In 2013, Dustin Cable of the University of Virginia released a map showing the racial makeup of different neighborhoods. In fact, in this map, one dot represents one person, and their dot is colored according to their race.
This data is based on the 2010 census, which, as a few redditors pointed out, may be a little out-of-date for Nashville:
Just how much of a change there will be in the 2020 census remains to be seen. While some urban neighborhoods may be gentrifying, a large part of the Nashville area may remain mostly unchanged.
Want to look at it in more detail? Check out the map for yourself.