Thirtle identified in the stand-alone psalm of Habakkuk a pattern for interpreting the structure of psalms elsewhere. The prayer of Hezekiah in Isaiah 38 is remarkably similar, leading Brevard Childs to comment:
The most striking feature of Isa. xxxviii. 9 is the similarity of form between the superscription and those of the Psalms. The similarity reaches to the technical Psalm classification, the designation of the author, and the specification in the infinitival form of a setting which referred to a historical event known elsewhere in the Old Testament.
This similarity further validates Thirtle’s thesis.
תְּפִלָּה לַחֲבַקּוּק הַנָּבִיא עַל שִׁגְיֹנֹֽות׃
A prayer of Habakkuk the prophet upon Shigionoth.
To the chief singer on my stringed instruments.
מִכְתָּב לְחִזְקִיָּהוּ מֶֽלֶךְ־יְהוּדָה בַּחֲלֹתֹו וַיְחִי מֵחָלְיֹֽו׃
The writing of Hezekiah king of Judah, when he had been sick, and was recovered of his sickness
יְהוָה לְהֹושִׁיעֵנִי וּנְגִנֹותַי נְנַגֵּן כָּל־יְמֵי חַיֵּינוּ עַל־בֵּית יְהוָֽה׃
The LORD was ready to save me: therefore we will sing my songs to the stringed instruments all the days of our life in the house of the LORD.
If Thirtle is correct then the merging of the postscripts with the superscripts of the following psalm must have happened early, before the translation of the psalms into Greek and before the production of the manuscripts from which the Qumran Psalms scrolls were copied, as both the earliest accessible Septuagint manuscripts and the Qumran scrolls include the postscripts and the superscripts on the same line without any distinguishing separation marks. However, the Isaiah and Habakkuk texts indicate that the arrangement of psalms into superscript, psalm and postscript was still understood in the late monarchic period.
There is some evidence in the Greek translation of the Psalms that the translators had difficulty in determining where one psalm ended and the next began. For example, the LXX adds the word αλληλουια alleluia (functionally equivalent to הללו יה hallelujah) to the beginning of nine psalms: 105, 107, 114-119 and 135. In all but Psalms 115 and 118 the hallelujah belongs in the MT to the preceding psalm. In the MT הללו יה hallelujah occurs at the end of Psalms 104, 105, and 115 but appears at the beginning of the subsequent psalms in the LXX. Psalms 9 and 10 in the MT have been combined in the LXX and numbered as 9. Psalms 114 and 115 in the MT have been combined in the LXX and numbered as 113. Psalm 116 has been divided in the LXX and numbered as 114 and 115. Psalm 147 in the MT has been divided in the LXX into 146 and 147. Wilson argues that this was deliberate and that “the LXX rectified the ‘nakedness’ of Psalm 114 in the MT and Targum by shifting the הללו יה postscript of Psalm 113 to the beginning of Psalm 114, by combining Psalms 114 and 115, and by shifting the postscripts of Psalms 115, 116, 117 to the beginnings of Psalms 116, 117, and 118”. It could equally be the case that there was uncertainty as to where some psalms ended and others began, and that the translators did not know whether הללו יה concluded or introduced a psalm (or both, in the case of Ps 113 in the MT).  There may have been some confusion about where one psalm ended and the next began, although it is also possible that the translators had access to a variant Hebrew Vorlage which reflected a different tradition of the arrangement of these Psalm headings.
Psalm 48 concludes with the strange phrase הוא ינהגנו על־מות he will lead us unto death and Kidner notes that if the final words על־מות are joined, as in some Hebrew manuscripts, they can be vocalised as עֹלָמוֹת evermore, which he regards as an intact postscript. The LXX apparently followed this reading with its εἰς τοὺς αἰῶνας to the ages (commonly translated as for ever). Herbert May argues that the על מות at the end of Psalm 48 may be an allusion to a melody, and “really belongs to the superscription of Ps. 49:1, as most commentators agree”. However, there is also the possibility that these words have been corrupted and should be read as על־עלמות as in Psalm 46:1 (which Thirtle understands to be a postscript to Psalm 45). Oesterley notes a similarity to Psalm 9:1 and the possibility of a corruption and suggests that עלמות לבן should read על־עלמות as in Psalm 46. If he is correct than the expression על־עלמות occurs three times in the Psalms: as a postscript to Psalm 48 and a superscript to Psalms 9 and 46. Perhaps all three should be read as postscripts, following Thirtle’s thesis, and the MT of Psalm 48 provides evidence of an original postscript. If so, it would be an example of an intact postscript retained in Psalms.
