Scripture repeatedly speaks of singing a “new song” (Psa. 33:3; 40:3; 96:1; 98:1; 144:9; 149:1; Isa. 42:10). The four beasts and 24 elders sang a “new song” (Rev. 5:9), the 144,000 followers of the Lamb who had gotten victory over the beast also sang a “new song” (Rev. 14:3). Therefore, we may (or should) compose new songs for public worship.
This article will demonstrate that the above referenced Scriptures make for a poor argument for composing uninspired songs for public worship. As such, proving Exclusive Psalmody over and against the Inspired Scripture Songs position is out of the scope of this article. We will briefly touch on the gift of composing worship songs, the content and meaning of “new song” and how it applies in the New Covenant.
The gift of composing worship songs.
First, many misread this phrase, and gloss the term “song” to “songs” and assume that the term sing means to compose. Pastor Daniel Kok gives a correction:
“In every reference the command or the description is that of a new song (singular), not new songs (plural). This would appear to be significant in that new songs would refer to an ongoing collection of songs to be written, whereas new song would refer to a particular song with its own particular elements and requirements.
“This is supported by the command that accompanies these descriptions. The new song is to be sung, not composed. The new song must then be provided by God Himself: that is, an inspired source other than the singer or singers who are called to praise God.” 
Hence, as Michael Bushell writes, commands to sing a new song “do not constitute a warrant for us to produce uninspired worship song any more than they did for the Old Testament saints.”  Matthew Poole comments on Psalm 33:3 that if by new song were meant newly written songs it would require the spiritual “gift of composing songs” which all of the righteous do not have and that it was not necessary to compose new songs when “there were so many made by David, and other holy prophets, for the use of God’s church and people.” For Poole, new song does not mean new in content. In the same way, John Cotton recognized the necessity of worship songs being inspired by the Holy Spirit:
“David’s exhortation to sing a new song, pertained to them in the Old Testament as well as to us in the New. And yet they upon new occasions sang the old songs of David, and that with acceptance (2 Chron. 5:13; 20:21; Ezra 3:11).
“Asaph, Heman, and Ethan, were men indued with an infallible measure of a Spirit of prophecy, in inditing [composing] those Psalms, which the Church of Israel received from them. Give us the like men with the like gifts, and we shall receive their Psalms, as the Church of Israel did the other.” 
Westminster Divine John Lightfoot appeals to the sufficiency of the Psalter and points out that God could have appointed more worship songs to be written for the use of the Church if there needed to be, but even our Lord was content with them:
“Here [Mat. 26:30] the Lord of David sings the Psalms of David…He that gave the Spirit to David to compose, sings what he composed. That all-blessed copy of peace and order, could have indited himself, could have inspired every disciple to have been a David, but submits to order, which God had appointed, sings the Psalms of David, and tenders the peace of the Church, and takes the same course the whole Church did… If you sing right, sing David’s Psalms, but make them your own. Let the skill of composure be his, the life of devotion yours.” 
In truth, there is no example or command to bring our own human composed songs before God as worship like there is for using our own words in preached sermons (Neh. 8:8; Mat. 28:19-20; Luke 24:47; 2 Tim. 4:2) and in prayers (Mat. 6:9; Phil. 4:6; 1 Tim 2:1-2; 1 John 5:14). The pattern of Scripture is that worship songs were always composed by the inspiration of the Holy Spirit, either for temporary and special occasions, or for perpetual use in public and private worship.
What song is being referred to?
Calvin comments on Psalm 149:1, that the human penman “calls this a new song.” Accordingly, throughout the Psalms, the phrase “new song” is placed at the beginning as an introduction, indicating that the Psalm itself is the content of the “new song.” Psalm 144:9 being the only exception, where the phrase is toward the middle, Pastor Kok writes:
“David says “I will sing a new song.” Of course this does not necessarily rule out others from joining in, but the context indicates that the previous statement is a personal one: “It is he that giveth salvation unto kings: who delivereth David his servant from the hurtful sword” (v. 10). In any case there is no command here to compose a new song. David, by the inspiration of the Spirit, is the composer; we are the choir.
