I read this book about 10 years ago (when I was still a kid) in a library which had mostly older books, so I would assume it is from the early 2000s or earlier.
The plot at first revolved around two species seemingly completely unrelated to each other. There was one race which was covered with fur and would make clay sculptures to communicate with their gods/spirit ancestors, and the sculptures would vanish. I remember one young female was very furry and was talking to her older female mentor figure about how even though most of the creatures were losing their fur to be more attractive to each other, they thought that closeness to the gods was lost with the fur.
At the same time there was a second species of flying creatures who would sing really beautifully in huge choruses. They were unaware of the other species but would pick up the clay sculptures and worship them. The two species depended on each other but were unaware of each other. There was possibly some biological dependence as well.
Humans got involved in this world somehow and I remember a scene with humans singing (badly) along with the flying race as a chorus starts up.
It seems to have some similarities to the short story "Hunter's Moon" by Poul Anderson, except I believe it was a book-length novel on its own.