20 times is not a lot to try taming, really. If the RNG doesn't like you, it can take a lot more than that, especially since your skill isn't max. Music also has a range of only 2 or 3 squares, so if the monster isn't close to you, it won't work. Monsters from vaults or tension rooms (or the SMC) tend to be harder to tame in my experience.
Honestly, though, rats probably aren't worth your time to tame anyway. Find yourself bear or a greater claw bug (bug infested temple area) and you'll probably have better luck with getting somewhere with pets.
Hoping to win with every class, doomed. Archer, Barbarian, Bard, Beastfighter, Druid, Elementalist, Farmer, Fighter, Monk, and ULE Priest down.