Middos 2:3 relates that there were twelve steps in the Cheil:
וּשְׁתֵּים עֶשְׂרֵה מַעֲלוֹת הָיוּ שָׁם
There were twelve steps there.
Later, in Mishnah 5, the Mishnah relates that there are fifteen steps connecting the Ezras Nashim to the Ezras Yisrael, but it also adds the significance of this number:
וַחֲמֵשׁ עֶשְׂרֵה מַעֲלוֹת עוֹלוֹת מִתּוֹכָהּ לְעֶזְרַת יִשְׂרָאֵל, כְּנֶגֶד חֲמֵשׁ עֶשְׂרֵה מַעֲלוֹת שֶׁבַּתְּהִלִּים
There were fifteen steps going up from in [the Ezras Nashim] to the Ezras Yisrael, corresponding to the fifteen ascensions in Tehillim [120-134].
Why does the Mishnah relate special significance to these fifteen steps, but not the earlier twelve steps?