As for the scruple that some take at the translation of the Book of Psalms into metre, because David’s psalms were sung in his own words without metre, we answer:
First, there are many verses together in several psalms of David which run in rhythms (as those that know Hebrew and as Buxtorf shows1) which shows at least the lawfulness of singing psalms in English rhythms.
Secondly, the psalms are penned in such verses as are suitable to the poetry of the Hebrew language, and not in the common style of such other books of the Old Testament as are not poetical; now no Protestant doubts but that all the books of scripture should by God’s ordinance be extant in the mother tongue of each nation, that they may be understood of all, hence the psalms are to be translated into our English tongue; and in it our English tongue we are to sing them, then as all our English songs (according to the course of our English poetry) do run in metre, so ought David’s psalms to be translated into metre, that so we may sing the Lord’s songs, as in our English tongue so in such verses as are familiar to an English ear which are commonly metrical: and as it can be no just offense to any good conscience to sing David’s Hebrew songs in English words, so neither to sing his poetical verses in English poetical metre: men might as well stumble at singing the Hebrew psalms in our English tunes (and not in the Hebrew tunes) as at singing them in English metre, (which are our verses) and not in such verses as are generally used by David according to the poetry of the Hebrew language: but the truth is, as the Lord has hid from us the Hebrew tunes, lest we should think ourselves bound to imitate them; so also the course and frame (for the most part) of their Hebrew poetry, that we might not think ourselves bound to imitate that, but that every nation without scruple might follow as the grave sort of tunes of their own country songs, so the graver sort of verses of their own country poetry.
Neither let any think, that for the metre sake we have taken liberty or poetical license to depart from the true and proper sense of David’s words in the Hebrew verses, no; but it has been one part of our religious care and faithful endeavour, to keep close to the original text.
From the Preface to the Bay Psalm Book (1640)
 Johannes Buxtorf, Thesaurus Grammaticus Linguae Sanctae Hebraeae, p. 629.
Likewise, Josephus states that the Psalms were “of several sorts of metre; some of those which he made were trimeters, and some were pentameters.”
“3. And now David being freed from wars and dangers, and enjoying for the future a profound peace, composed songs and hymns to God [“ᾠδὰς εἰς τὸν θεὸν καὶ ὕμνους”] of several sorts of metre; some of those which he made were trimeters, and some were pentameters.” —Josephus, Antiquities of the Jews, Book 7, Chapter 12, Section 3.