Singing/music as a programming language (like Bell did)Edit
Singing appears to be a later addition to Ah! My Goddess, since in the first early chapters when Belldandy programmed a code from Yggdrasil it sounded very rough and coarse to Keiichi (In the Spirit Photography episode). Singing is revealed to be a programming language in volume 21, when Belldandy had to sing an antithesis for Peorth.
Goddesses and demons have access to the most powerful of spells, which must be sung. Song spells tend to be quite lengthy, and must be performed precisely without error. What is heard as a song are actually compressed spell commands, and cannot be even one hertz off.
Hild demonstrates that song spells don't only belong to goddesses when she creates the mandala for turning Peorth back into an adult. Hild displays extraordinary power; while it would take Belldandy a long amount of time to recite the same spell, Hild did it in a matter of seconds. And that's /with/ her limiters in place.
Urd's and Mara's weaknesses for certain kinds of musicEdit
Urd and Marller have weaknesses to specific kinds of music. It's assumed that those with demon blood have musical weaknesses. Urd falls asleep when she hears Enka (think of it as the Japanese equivalent to country music, although DH translated it as Austrian Polkas) and Marller dances uncontrollably when she hears rock music (disco in the DH release). It's interesting how their weaknesses contrast with each other (soft versus hard).
Other things (the Midgard flute, ...)Edit
The Midgard flute is a music instrument that summons Midgard. Midgard it the vaccine to the Ultimate Destruction Program.
Troubador, Urd's old lover, is also a musician who seeked out the Golden Nightingale and the ultimate song.It may be a far-fetched thing, but it's possible that the importance of music in Ah! My Goddess stems from Christianity. Christianity is often called the "religion of songs" because of the fact that Christian music is so plentiful, as Christians believe themselves to have much to celebrate. Also, music may be very important psychological and spiritually; the fallen angel, Lucifer, knows this importance. He was once the choir director in Heaven.