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I know that it has become passé in some corners of biblical studies to reject the superscriptions or titles of the Psalms. But I believe this is a mistake. Apparently Gordon Wenham does so as well. In a chapter on reading the Psalms messianically he writes:
“The main assault on the Psalms took the form of discarding the titles. It was argued that the title were later additions to the text and were therefore worthless as a guide to the authorship of psalms or their content. At a stroke they were no longer the psalms of David or Asaph or the sons of Korah, dating from the time of the early monarchy—i.e., tenth century BC—but anonymous compositions mostly from the postexilic era down to the Maccabean era, roughly 500 to 150 BC. By writing off the titles in this way, skeptics eliminated the clearest marks of order in the Psalter. In the Psalms’ final form the sequence of titles does point to careful arrangement. For example all except one (untitled) psalm in Psalms 3–41are called psalms of David.”