In D&D 5e, the harpy has the Luring Song action option:
Luring Song. The harpy sings a magical melody. Every humanoid and giant within 300 feet of the harpy that can hear the song must succeed on a DC 11 Wisdom saving throw or be charmed until the song ends. [...]
Would changing one (or more) specific ability scores modify the DC for the saving throw against the harpy's Luring Song? Are monster spell-like abilities (such as this one) linked and/or attached to specific ability scores in the first place?
Reason for asking: A harpy + bard (VGtM, p. 211) would require changing basic harpy stats - does this even matter for her preexisting & innate song ability? Related questions obviously include examples like a Beholder (MM, p. 28) (and their eye-rays) finding the right ability-modifying tome. And so on with creatures like Medusas (gaze), Dryads (charms) and Angels (spell-like abilities) with ability score changes.
If this is addressed in the Monster Manual somewhere (or even in StackExchange already), my apologies in advance for failing to find it.