David is "prudent in speech," (1 Sam. 16:18) which, when relating to his musical ability and charisma, soothes Saul of the "evil spirit". It is literally his speeches which turn Saul from his mission of killing David.
(The first time, David speaks to Saul directly in 1 Sam. 24:8-15, Saul responds in 24:16-21; The second time, David speaks to Abner, and then to Saul in 1 Sam. 26:14-20, Saul responds in 26:21-25)
There is a tension of sorts within David between his side who is "a man of valor, a warrior" and his side who is "prudent in speech".
The former intensifies Saul's anger toward David, and the latter relieves it, with the sole exceptions in 1 Samuel 18:10 and 19:9-10.