How many Psalms of David? Qumran's answer

The entire canonical collection making up the biblical Psalter claims in some fashion the authorship of David, the revered king and founder of the Judahite dynasty that would eventually give us Jesus Christ, "great David's greater Son." This suggests, not that David literally composed every Psalm, many of which (for example, 79, 80, and 137) address conditions and events long after his death. It suggests rather that he initiated the project of creating a collection of hymns for God's people which continued for centuries afterwards until the exile and possibly later.

One of the texts uncovered at Qumran (11Q5/11QPs^a) asserts that David wrote many more psalms than those that would come to be included in the Bible:

[2] And David, the son of Jesse, was wise,
  and a light like the light of the sun, and literate,
  [3] and discerning and perfect in all his ways before God and men.
[4] And the Lord gave him a discerning and enlightened spirit.
And he wrote 3,600 psalms; [5]
  and songs to sing before the altar over the whole-burnt
    perpetual offering [6] every day,
  for all the days of the year, 364;
  [7] and for the offering of the Sabbaths, 52 songs;
  and for the offering of the New [8] Moons
    and for all the Solemn Assemblies
    and for the Day of Atonement, 30 songs.
[9] And all the songs that he spoke were 446,
  and songs [10] for making music over the stricken, 4.
And the total was 4,050
[11] All these he composed through prophecy
  which was given him from before the Most High.

This document finds its place, of course, within the unique context of the Qumran community, which maintained distinctive traditions setting it apart from the mainstream of Judaism. The community sang from its own psalter, a copy of which was discovered in 1956 and from which these introductory comments are taken.

Of course, given the lack of manuscript evidence, we have no way of confirming this tradition. Did David really write four-thousand-some psalms over the course of his life? We know that Charles Wesley (1707-1788) wrote some 6,500 hymns. Isaac Watts (1674-1748) apparently wrote 750 hymns, along with setting the Psalms to paraphrased verse. Fanny Crosby (1820-1915) was even more prolific, penning over 8,000 hymns and gospel songs during her exceptionally long life. We will never know for certain whether the tradition recorded at Qumran is accurate, but I don't think we can rule it out altogether.