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Fausset's Bible Dictionary [1]

The title of Psalm 57; 58; 59; 75: The maxim of David amidst persecutions, embodying the spirit of his psalm (Kimchi); drawn from  Deuteronomy 9:26, Moses' prayer, "Destroy not Thy people and Thine inheritance, whom Thou hast redeemed." He used the same "destroy not" in  1 Samuel 26:9, to Abishai, who urged him to slay Saul when in his power. We can say "destroy not" to God only when we ourselves beat' no malice to our enemies. Aben Ezra less probably explains "some song named so, to the tune of which the psalm was to be chanted."

Morrish Bible Dictionary [2]

Two Hebrew words untranslated in the titles of Psalm 57,58,59 , and 75: reading in the margin 'destroy not,' and thus rendered in the LXX. The general thought is that reference is made to some air to which these Psalms were sung. The words, however, may have been taken from what David said in  1 Samuel 26 :9, "Destroy him not."

Smith's Bible Dictionary [3]

Al-taschith. (Destroy Not). Found in the introductory verse to Psalms 57; Psalms 58; Psalms 59; Psalms 75. It was probably the beginning of some song or poem to the tune of which those psalms were to be chanted.

Easton's Bible Dictionary [4]

 Psalm 575859,58,59