The superscript of Psalm 9 contains the phrase:
BHS: עַלְמ֥וּת לַבֵּ֗ן
RSV/ESV: according to Muth-labben.
NIV: To the tune of “The Death of the Son.”
Most translations have chosen something similar to one or the other of these. The first seems to have pulled a preposition off the beginning to get “according to” and then transliterated the rest, which I presume indicates that the translators didn’t think the meaning could be ascertained with certainty. The second seems at least loosely like a reasonable translation, again pulling apart the first word. The LXX weirdly has ὑπὲρ τῶν κρυφίων τοῦ υἱοῦ ("over the secrets of the son"?).
Despite the fact that these English translations (and I guess that Greek) seem to understand על as a separate word, there is a entry in HALOT עַלְמוּת (“uncertain”, with a comment about the LXX that I don’t follow).
Is there a reason to think that there was a tune called “The Death of the Son” that would help this make sense? Or is there any other speculation about what “Muth-labben” (or “Almuth-labben”) refers to?