The thing is, I have nothing against stream of consciousness. In fact, I liked James Joyce's Ulysses. Similar to Ulysses, this book also has plenty of material. Both books are tough books to read. Contrary to Ulysses however, Celestial Harmonies covers material from several hundred years, while all the events Ulysses covered happened in one day.
Hence, this results in a bipolar book. On the one hand, it uses artistic devices indicating that this is a literary work of art, but on the other hand, there are just plenty of events covered that it makes it very hard for the reader not to treat it as an historical novel. This divide is particularly evident in the division the author imposed on the text: Book 1 is more a collection of numbered sentences describing events several hundred years ago; while Book 2 covers more the Soviet period as seen by the House of Esterházy.
So overall, I came out of Celestial Harmonies disappointed, and with a headache, wishing that I never picked this book up in the first place. The literary devices were overused, and the form of narration was incompatible with the material. Instead of appearing as a spectacular piece of literature, it feels more like a transcript of a monologue by a senile individual, someone suffering from Alzheimer's disease, recalling events in his past, in random order. He recalls and retells whatever event he remembers, in no particular order, in no particular causal relation, with no attention whatsoever to whether his stories were coherent or not.
I give this 2 out of 5 stars.