What is the ruling on calling one's father when his phone is playing music while he is in the Grand Mosque, if the father requested that?

If you need to call someone whose phone ringtone is music, there is no harm or sin upon you for doing so. The sin falls upon him. He is at risk of increasing his sin if this occurs in the mosque, especially the Grand Mosque (Masjid al-Haram). You should continue to advise him, while observing proper etiquette with your father.