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Other than the current coordinate notations used in chess, are there any other notations that anybody knows about? I am looking for anything that does not employ the coordinate system like naming all squares or any other sharp ideas.

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Other than the algebraic nomenclature: Two off the top of my head are

Correspondence chess used 1:1 to 8:8 to label the squares.

Descriptive notation predated algebraic: 1. P-K4 P-K4 2. KN-B3 QN-B3 and so on.

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  • Can't find a reference at the moment but I thought algebraic notation predated descriptive, coming from the Muslim world
    – Ian Bush
    Commented Jul 6, 2020 at 6:56
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    The second move listed in the answer would generally be written as 2. N-KB3 N-QB3. Descriptive labels each destination square uniquely, but you can omit K or Q from e.g. KB3 if only one is possible. You'd only use e.g. KR-Q1 if either of them could move to the exact same square.
    – Especially Lime
    Commented Jul 6, 2020 at 7:29
  • @cousin_pete can you elaborate on the first one. The second one seems very similar to the algebraic one , only more confusing. Can you list some games. very helpful.
    – shashank shekhar singh
    Commented Jul 7, 2020 at 12:05
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Older players such as myself (I'm 83) learned with descriptive notation. Descriptive notation names the files based upon the piece standing originally on the 1st rank square, e.g. the QB file for what is the "c" file in Algebraic and the Q file for the Algebraic "d" file.

I preferred it to Algebraic, which became popular later on, since I found it easier to record the moves during a game or to follow the written moves on a scoresheet or in a magazine or book without a board. It is, as the name implies, more descriptive of the move. The downside was that you had to count from both sides of the board, e.g. my KB3 as White was Black's KB6 and vice versa, i.e. Black's KB3 was White's KB6, etc.

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    There were many advantages to Descriptive Notation, which has given us such useful phrases as A rooks pawn or a Bishops Pawn. A Knight outpost on the fifth Connected passed Pawns on the sixth
    – Philip Roe
    Commented Jul 8, 2020 at 1:26

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