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.
Best Answer
You can make your monsters however you like
Originally, I was very into making consistent monsters where the hit points align with the size category and con modifier. Similarly, the calculation of save DCs. This is nice for published material. I do not do it anymore for my own games since it takes time but does not add any value. My players never get to see the nice alignment of numbers.
In the end the question is what you want to achieve. If you want to build the harpy bard like a player character, it seems reasonable to assume that the luring song is a race feature. In this case you could adopt a calculation like for a dragon born breath weapon, i.e. 8 + proficiency + ability, except you would use charisma instead of constitution. If you just want to be consistent with the MM, the same calculation method is also good.
The MM save DCs are consistent with spell save DCs
In my consistent monster days I disassembled all the DCs in the MM, and found that the vast majority is consistent with 8 + proficiency + ability.
The ability changes depending on the feature. Pushing, pulling and knocking prone uses str, charm and fright use charisma. Some abilities of spellcasters use their spellcasting ability. Almost everything else uses con, including breath weapons and poisons.
It is not explicitly stated in the MM and I cannot prove it, but it mostly works out.
There are some exceptions. The solar and the gas spore have DCs which seem to be set differently. Some, e.g. the dragon turtle and demilich seem miscalculated. But these are few and far between.