James Charlesworth writes (The Pseudepigrapha and Modern Research, pp. 202-204):
Some Syriac manuscripts preserve five apocryphal psalms, frequently entitled Psalms of David. An edition of the Syriac was published by M. Noth ("Die fünf syrisch überlieferten apokryphen Psalmen," ZAW 48  1-23; repr. in M. Delcor, no. 1374), and a critical edition of the Syriac was published recently by W. Baars (no. 1370). The Five Syriac Psalms were translated by W. Wright ("Some Apocryphal Psalms in Syriac," Proceedings of the Society of Biblical Archaeology 9  257-66) and by A. Mingana, who also appended a facsimile of Mingana Syr. 31 ("Some Uncanonical Psalms," Woodbrooke Studies. Cambridge: Heffer, 1927. Vol. 1, pp. 288-92 [trans.], pp. 293f. [facsimile]). The Hebrew text of Syriac Psalms 1, 2, and 3 has been found in Qumran Cave Eleven; these have been edited with an English translation by J. A. Sanders (no. 1380). The first psalm is also extant in Greek, since the Psalter in the Septuagint contains 151 psalms (Sanders, no. 1380, pp. 54f., 60, conveniently juxtaposes the Greek and Hebrew; for the Latin version see R. Weber, no. 1395).
The prerequisite, unfortunately sometimes ignored, for an understanding of these five psalms is the recognition that they must be examined separately. The first three Syriac Psalms are at least as old as the Qumran Psalms Scroll, which was copied in the first half of the first century A.D. (Sanders, no. 1380, p. 9; J. Strugnell, no. 1391d, p. 207). Syriac Psalm 1 is the oldest, and is pre-Christian, and perhaps pre-Qumranian (Sanders, nos. 1380, 1384, 1387; J. Carmignac, no. 1372; W. H. Brownlee, no. 1371). Most scholars (viz. Sanders, nos. 1380, 1383, 1387; A. Hurvitz, nos. 1377j, 1378; S. Talmon, no. 1393; J. A. Goldstein, no. 1377b; R. Polzin, no. 1378k; and S. B. Gurewicz, no. 1377d) conclude that both Psalm 1 and the others date from the hellenistic period; thus they reject both the contention, which was never developed, that Psalm 1 is earlier than the sixth century B.C. (cf. W. F. Albright, no. 1369a), and the interpretation that it is late and Karaitic (cf. S. B. Hoenig, no. 1377g, p. 332).
Several scholars have concluded that one or more of these psalms were composed by the Essenes (viz. M. Philonenko, "L'origene essénienne des cinq psaumes syriaques de David." Sem 9 (1959) 35-48; idem, nos. 1378i, 1378j; Delcor, "Cinq nouveaux psaumes esséniens?" RQ 1 (1958) 85-102; idem, nos. 1374, 1375; A. Dupont-Sommer, no. 1376; cf. F. Christ, no. 1373b). Most contend correctly that while some passages can be interpreted in line with Essene theology, there are not sufficient data to conclude that they are Essene (viz. Sanders, no. 1387, p. 73; Carmignac, no. 1372; Brownlee, no. 1371; A. S. van der Woude, no. 1397, p. 35). There is a consensus that the original language of at least the first three Syriac Psalms is Hebrew.
Psalm 1 apparently consists of two originally separate psalms, Psalm 151A and Psalm 151B, which recount respectively how David was elevated from a common shepherd to the anointed ruler (7 vss.) and how he defeated the Philistine Goliath (11QPsa is fragmentary; cf. Syr. MS Mingana 31). Psalm 2 contains 20 verses which exhort the worshipper to glorify God. Psalm 3, of 19 (in Hebrew) or 21 (in Syriac) verses, is a personal thanksgiving (individualles Danklied) because the Lord answered the sinner's cry. Psalm 4 isa plea to be delivered from the lion and the wolf who prey upon the "flock of my father"; hence it is a David pseudepigraphon (cf. 1Sam 17:34-37). Psalm 5 is a personal thanksgiving for deliverance, and is conceivably also a David pseudepigraphon since the psalmist was about to be devoured "by two (wild) beasts."
The early date and pseudepigraphical character indicate that these Psalms should be contained in the Pseudepigrapha. It is improbable that 11QPsa is either the earliest Jewish prayer-book, as M. H. Goshen-Gottstein (no. 1377c) and Talmon (nos. 1393, 1393a; according to Sanders, no. 1385, p. 96, Talmon has now abandoned this hypothesis) suggested, or a "library edition" of the already canonized Psalter, as P. Skehan (nos. 1391, 1391a, 1391b) claims. The presence of so-called apocryphal psalms within the "Psalter" indicates that the distinction between canonical and apocryphal psalms was not clarified before the advent of Christianity (cf. Sanders, nos. 1380, 1381, 1382, 1382a, 1383, and esp. 1385; and Hurvitz, no. 1378).
James Charlesworth and J. A. Sanders write: "The presence of these psalms within the Qumran Psalter (11QPsa) raises the question of the extent of the Davidic Psalter prior to the destruction of Jerusalem in A.D. 70. At Qumran, of course, the Psalter was appreciably different from the present collection in Hebrew; but what was the shape of the Psalter elsewhere? M. H. Goshen-Gottstein has argued that the Psalter was already set (and canonized) by the second century B.C. and that excerpts from it, along with apocryphal compositions, were placed in 11QPsa, which is therefore the earliest 'Jewish prayerbook.' A similar interpretation is defended by P. Skehan, who contends that 11QPsa is a 'library edition' of the 'standard collection of 150 Psalms.' The presence of 'apocryphal' psalms such as the Prayer of Manasseh, and the Psalms of Solomon, which were considered inspired by many Jews around the turn of the era, along with the presence of apocryphal psalms in 11QPsa indicate the distinction between canonical and apocryphal psalms had not been clarified before the advent of Christianity." (The Old Testament Pseudepigrapha, vol. 2, p. 610)
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