Dating old testament
The Psalms have been intentionally omitted because they were written over a period of many centuries by a number of different authors.See also the Chronology of the Prophets, the Chronology of the Old Testament Kings, and the Chronology of Latter Prophets and Intertestamental Period for more information.
[p.16] It is important to notice that the presentation of the law in Deuteronomy is different in character from that found in the earlier books of the Pentateuch.
Also, not all of the prophets were necessarily writers.
In some cases the books are a combination of the prophet's words along with later stories about the prophet as well as much later application of the prophetic message to new historical contexts. On the other hand, some prophetic books, such as Ezekiel, are relatively coherent indicating a great deal of unity of composition.
This suggests that the book uses much older traditions from the Assyrian era as a means to address a different set of problems in the post-exilic community.
Sons of Korah wrote Psalms 42, 44-49, 84-85, 87; Asaph wrote Psalms 50, 73-83; Heman wrote Psalm 88; Ethan wrote Psalm 89; Hezekiah wrote Psalms 120-123, 128-130, 132, 134-136; Solomon wrote Psalms 72, 127.