“We see this clearly in Psalm 40:3 which reads “he hath put a new song in my mouth.” In this verse David, who was the “sweet psalmist of Israel” (2 Sam. 23:1), acknowledges that the new song has been given to him by God. This could not more clearly refer to the inspiration of the Holy Spirit.” 
“New” in quality, not in content.
Psalm 96 is called a “new song,” but its content was not novel at the time of its composition. It is an inspired rendition of the psalm written by David and Asaph recorded in 1 Chronicles 16:8-36, yet adapted to a more general and perpetual use than the immediate context from which it was originally written. Thus, the footnote in Calvin’s commentary on this verse concludes:
“Consequently, strictly speaking, this is not a “new” song. But it may be called “new,” from its having been adapted to a new purpose—from its having been intended to celebrate new mercies conferred upon the Jews, and to lead the mind forward to the glorious era of the coming of the Messiah, and the establishment of his kingdom, which probably was the matter of more general expectation among the chosen people, at the period when the temple was rebuilt, than when the ark was brought to Mount Zion from the house of Obed-edom. It may be observed, that the first verse is not in the original poem, as recorded in the book of Chronicles, but appears to have been added for the new occasion to which this shorter psalm was adapted.”
Scripture often refers to a “new song” in the same sense that it refers to a “new commandment” (John 13:34), a “new covenant” (2 Cor. 3:6-7; Heb. 8:8), a “new creation” (2 Cor. 5:17), a “new man” (Eph. 2:15), and a “new heavens and earth” (2 Peter 3:13). That is, these things are not entirely novel creations, rather, they are fresh or new in quality, virtue, efficacy, or purpose. John Cotton explained:
“There is no estate and condition that ever befell the church and people of God, or can befall them, but the Holy Ghost, as he did foresee the same, so he hath provided and recorded some Scripture-Psalm suitable thereunto. And these Psalms being chosen out suitably to the new occasions and new conditions of God’s people, and sung by them with new hearts and renewed affections, will ever be found new songs. Words of eternal truth and grace, are ever old (as the gospel is an eternal gospel) and ever new; as the commandment of love is a new commandment as well as old [Lev. 19:18; John 13:34; 2 John 1:5]. And to the new creature all things are become new (2 Cor. 5:17-18). Daily mercies are to him new mercies (Lam. 3:23). Duties of humiliation, which have been of ancient practice in the Church, are to him as new wine [Psa. 4:7]. But to an old and carnal heart that lieth under the state of vanity and corruption of nature there is nothing new, no new thing under the sun (Ecc. 1:9).” 
When we sing a new song we sing the same content with a renewed significance. Basil of Caesarea understood this in the 4th century, when he wrote:
“’Sing to the Lord a new song.’ That is, serve God not in the oldness of the letter but in the newness of the spirit. He who receives the law bodily but understands it spiritually is the one who sings the new song. That which becomes old of the covenant departs, but the new and renewing song of the Lord’s teaching has been delivered to us. 
Matthew Poole comments on Revelation 14:3 regarding the intended sense of “new song” used in Scripture, “And quite through the Scriptures generally, a new song signifies a song which praiseth God for some new benefits received from him.” Poole also comments on Psalm 33:3, “So this song is here called new, not so much from the matter, as from the singing of it; because sung afresh, or again.“
All things considered, the Psalms ought to be sung in a new way in light of new mercies (Lam. 3:22-23). “Sing a new song” is never an exhortation to compose a new song, rather it is an exhortation to sing the very Psalm in which the phrase occurs in view of redemptive history and our personal and corporate experiences of God’s blessings and trials. In the New Covenant, the whole Psalter has been made new to the Church, now that it is sung in light of the accomplished and more fully anticipated work of Christ (Luke 24:44-45). Douglas Comin writes:
“How must the words of Psalm 2, or 22, or 45, or 110, or 118 have sounded like new songs to those who had been accustomed to singing them in the shadows of unrevealed realities! The effect of the light of the Gospel upon the remnant of Israel redeemed by His grace was to cause them to sing “as it were, a new song” unto the Lord – not “new” in substance or content, but “new” in richness of meaning and fullness of glory to the God and Savior of men! Seen in this light, the song of the redeemed, which was “as it were, a new song,” and which could only be learned by them [Rev. 14:3], shows us the wonderful way in which the Psalms come alive with meaning in the full light of Christ’s redemption to those whose eyes are opened to see their testimony concerning Jesus.” 
