Reformed Principle of Worship
Chapter 21.1 in the Westminster Confession:
The underlined and bolded portion of WCF Ch. 21 above is the definition that I will follow in this discussion. One may (and some do) disagree with this definition of the RPW but this is undoubtedly the way 99% of the descendant denominations of Westminster define it.
The light of nature shows that there is a God, who has lordship and sovereignty over all, is good, and does good unto all, and is therefore to be feared, loved, praised, called upon, trusted in, and served, with all the heart, and with all the soul, and with all ones might. But the acceptable way of worshiping the true God is instituted by himself, and so limited by his own revealed will, that he may not be worshiped according to the imaginations and devices of men, or the suggestions of Satan, under any visible representation, or any other way not prescribed in the Holy Scripture.
1. Rom. 1:20; Psa. 19:1-4a; 50:6; 86:8-10; 89:5-7; 95:1-6; 97:6; 104:1-35; 145:9-12; Acts 14:17; Deut. 6:4-5
2. Deut. 4:15-20; 12:32; Matt. 4:9-10; 15:9; Acts 17:23-25; Exod. 20:4-6, John 4:23-24; Col. 2:18-23
Further Reading on the RPW:
Banner of Truth
D.G. Hart and John Frame Debate Long, but well worth the time
Moving On to the Heart of the Matter
Having established that the Westminster Confession states that God has prescribed how it is that we should worship him as the New Testament church I want to begin by saying that from now on we will stay in Scripture and I will not use secondary sources and I would appreciate it if when we discuss this we all do the same because I believe this is primarily a primary text question.
Colossians 3:16 and Ephesians 5:19
The two main texts in question are Colossians 3:16 and Ephesians 5:19, both having the refrain "Psalms, hymns, and spiritual songs". Interestingly enough both camps use these verses as keystones in their argument, even more interesting is that the 1780 Presbyterian psalter uses these two verses as source texts on its title page. So why is it that both parties can use these verses to prove their point? Well to give a little background the RP's and the forefathers of nearly all American presbyterians gave greater credence to the Greek Septuagint than the Hebrew Masoretic text (this is vital to understand and there are many reasons for it but that is not the purpose of this post). Therefore when an RP takes the New Testament Greek words ψαλμοις, υμνοις, and ωδαις πνευματικαις (Psalms, Hymns, and spiritual songs) and sees their use in the Septuagint Book of Psalms one notices that all three are used to describe the Psalms themselves. For example Psalm 72:20 says "The prayers of David the Son of Jesse are ended" and in the Greek Septuagint the word translated "prayers" is υμνοις or "hymns". Also the intro to Psalm 76 (Psalm 75 in the Greek) uses ψαλμος and ωδoς interchangeably referring to Asaph's Psalm as a song. This same thing can be seen in the introductions to Psalm 65, Psalm 66, Psalm 67, Psalm 68, Psalm 75, and Psalm 76.
Therefore what Paul is saying in Col. 3:16 and Eph 5:19 can be seen as a hendiatris, or in plain English, it is nothing more than a Greek figure of speech intended on saying one thing through three words. Furthermore Nehemiah 12:27 and Nehemiah 12:46-47 are also key verses for the EPer in this defense of the hendiatris. Lets look at them now.
Verse 27: Now at the dedication of the wall of Jerusalem they sought out the Levites from all their places, to bring them to Jerusalem so that they might celebrate the dedication with gladness, with hymns of thanksgiving and with songs to the accompaniment of cymbals, harps and lyres.Compare the two and ask the question: What were the songs of praise and hymns of thanksgiving led by David and Asaph? Ergo what might Paul be referring to in Colossians 3:16 but the Psalms, hymns, and spiritual songs of David and Asaph? Again Colossians 3:16 and Ephesians 5:19 are not commanding them to sing the Psalms and Hymns and spiritual songs but is specifically telling them to sing the Psalms to each other.
Verses 46 and 47: For in the days of David and Asaph, in ancient times, there were leaders of the singers, songs of praise and hymns of thanksgiving to God. So all Israel in the days of Zerubbabel and Nehemiah gave the portions due the singers and the gatekeepers as each day required, and set apart the consecrated portion for the Levites, and the Levites set apart the consecrated portion for the sons of Aaron.
Now I want to end there to allow for some more in depth discussion in the comments.
Update: Here is a good site for some quotes on EP