Why can't a class instance variable be accessed in a singleton-class definition in Ruby?

class MyClass
  @my_class_instance_variable = "here"

  p @my_class_instance_variable # => "here"

  class << self
    p @my_class_instance_variable # => nil
  end
end

class MyClass
  p @my_class_instance_variable # => "here"
end

Why does the second p print nil, when the third p prints "here"? My understanding of a singleton class definition (class << self) is that it has the same scope as a class definition (class MyClass).

(This question has a similar title, but it has a different focus.)

My understanding of a singleton class definition (class << self) is that it has the same scope as a class definition

Nope. The scope is different. You defined @my_class_instance_variable in the scope of MyClass, but are trying to access it in the scope if MyClass's singleton class.

It is as easy to check as:

class Foo
  puts self #=> Foo

  class << self
    puts self #=> #<Class:Foo>
  end
end

With the output of:

Foo
#<Class:Foo>