I could elaborate on my question but all I can say is that it's for a research paper.
The use of archetypes in musical lyrics may be one way to connect mythology and music.
Artists like Bjork and U2 tend to write songs with a literary bent that is sometimes seen in references they make to mythology and sometimes in specific perspectives and premises presented in their songs.
You might also want to think how the archetypes created in such mythological classics as Ovid's Metamorphoses, The Illiad, The Odyssey and The Aeneid are carried on through the ages and find expression in music. Consider, for example the journey home that Aeneas and Odysseus embark on and how this might be reflected in popular music through the ages.
There are many popular songs that refer to mythology. You can search for the lyrics of these songs. They often retell the mythological story or use the myth as a way to talk about another subject. I once wrote a paper on mythology represented in various art forms, so I know there is a lot of research out there. Here is a list of some of the popular music that refers to mythology:
Flight of Icarus by Iron Maiden
Achilles Last Stand by Led Zeppelin
Eurydice by Noe Venable
Isis by Bob Dylan
Sisyphus by Pink Floyd
Without knowing the specifics of your assignment, I am not sure how to answer.
I can suggest (as a starting point), you read the works of Joseph Campbell. He wrote extensively on the role of myth in society and uses various cultures as support.
You may also want to consider how epic poems such as The Iliad, The Odyssey and Beowulf began and how they were passed on by the people of their respective cultures.
What I can say is that the subjects of many early written and oral works were the myths of a group of people.
Try this link:
How about the prevalence of themes of classical mythology in Renaissance secular vocal music? Italian and English composers of Madrigals (a cappella, often polyphonic, secular vocal music involving lots of fa-la-las) often made reference to various nymphs and mythological characters from Greek and Roman Mythology (Bacchus and Amaryllis were particularly popular).