I'm probably missing something fundamental here.
When YOU call someone, the "ringing" sound you here is not the physical sound of their phone ringing -- it is a tone generated by the phone network. If you ring someone abroad, the foreign phone network may generate a different tone.
When YOUR phone rings with an incoming call, the sound is generated BY YOUR PHONE. How could it change for a different incoming number?
(Yeah, yeah, I'm old enough to remember when the ringer on the phone was a physical bell and I realise that's not the case anymore. And yes I know fancy phones can have different tones based on incoming caller id, but this doesn't sound like what the OP was asking. By and large the sound the recipient hears is their phone's analogue of the old bell ringer ... not something generated by the phone network and therefore not dependent on where the caller is calling from).