The Sons of Korah have the prophetic spirit almost always for Christ’s incarnation rather than for His Passion. David in his spirit speaks of the mysteries of the Passion more clearly. Thus any one prophet seems to have the Spirit more for one matter than for another. Hence the sons of Korah rarely speak about the Passion, but almost always speak with joy about Christ’s incarnation and His marriage with the church, so that also their psalms are joyful and full of mirth. David, on the contrary, deals more with the Passion and the Resurrection and the things the Lord did in His maturity. Asaph, in turn, talks mostly about the separation of the wicked from the fellowship of the godly, about the destruction of the ungodly and of the synagog, as is clear from his psalms. And this is perhaps what the significance of the names calls for. The sons of Korah are many, denoting the new people of faith who were born spiritually of water and the Holy Spirit (John 3:5), as Christ was born of the Virgin. This is the mystical incarnation of Christ, that He is born in them spiritually, indeed, that they are born of Him. Therefore every one of their psalms echoes this twofold birth, namely, of Christ the Head and of the church, His body. But David, “strong of hand,” shows Christ now doing miracles and bearing the cross, and therefore his psalms almost always speak about these things. Finally, Asaph means “gathering,” the people separated and gathered from those who remain and are not gathered.
Luther’s works, vol. 11: First Lectures 2