The Hebrew expression Shir ham·ma·ʽalohthʹ, forming the superscription for 15 psalms (Ps 120-134), is variously translated as “A Song of degrees” (KJ), “A gradual canticle” (Dy, Ps 119-133), “A Song of the Stairsteps” (NW ftn on Ps 120:Sup), “A Song of [or, “for the”] Ascents” (AT, RS).
... At one time Jewish tradition (Mishnah, Middot 2:5) held that these 15 songs were sung by the Levites in ascending the 15 steps from the Court of Women to the Court of Israel at the temple in Jerusalem, but this view is generally discounted today.