How do I stop Melody's terrible music?

Solution 1:

There are 3 soundtracks in the game (named after composer/remixer):

• Danny B for Cadence
• A-Rival for Melody
• FamilyJules7x for Aria
• Other characters use Danny B

That is, these are the soundtracks by default.
You can changes these to whatever you want in the Pause menu => Options => Change soundtrack. The soundtrack option is selectable on character by character bases and the latest patch even introduced a new option, Random.

To get what you want, navigate to Change soundtrack and change Melody's soundtrack to either Danny B or FamilyJules7x.

Also, there are Steam Workshop mod that can change the soundtrack even futher. For example, here's one that replaces Danny B's sountrack with a remix that combines all three: http://steamcommunity.com/sharedfiles/filedetails/?id=431443857