I just ran across your post of over a year ago. I don't speak Danish, but I will give it my best. Frederich's parents are listed as Frederich Gottlieb Frey and Inger (no last name given). I looked at Frederich's confirmation in 1833 in Skt Mariæ, opslag 35 nr 7, and it confused me. Frederich's father is listed as Johan Frederich Frey and the mother is only listed as Inger.
I will try to get a Danish friend to take a look at the birth record and see if there is any further information.