Origin of the Psalter

Bruce Waltke writes that

The Psalter began with songs by individuals composed under unique historical circumstances. These poems were then used in the liturgical life of worshipping Israel and were later gathered into earlier collections.

This is quite similar to the view taken by Gerstenberger however I disagree with the overarching premise that the original Sitz im Leben of the Psalms was historical as opposed to cultic. I far prefer Engnell’s take as he explains here

For the most part, they originated within official priestly or prophetic classes at different sanctuaries in the land of Canaan, particularly at the temple in Jerusalem. The psalms which did not emanate directly from the Jerusalem temple were taken over in the cult there and – perhaps after censorship and revision – gained a respectable standing and were canonized.