The New Covenant Psalter.
“And he that sat upon the throne said, Behold, I make all things new.” (Rev. 21:5). “And he hath put a new song in my mouth, even praise unto our God.” (Ps. 40:3). “Behold, the former things are come to pass, and new things do I declare: before they spring forth I tell you of them. Sing unto the Lord a new song, and his praise from the end of the earth, ye that go down to the sea, and all that is therein; the isles, and the inhabitants thereof.” (Isa. 42:9-10).
“In Isaiah 42:10, the prophet borrows the idea of a new song from the Psalms and applies it to a new people “from the ends of the earth,” namely, to the Gentiles (cf. v. 6 where Israel will be a light to the Gentiles). This could either mean that, with the inclusion of the Gentiles, new songs would have to be written to celebrate the creation of a “new man” (Ephesians 2:15), or the ‘old‘ songs would take on new meaning by being sung by the Gentile converts. It would seem the latter is the case since in Psalm 96 the Psalmist speaks of singing to the Lord a new song in verse 1 and then calls upon the nations (v. 7ff) to join him in his praise of God.
“In fact, the singing of Psalms (as a canonical book) is more suitable to the new covenant church than it ever was to the old. The Psalms proleptically anticipate the day when Japheth will dwell in the tents of Shem [Gen. 9:27].  So the language of Israel’s faith as applied to the Gentiles becomes a ‘new song‘ i.e. new in meaning without being newly written. In fact it is impossible that a ‘new song’ could only refer to a new situation (i.e. the necessity of songs to be written as the Gentiles were enfolded into Israel) since Israel was commanded to sing a new song before the inclusion of the Gentiles.
. . .
In Revelation (5:9 & 14:3) a “new song” is sung in the heavenly realm where the saints are ‘contributing‘ to the prophetic whole of the book. It is not a new song in terms of being written by someone for a particular occasion (as with an uninspired hymn). Rightly then, G.I. Williamson has noted: “To learn a new song taught by the Lord, is very different from writing a new song of our own” (The Singing of Psalms in the Worship of God). Furthermore the song in Revelation 14:3 cannot even be learned except by the redeemed of God. That the church is a mixed multitude here below reinforces that this song cannot be an example of new compositions in the militant church for we are not all redeemed in the here and now. 
 Daniel Kok, Psalmody and a “New Song”.
 Michael Bushell, Songs of Zion: The Biblical Basis For Exclusive Psalmody 4th edition, pp. 236-238.
 John Cotton, Singing of Psalms a Gospel Ordinance (1647), pp. 25-27.
 John Lightfoot, Works, vol. vii, 1 Cor. 14:26: “Everyone hath a psalm,” pp. 40 & 43. Cf. Pastor Matthew Winzer’s critical examination of Nick Needham’s misrepresentation of this quotation in Westminster and Worship Examined: A Review of Nick Needham’s essay on the Westminster Confession of Faith’s teaching concerning the regulative principle, the singing of psalms, and the use of musical instruments in the public worship of God, Confessional Presbyterian Journal 4 (2008), pp. 263-264.
 Kok, ibid.
 Cotton, ibid.
 Basil of Caesarea (330-379), Homily on Psalm 33; Patrologia Graeca 29:325C-328B.
 Douglas Comin, Worship from Genesis to Revelation, p. 603.
 Kok, ibid.