One commonality of many religions is the reliance on music as a part of worship. It is so widespread I wouldn't be surprised if human music originated from spiritual needs.

I heard a radio program from the BBC today about Islam and it mentioned how important chanting is when reciting the Qur'an (Koran). Singing is essential to convey its message. It reminded me of when I attended my nephew's Bar Mitzvah last year and was struck by how much singing appeared in the ceremony (it's been a while I went through the process myself).

Basically, the Torah is only sung, never just spoken. Even if you don't know a lick of Hebrew, you can still appreciate the lilting of the "cantillation," as it's called. Wikipedia has a good audio example of Hebrew cantillation here (compliments of moi, btw):

http://en.wikipedia.org/wiki/Cantillation

Christianity has an incredibly rich musical tradition, encompassing hymns, choral music, negro spirituals, and Christian rock. The musical aspects of major religions could perhaps be better exploited to improve inter-faith relations.

What about non-believers though? There are no atheist or agnostic musical traditions that I'm aware of. Perhaps this lack of musical unity contributes to the distrust many believers have towards non-believers? Just speculation.