Commenting on Thirtle’s suggestion that the musical directions were originally attached as postscripts to the preceding psalms, Jeremy Montagu raises the issue that “there is no certainty that the psalm which precedes any title now has always done so – the order of the Psalter has almost certainly changed over time”. This valid point highlights the view that Thirtle appears to have given little if any consideration to the likely development of the Psalter over a long period of time. While the connection between the titles of certain psalms with material in the preceding psalm is persuasive, in other cases Thirtle’s attempts to find a connection seem somewhat strained. So, in the case of Psalm 9 the title עלמות לבן is interpreted as עַל מוּת לַבֵין concerning the death of the champion and certain phraseology in the preceding psalm is interpreted in the light of this rendering to refer to the death of Goliath. He appeals to the similarity with אִישׁ־הַבֵּנַיִם in 1 Samuel 17:4, 23 and the Targum of Psalm 9 which has על מיתותא דגברא רי נפק מביני משריתא “concerning the death of the man/warrior who went out between the armies”. However, the connections between Psalm 8 and the death of Goliath are strained and unconvincing. It is possible, if the title of Psalm 9 did indeed refer to the death of the champion Goliath, that it was attached as a postscript to another psalm which has been displaced, as Montagu’s caution might suggest.
Psalm 22 (21 in LXX) has the Hebrew title על־אילת השחר on (or concerning) the doe (or hind) of the dawn but in the LXX is ὑπὲρ τῆς ἀντιλήμψεως τῆς ἑωθινῆς Over the support at dawn. Thirtle suggests this may have been an attempt by the translators to relate the title to the words of verse 20 (19).  “But you, O Lord, do not put my help far away! Attend to my support!” The Hebrew is enigmatic and this has led to several possible explanations. Thirtle regards this as a postscript to Psalm 21 which he considers to be a kind of “national anthem” for Davidic Israel. Other scholars agree that Psalm 21 belongs in the class of “Royal Psalms” with echoes of Judah’s most ancient royal traditions. Thirtle therefore reads “hind of the dawn” as a kind of term of endearment for the king, a description of him in royal beauty. This, however, is hardly more convincing than any other explanation of this difficult phrase. Again this could very well be another case of a postscript which was originally attached to another psalm which once stood immediately before Psalm 22 but was displaced in the process of compiling and editing the various collections which eventually became the Psalter.
To be continued …
 Brevard S Childs, “Psalm Titles and Midrashic Exegesis,” Journal of Semitic Studies 16, no. 2 (1971): 142.
 It should be noted that the earliest extant complete manuscripts of Greek translations of the Psalms are the uncial codexes, Vaticanus (c. 325-350 CE) and Sinaiticus (c. 330-360 CE). Uncial manuscripts were written in scriptio continua with very few divisions between words. Although scrolls and fragments in Greek of Exodus, Leviticus, Numbers, Deuteronomony and the Twelve Prophets have been found at Qumran, no Greek portions of Psalms have been discovered.
 Wilson, The Editing of the Hebrew Psalter, 180.
 Nahum M. Sarna, “Psalms, Book of,” in Encyclopaedia Judaica (ed. Skolnik: Macmillan Reference, 2003), 665.
 Peter Flint has provided considerable evidence which suggests that, “while the Vorlage of the Septuagint Psalter is not evident in any single Psalms manuscript, several shared variants and passages show that the translator’s Hebrew text contained many readings found in specific scrolls but not in the Masoretic Text.” See Peter W. Flint, The Psalters at Qumran and the Book of Psalms (Ann Arbor: UMI Dissertations Publishing., 1993), 199-207.
 Kidner, Psalms 1-72, 181 n.1.
 Herbert Gordon May, “‘AL….’ in the Superscriptions of the Psalms,” The American Journal of Semitic Languages and Literatures 58, no. 1 (1941): 77.
 W.O.E. Oesterley, The Psalms: Translated with Text-Critical and Exegetical Notes (London: S.P.C.K., 1962), 13.
 Jeremy Montagu, Musical instruments of the Bible (Lanham, Md: Scarecrow Press, 2002), 73.
 Edward M. Cook, The Psalms Targum: An English Translation (2001 [cited 12 July 2014); available from http://targum.info/pss/ps1.htm.
 Thirtle, The Titles of the Psalms, 17.
 Ibid., 86.
 For example, David M. Carr, The Formation of the Hebrew Bible: a New Reconstruction (New York: Oxford University Press, 2011), 389.