While I agree with most of this statement, the third category is not entirely true. I think accuracy is vital here. "Spiritual songs" (with this adjective) is not found in the LXX to my knowledge. Yes, "songs" ("odes") is found in the LXX in addition to many other places in the LXX that are not the 150 Psalms, as are also "psalm" and "hymn," though these are less numerous. "Spiritual" is not found in connection with "song" in the LXX which could suggest that Paul was distinguishing between just any song (i.e. non-religious) and ones appropriate for worship. If the term could only apply to the 150, "spiritual" would be redundant. I doubt this is a game changer in anyone's opinion, but it's a technicality worth noting so we can all be more accurate in the connections we are making.