Q: How do you tell if a given class is an ordinary class or a singleton class?

A: Test whether the class is the first element in its own ancestor list.

class NotASingleton
  self == ancestors.first       # => true
end

class << Object.new
   self == ancestors.first       # => false
end

As you can see, ordinary classes have themselves as first ancestor. Singleton classes do not have themselves as an ancestor.