Nd4  Ra-d8  16 Ne6  Rd7  17 Rs-d1  Nc8  18 Rf2  b5
19 Rf-d2  Rd-e7  20 b4  Kf7  21 a3  Ba8   22 Kf2  Ra7
23 g4  h6  24 Rd3  a5  25 h4  axb4  26 axb4  Ra-e7  27 Kf3!  Rg8
28 Kf4  g6   29 Rg3  g5+  30 Kf3!  Nb6  31 hxg5  hxg5
32 Rh3  Rd7  33 Kg3!  Ke8  34 Rd-h1  Bb7   35 e5!  dxe5
36 Ne4  Nd5  37 Nc5  Bc8  38  Nxd7  Bxd7  39 Rh7  Rf8  40 Ra1  Kd8
41 Ra8  Bc8  42 Nc5   Black resigns

In the new notation using the numerical notation, LASKER-CAPABLANCA game is written as:

1 e13-29, 53-37  2 N7-22,58-43   3 B6-34  a49-41  4 B34xN43 d52xB43
5 d12-28  e37xd28  6.Q4 xd28  Q60xq28  7 N22xQ28  B62-44
8 N2-19, 63-53  9 0-0  0-0   10 f14-30  R62-61  11 N28-18  f54 -46
12 f30-38  b50 -42  13 B3-30, 59-50  14 B30x44  c51xB44
15.N18-28 R57-60  16 N28-45  R60-52  17 R1-4  N53-59
18 R6-14  b42-34  19 R14-13, 52-53   20 b10-26  K63-54
21 a9-17  B50-57  22 K7-14  R53-49  23 g15-31, 56-48
24 R4-20 a41-33  25h16-32, a33xb26  26 a25xb26  R49-53
27 K14-22!  R61-63  28 K22-30!  g55-47  29.R21-23  g47-39+
30 K30-22!  g55-42   31 h32xg39  h48xg39  , etc. black resigns

Now instead of considering the numerical chessboard with the squares identified by 1 to 64 we can identify them by any other type of numbers and record the chess game. For example if we consider the the first 64 prime numbers from 2 to 317 with initial arrangement of pieces (see board(2)), we can rewrite LASKER- CAPABLANCA chess game as:

 

271 R

 

277 N

 

281 B

 

283 Q

 

293 K

 

307 B

 

311 N

 

313 R

 

233 P

 

239 P

 

241 P

 

251 P

 

257 P

 

263 P

 

267 P

 

271 P

 

191

 

193

 

197

 

199

 

211

 

223

 

227

 

229

 

139

 

149

 

151

 

157

 

163

 

173

 

179

 

181

 

101

 

103

 

107

 

109

 

113

 

127

 

131

 

137

 

59

 

61

 

67

 

73

 

79

 

83

 

89

 

97

 

23 P

 

29 P

 

31 P

 

37 P

 

41 P

 

43 P

 

47 P

 

53 P

 

2 R

 

3 N

 

5 B

 

7 Q

 

11 K

 

13 B

 

17 N

 

19 R

Board (2)

1 P41- 127, 257-167  2 N17-83 ,281-197  3.B13-151  P233-191
4 B151xN197  P251xB151  5 P37-113, 167x113  6 Q7xP113  Q293x113
7 N83xQ113  B311-197  8.N3-71, 313-257  9 0-0  0-0
10 P43-131  R311-307  11 N113-76  P263-223  12 P131-173, 239-193
13 B5-131,283-239  14 B131x199  P241 xB131   15 N67-113  R277-293
16 N113-211  R293-251  17 R2-7  N257=283  18 R13-43  P193-151
19 R43-37  R251-257  20 P29-107  K313-263  21 P23-61  B239-277
22 K17-43  R257-233  23 P47-137, 271-229  24 R37-73  P191-149
25 P53-139, 149x107  26 P61x107  R233-257  27 K43-83!  R307-313
28 K83-131  P263-227  29 P73-89, 227-179   30 K131-83!  N283-193
31 P139x179 ,229x179  32 R89-101, 257-251  33 K83-89!, 263-307
34 R7-19 B277-239  35 P127-167!, 199x167  36 N71-127, 193-163
37 N211-157  B239-283  38 N257xR251  B283xN251  39R101-271 R313-311
40 R19-2  K307-293   41 R2-277  B251-283  42 N113-151  Black
resigns

The interest in using this new Algebraic-Numerical chess notation is that each recorded chess game can have application in practice. For example, the previous recorded chess game in terms of prime numbers gives rise to sequences of unordered prime numbers which can be applied in mathematics. Thus we see that from the first move to the 10th moves of the respective white and black we get the sequence 41,127, 257, 167, 17, 83, 281, 101, 197, 13, 151, 233, 191, 151, 197, 251, 151, 37, 113, 167, 113, 7, 113, 293, 113, 83, 113, 311, 3, 71, 313, etc..

Now instead of using the prime numbers we can for eample use the Fibonacci numbers, perfect numbers, Mersenne numbers, Fermat numbers, and othe types of numbers to record chess games. We can also use binary, hexadecimal, octal, code numbers for the squares of the 8x8 chessboards. Also, we can use alphabetic and specific characters. The recorded chess will give special formed words. We can also use electronic gates (as AND, OR, XOR, and their combination) to identify the squares of the 8x8 chessboard. In that case a recorded chess game will give rise to electronic circuitry which cxan be useful in electronic applications. We can also use the Mendeleiv chemical elements to identify the squares of the 10x10 chessboard. So, a recorded chess game may give rise to (probably) important chemical combinations which can be useful in chemistry and biology. There are a number of fields which this Algebraic-Numerical chess noation may very practical, not in chess games, but in mathematics, physics, biology, electronic, computer programming, secret coding, and many other social and artistic fields. In other words, using this new notation, a recorded chess game (from ordinary chess players to grandmasters) can be practically used in life and not only as an entertainement as it is now.


[Missoum responded with the following email when prompted for an example. -- DH]

I was taking a walk with my 4 year old son ALGORITHM, and at one moment he sang HIHOAAA, etc. I said to him: "ALGOR! Do you think that you will have a winning award with this bizarre song." But suddenly, this gave me the idea that a chess game can lead to a new musical melody, using the algebraic numerical chess notation. Here is a simple practical example of application of my article:

Take the 64 piano musial notes from the bass to the sharpest:

   CDEFGABCDEFGABCDEFGABCDEFGABCDEFGABCDEFGABCDEFGABCDEFGABCDEFGABC

Identify each square of the 8x8 chessboard by one of these notes, starting with c for square 1, D for square two, etc... up to the 64th square following the previous note order. Play a chess game and translate the moves with the Algebraic-Numerical chess notation using the notes for departure squares and arrival squares.

Example: let's say that the moves d2-d4 d7-d5 are d(D)-d(E) d(B)-d(G), where D, E, B, G are piano notes representing the departure and arrival squares. Then using this notation, the played chess game will give a rise to a new musical melody (perhaps terrific, or very bizarre). We can also also use the guitar musical notes instead of the piano notes and apply the Algebraic-Numerical chess notation. So, a played chess game will give rise to a new guitar musical melody. In other words, we can compose new music using a chess game and the Algebraic-Numerical chess notation.


Written by A. Missoum. Edited by David Howe.
WWW page created: October 7, 1997.