Answer: The Talmud (Bava Basra 14b) mentions ten people, in addition to David, who authored Psalms: Adam, Melchizedek, Abraham, Moses, Heiman, Yedusun, Asaf, and the three sons of Korach. Rashi explains that these were (respectively) Psalms 139, 110, 89, 90, 88, 62 and 77, 50ff, and 42ff.
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