Let's get this out of the way real quick: these are not the #1 artists in these states, and those colors refer to population densities. These are the most distinctive popular artists in their state (bands that certain states like and other states can't stand), according to Paul Lamere of MusicMachinery.com. If it were the most popular artists, this would be one map which would read "Either Beyonce, Drake, Toby Keith or Lorde depending on what Clear Channel wants today."
There have been a lot of great US maps recently, including the best movies set in each state, what each state's reputation is on Google, and finally a straight-up, best-to-worst ranking. That being said, people get worked up over favorite movies and clichés, but fights about music can lead to friendships ending in the blink of an eye. I hope this map doesn't lead to civil war.
So, "distinctiveness" is measured by looking at the top 100 artists in each state, and then seeing which of those lands furthest down the charts in other regions. Additionally, states could not have the same distinctive artist—artists were assigned to states in order of population. So, "Bonobo" may be distinctive in other weird liberal states, but California got it first, so Vermont will have to settle for Phish (as they have for 20-odd years).