John Gill's Exposition of the Whole Bible
Psalms 13 - Introduction
INTRODUCTION TO PSALM 13
To the chief Musician, a Psalm of David. According to Theodoret this psalm was written by David, not when he fled from Saul, but from Absalom; and gives this reason for it, what happened to him from Saul was before his sin, and therefore he could speak with great boldness; but what befell him from Absalom was after it, and therefore mourning and groans were mixed with his words.