It seems likely that Ps 72:20, "The prayers of David the son of Jesse are ended", refers to the completion of an early collection of Davidic psalms. The evidence does not really fit together seamlessly, but still converges on this conclusion.
The text reads:
כָּלּוּ תְפִלּוֹת דָּוִד בֶּן־יִשָׁי
kālû tĕphillôt dāwīd ben yišāy1
(1) Ps 72:20 follows a "doxology"
The 150 psalms in the Hebrew Bible (Masoretic Text) is divided into five "books", and each of the five concludes with a "doxology":
+----------+---------------+----------------+
| Book: | Comprised of: | Doxology: |
+----------+---------------+----------------+
| Book I | Pss. 1‑41 | 41:13 [Heb 14] |
| Book II | Pss. 42‑72 | 72:18‑19 |
| Book III | Pss. 73‑89 | 89:52 [Heb 53] |
| Book IV | Pss. 90‑106 | 106:48 |
| Book V | Pss. 107‑150 | 150 (?) |
+----------+---------------+----------------+
Psalm 150 is a special case, in which a whole psalm provides a "doxology" not only to Book V, but to the Psalms as a whole. The other four have a similar shape:
41:13[14] Blessed be the LORD, the God of Israel, from everlasting and to everlasting. Amen, and Amen.
72:18-19 Blessed be the LORD God, the God of Israel, who only doeth wondrous things; And blessed be His glorious name for ever; and let the whole earth be filled with His glory. Amen, and Amen.
89:52[53] Blessed be the LORD for evermore. Amen, and Amen.
106:48 Blessed be the LORD, the God of Israel, from everlasting even to everlasting, and let all the people say: 'Amen.' Hallelujah.
These "doxologies" appear to have been in place at least since the time when Psalm 106:48 was put to use in 1 Chronicles 16.
Given this sort of "collection marker" at 72:18-19, it seems unlikely that 72:20 refers only to the preceding psalm. More likely is that it serves as a supra-collection marker, refering back to the collection of collections in Books I-II.
(2) The Distribution of "David" Psalms
The superscriptions to the individual psalms often include the rubric לְדָוִד "lĕdāwīd", which is difficult to translate: for David? of David? by David? belonging to David? Whatever precisely it means, it is generally taken as an indicator that the psalm bearing the superscription belongs to a "Davidic psalter".
Psalms 1-2 have no superscription, and are thought to introduce the collection as a whole. But thereafter, Pss 3-41 all have the lĕdāwīd title, with exceptions for Psalms 10 (in the Septuagint, a single psalm combining with Ps 9; together they form a continuous acrostic), and 33. This span of psalms corresponds nicely with "Book I".
The next time we see lĕdāwīd, it is in the superscriptions of Pss 51-70 (excluding 66-67). Note that this brings us nearly to the conclusion to Book II, and the thus the notice in 72:20, that "The prayers of David the son of Jesse are ended".
There is thereafter only a sprinkling of "Davidic" psalms: lĕdāwīd appears in a superscription to Pss 86, 101, 103, 108-110, 122, 124, 121, 133, and 138-145. Other than that concluding set of eight psalms, we really don't get another "collection" of David psalms in the body of the book of Psalms again.
It thus seems likely that Ps 72:20 concludes the major collection of Davidic psalms.
(3) Collections of Collections in the Psalms
Why would 72:20 claim that "David's psalms" are completed when there are more to follow?
It seems fairly clear that the book of Psalms is itself a collection of collections. The two great blocks of David psalms (along with the smaller, closing collection) themselves point in this direction. But there are also the following:
- Korah psalms = Pss 42-49; 84-88
- Asaph psalms = Pss 73-83
- "Ascent" psalms = Pss 120-134
Klaus Seybold has a nice discussion of phenomenon in more detail in his Introducing the Psalms (T. & T. Clark, 1990), pp. 18-23, and see the somewhat complex chart on p. 22, but this gives the idea.
It seems plausible, then, that the notice at 72:20 was added while the collection was still in its growth phase. How long did that phase go on, though?
(4) The Psalms Scroll from Qumran Cave 11
Enter the evidence of the great Psalms scroll found in 1956, and published very rapidly by James Sanders, The Psalms Scroll of Qumrân Cave 11 (11QPsa) (Clarendon Press, 1965).
As the online article by Tyler Williams notes, the dominant interpretation of the unusual contents of this scroll holds that the first three Books of the Psalms were fixed at an earlier stage than the last two books. (Williams fairly notes also that this view is still debated.)
This could explain, though, why the compiler who added the notice at 72:20 believed that the Davidic collection was complete: because at the time the notice was included, that was in fact the case.
(5) Psalm 151
And finally, Psalm 151. This appears in 11QPsa in both a longer and shorter form, but is best known as the 151st psalm in the Septuagint Psalms. Its superscription reads as follows:
Οὗτος ὁ ψαλμὸς ἰδιόγραφος εἰς Δαυιδ καὶ ἔξωθεν τοῦ ἀριθμοῦ· ὅτε ἐμονομάχησεν τῷ Γολιαδ.
This Psalm is a genuine one of David, though outside the number, [composed] when he fought in single combat with Goliad.
This composition has an almost unusual level of self-consciousness for the Davidic psalms, both "protecting" the special status of those from within the "official 150", and also claiming Davidic status for this composition itself.2
This "consciousness" is yet a further indication (I suggest) that there was an awareness of a developing "David" collection, and of what was in, and what was out.
Conclusion
Taking this evidence together, we see an extended period of time over which the canonical psalms were collected, and that there are sub-collections incorporated into our 150 Hebrew psalms. At one point in this phase, the two large collection of David psalms were included, and the end point of this marked in 72:20.3 Subsequently, other psalms were added, including some ascribed to (or "belonging to") David. This process (of David's "influence" extending more deeply and broadly into the psalms collection) can be seen to continue in the Greek Psalms (again, see n. 2 below).
Notes
- It is always instructive to see what Rashi has to say, and here he has a fair bit:
The prayers of David… are completed: Heb. כלו. Our sages expounded on כָּלוּ to mean כָּל אֵלוּ, all these are the prayers of David son of Jesse, to include the entire Book on David’s name, even what the sons of Korah and the ten elders said because he was known as (II Sam. 23:1) “the sweet singer of Israel.” כָּלוּ may also be interpreted as “were completed.” The construction of כָּלוּ is like (Job 24:24): “They are taken away (רֹמוּ) in a second” ; (Jer. 2:12), “O heavens, be astonished (שֹׁמוּ).” If this is so, this psalm was not written in its place, and there is no chronological order in the Book. The [subject] matter indicates that he said this in his old age, when he enthroned Solomon.
- For a fascinating insight (a) into the way in which David's influence over the Greek Psalms came to be pervasive, and (b) into the work of the text critic, see Albert Pietersma, "David in the Greek Psalms", Vetus Testamentum 30/2 (1980), pp. 213-226.
- One might add by way of analogy the "marker" notice in Jeremiah 51:64, עַד־הֵנָּה דִּבְרֵי יִרְמְיָהוּ "Thus far the words of Jeremiah", a notice that does not appear in the different form of the book in the Septuagint version of Jeremiah. Here, the Hebrew seems later than the Greek, reversing the pattern from the Psalms.