string music: the sound of a plucked instrument and the song set to it, whether played in worship or aimed at someone in mockery
This noun belongs to the verb for plucking the strings of a lyre or harp (נָגַן), and it names the result of that plucking: the music the strings make, and the song performed to them. It is a small word, used only fourteen times, and it turns up in three fairly different settings.
- In worship it is the music of God's people: Hezekiah, promised recovery, says that he and his household will play his music at the house of the LORD all their days.
- In seven psalm titles it is a performance direction, usually put into English as "with stringed instruments", telling the music leader how the song was to be accompanied.
- In the mouths of enemies it is the song they compose about a sufferer: Job says he has become their song, and the poet of Lamentations says he is their song all day long.
The mocking use is not a second word. A song is still a song; what changes is who sings it and about whom. To become someone's song is to be the subject of a tune everyone in town knows, and that is humiliating rather than flattering. The lines around it say the same thing other ways: the same person is called a laughingstock, a byword, and the entertainment of drunks.
What the psalm titles actually asked for is less clear. The word plainly has to do with playing strings, but whether the direction named the instruments, named the tune, or described a whole manner of performance cannot be settled from the handful of lines that carry it. Older English Bibles simply left it as a foreign word ("upon Neginah"); modern ones expand it into a phrase.