Does the Bible teach that we have only one book of inspired praise and that is the book of Psalms and therefore nothing of mere human composition is ever to be sung? I do not believe that it does. I don't believe that the Scriptures nor Church History agrees with the exclusive Psalmist position.
Here are a over a dozen reasons for believing so.
It is the premise of exclusive psalmists that these terms refer to the divisions of the Psalter in the Greek Septuagint version of the Old Testament.