that's not actually what classes are. class is not just a braket of incomes, it is a role in economic production. if you get your money by trading your work for it, you're working class. if you get your money by virtue of what you own, you're capitalist. a bit of both is what middle class is.
This is my preferred understanding of class as well, but I've noticed that my conversations are more enjoyable if I don't try to insist others use the term the 'right' way.
