Ran across some interesting thoughts by Stoddard on Psalm singing in doing some research on Jonathan Edwards. He approves of uninspired hymns in worship.
The second part of worship to be performed in the church, is singing of Psalms; this is a moral duty not belonging peculiarly to the time of the Old Testament, as Christ with his disciples did practice it. So afterwards Paul and Silas, Acts 17. And we have positive commands for it, Eph. 5:16, Col. 3:16, James 5:13. In the primitive times when God gave to all extraordinary gifts of his Spirit. It was the manner sometimes for one man to sing a Psalm, and the congregation to say Amen, 1 Cor. 14:15-16. But now it is most proper for us to join together in singing of Psalms, as Christ and his disciples did, and as Moses and the children of Israel did, Exod. 15:1. As the church of Israel were wont to sing the Psalms of David, so (though we are not forbidden to sing Psalms of a private composure) it is lawful for us to sing the Psalms of David and other Scripture Psalms, the Apostle when he directs us to sing Psalms, Hymns, and Spiritual Songs, Eph. Col. 3. hath a manifest respect to the division of David’s Psalms, some things in those Psalms are not so suitable to our present case, so it is in what we read, yet those Psalms are very suitable for us to meditate upon; and contained in them much introduction and encouragement, and because they were indicted by the Spirit of God, are more proper to affect our hearts and excited the workings of Grace, then such as are of private composure.
Solomon Stoddard, The Doctrine of Instituted Churches (London, 1700), 16.