Term for checkmate where every participating piece attacks exactly one square around king 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 &quot;The Evergreen Game, Anderssen- Dufresne (1852)&quot;]
[FEN &quot;1r3kr1/pbpBBp1p/1b3P2/8/8/2P2q2/P4PPP/3R2K1 w - - 0 1&quot;]

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 &quot;3B1nqr/6kp/3N1P1p/8/8/3B4/2K5/8 w - - 0 1&quot;]

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.
As a problemist, I can assure you that the term as such does not exist in problem language. Bohemian school did only know three concepts: pure mate, economic mate (all pieces - but not necessarily king or pawns - participate) and both at the same time.
Yet, not all hope is lost. At least one Bohemian troll had the following idea: What is the most uneconomic economic mate? Well, obviously one where each white piece idles as much as possible, i.e. guards only one flight, i.e. exactly which you describe. I don't remember the position offhand, but I'm fairly sure &quot;the swarm&quot; could dig it up if I take your request to a specialist forum. I edit it in if I can come up with it and you are interested, but don't expect that its historical solution comments contain the &quot;Oh, look, an XYZ mate!&quot; notion you seek.