In 1 Corinthians 14:13-17 (NIV), Paul is initially addressing the gift of tongues, but in V15 he suddenly introduces the concepts of "praying with one's spirit" and, in particular, "singing with one's spirit":
13 For this reason the one who speaks in a tongue should pray that they may interpret what they say. 14 For if I pray in a tongue, my spirit prays, but my mind is unfruitful. 15 So what shall I do? I will pray with my spirit, but I will also pray with my understanding; I will sing with my spirit, but I will also sing with my understanding. 16 Otherwise when you are praising God in the Spirit, how can someone else, who is now put in the position of an inquirer, say “Amen” to your thanksgiving, since they do not know what you are saying? 17 You are giving thanks well enough, but no one else is edified.
What does it mean to "sing with one's spirit"? Is it the same gift of tongues but retargeted to melodic ends? Is it a different spiritual gift? Is it something else?