From the book by Marty Bergen (1985), Better Bidding with Bergen — Volume One, Uncontested Auctions.
4
says let’s play in a Part Score 4 or 4
4 is asking opener to bid a singleton: responses are
4
= singleton, 4
= singleton, 4NT=minor suit singleton, and 5 no singleton.
Depending on the location of the singleton and your hand, responder is usually interested in playing in a game, 5 or 5 or a slam, 6 or 6.
Example: Responder has: A K Q x x x A K Q x x x x
With a heart singleton, you want to play in 6 otherwise you would bid 5.
4 and 4S are signoffs in responders long suit. Opener must pass.
4NT is invitational to slam, asking opener to bid a minor suit slam with an extra trick.
Example: Responder has like Q x x x x x A K Q J x x x
5 asks opener to play in a game, either 5 or 5.
5 is a signoff by responder, responder knows that the opener has long diamonds and wants to play game from his
side.
6 is to play slam in 6 or 6, opener is to pick the suit.
Again, a bid of 6 by responder is to play slam in diamonds, responder knows that it is the long suit.