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With psalteries on Alamoth - Some suppose that the word signifies virgins, or women singers, the persons mentioned here being appointed to accompany them with psalteries, and preside over them.

The Vulgate says arcana cantabant, they sang secret things or mysteries; probably prophetic hymns.

Psalteries on Alamoth - Probably, psalteries whose tone resembled the voices of girls (עלמות ‛ălâmôth ). Compare the “female flutes” of the Lydians.

Wise and good men may be guilty of oversights, which they will correct, as soon as they are aware of them. David does not try to justify what had been done amiss, nor to lay the blame on others; but he owns himself guilty, with others, of not seeking God in due order