I think we feel the connection to the divine in the moment when we have something inside us, without form and then we happen to create it or see its form in the outside world.
So for example a good art is the one where the artist tries hard to give form to his formless thoughts, beliefs and instincts..and then the audience experience some connection between their insides and the art piece in the real word. which they are unable to create themselves.
sometimes wht may happen is that just the way the outside world is shaped by artists inspired by inner ideas, instincts etc, even the outside world changes the inner ideas. generally happens a lot of people who don't try to give shape to their own instincts and so by exposure to various arts ( which are in turn manifestations of others instincts) leads to them believing that their own instincts are shaped like the art they see...this is the "connection " that people feel with some or the other art forms.
probably why we like to listen to the same song again and again..because with time there is this resonance between the outside art form and the inside instincts, ideas feelings emotions or whatever we want to call them...because now the insides are shaped based on the art form and the art form was initially based on the insides..so once they both are in tune we feel the euphoria or divine connection.