I am looking for the term for a checkmate position which is an aesthetic feature for a chess composition. It is closely related to pure mate. I shall say that a piece (incl. pawn) participates in the mate if the piece attacks the king or a square around it.
Pure mate:
The checkmating position in which the square occupied by the mated king and all vacant squares around it are attacked exactly once, and squares around the king occupied by friendly pieces are not attacked by any opponent piece.
What I am looking for:
The checkmating position in which the square occupied by the mated king and all vacant squares around it are attacked exactly once, and every piece (or pawn) participating in the mate attack exactly one of these squares.
[Title "The Evergreen Game, Anderssen- Dufresne (1852)"]
[FEN "1r3kr1/pbpBBp1p/1b3P2/8/8/2P2q2/P4PPP/3R2K1 w - - 0 1"]
This is a pure mate, but not the type of mate I am looking for because the f6 pawn attacks both g7 and e7.
[FEN "3B1nqr/6kp/3N1P1p/8/8/3B4/2K5/8 w - - 0 1"]
This is the type of mate I am looking for, but not a pure mate because the h7 pawn is attacked by the bishop on d3.