History of the composition of the psalms

Before tackling the formation of the collection of the psalms, Delitzsch asks who wrote them and when? 

His summary of the Mosaic stimulus is an example of integrated thinking the like of which I find hard to imitate in this age of constant electronic interruption. I could spend several posts on this one paragraph.

The time of Moses was the period of Israel's birth as a nation and also of its national lyric. The Israelites brought instruments with them out of Egypt and these were the accompaniments of their first song (Ex. xv.) — the oldest hymn, which re-echoes through all hymns of the following ages and also through the Psalter (comp. ver. 2 with Ps. cxviii. 14; ver. 3 with Ps. xxiv. 8; ver. 4, xiv. 27 with Ps. cxxxvi. 15; ver. 8 with Ps. lxxviii. 13; ver. 11 with Ps. lxxvii. 14, lxxxvi. 8, lxxxix. 7 sq.; ver. 13, 17 with Ps. lxxviii. 54, and other parallels of a similar kind). If we add to these, Ps. xc and Deut. xxxii, we then have the prototypes of all Psalms, the hymnic, elegiac, and prophetico-didactic. All three classes of songs are still wanting in the strophic symmetry which characterises the later art. But even Deborah's song of victory, arranged in hexastichs, — a song of triumph composed eight centuries before Pindar and far outstripping him, — exhibits to us the strophic art approximating to its perfect development. It has been thought strange that the very beginnings of the poesy of Israel are so perfect, but the history of Israel, and also the history of its literature, comes under a different law from that of a constant development from a lower to a higher grade. The redemptive period of Moses, unique in its way, influences as a creative beginning, every future development. There is a constant progression, but of such a kind as only to develope [sic] that which had begun in the Mosaic age with all the primal force and fulness of a divine creation. We see, however, how closely the stages of this progress are linked together, from the fact that Hannah the singer of the Old Testament Magnificat, was the mother of him who anointed, as King, the sweet singer of Israel, on whose tongue was the word of the Lord.

Echoes of the oldest hymn? 

Here's a table where you can see the translations in the tooltip and I will point out the allusions - if any. The allusions Delitzsch points out are not as strong as I expected in the use of the language of Exodus. In fact it does suggest that the Psalms are generations later than this Exodus poem.

Postulated source stimulus	Psalms allusion	Other comments	Common Hebrew phrase
Exodus 15:2	Psalms 118:14	=Isaiah 12:2, contrast Job 13:16 gm-hua-li liwuyh	yozi vzmrt ih vihi-li liwuyh
Exodus 15:3	Psalms 24:8 limited, only yhwh as subject of lkm	Similar to Isaiah 42:13	lkm modifying ihvh
Exodus 15:4, 14:27	Psalms 136:15	The allusion to 14:27 is not required	pryh vkilo.
Exodus 15:8	Psalms 78:13	no other uses	cmo-nd an archaic particle? - 139 uses and widespread - so maybe not.
Exodus 15:11	Psalms 77:14, 86:8, 89:7	Job 19:22?	cmo-al? Psalm allusions are single words only.
Exodus 15:13,17	Psalms 78:54

Ex. 15:17 shares a pair of roots pyl yhvh in sequence with Psalms 28:5 and 46:9,  Verse 13 has no pairs in sequence with any psalm. Ex 15 has a lot of unique language use. It is good to be introduced to this as a source for some Psalm allusions, but it is nowhere near as important a source for the Psalms as Ex 34:6. 

Still Dr D is very impressed with the poetry going back to the Song of deliverance from Egypt. 

It's a start - now I see I must do a lot more checking of his lists concerning e.g. Psalms 90 and Deuteronomy 32, a pair that Forbes also discusses, noted here, Deborah's song (several verses Judges 5:3,4,5,16 anticipate Psalms 68:9, 14), the Old Testament Magnificat (1 Samuel 2), and any other songs in other books.

There are a few unexpected suggestions as to source. It appears that he will admit composition right up to the time of the Maccabees. It's a long section that you can find at the link to my editing in process.

Ending with this conclusion (revealing his real attitude to the powers of the time):

And if Maccabean psalms be supposed to exist in the Psalter they can at any rate only be few, because they must have been inserted in a collection which was already arranged. And since the Maccabean movement, though beginning with lofty aspirations, gravitated, in its onward course, towards things carnal, we can no longer expect to find psalms relating to it, or at least none belonging to the period after Judas Maccabaeus; and from all that we know of the character and disposition of Alexander Jannaeus it is morally impossible that this despot should be the author of the first and second Psalms and should have closed the collection.

To be fair to the despot, I don't think I would have felt comfortable in  the company of either David or Solomon either. Abuse of power is there in every age. Psalms 146 gets it - Do not trust in princes, in a human child where there is no salvation to it. Its spirit goes forth. It returns to its humus. In that day its gleams perish.