Do we instinctially interpret birdsongs as a sign that there are no predators present?
Crows and gulls would probably also flee predators but their songs are definitely not really pleasant to listen to! I know it, they woke me up last week-end $\ddot \smile$. The canadian goose or the common starling (see here) are other examples of not really pleasant songs.  

Too a selectionist view of evolutionary processes

It is important not to make the mistake to see anything as an adaptation (a result of natural selection only). Evolution is way more than natural selection and it encompasses tons of stochastic processes. This answer has a paragraph on the subject of not thinking of anything as a result of natural selection. This kind of over-consideration of adaptive processes in evolution is a common mistake especially when thinking about how human behaviour evolved.

Evolutionary psychology and evolution of appreciation of bird songs

The field of evolutionary psychology may interest you but note that it is a field that is sometimes still at the limit between psychology, philosophy and biology.

Appreciation of art as a by-product

Appreciation of art (like birds songs) and beauty is a pretty poorly understood subject yet. The first hypotheses came from Darwin and Gould. They pretty much argued that we enjoy sex, grasp facial expressions (kin recognition), have to like logical proof to appreciate learning and acquire language, efficient communication (cooperative hunting), appreciate put oneself into others thoughts (Machiavellian intelligence),  etc... As a result of those selection pressure, we may have evolved, so-called by-products. A by-product is a phenotypic trait that hasn't been directly selected for but that has been  selected via its correlation to some other phenotypic trait that is under positive selection and that is correlated. If this is true, then there would have a correlation between cognitive abilities and art appreciation and therefore a correlation between art appreciation and fitness.

Appreciation of art due to sexual selection

Some have argued that looking at the importance of art appreciation and intelligence in today's mate choice, it is likely that art appreciation may have been reinforced by sexual selection.

Either sexual selection may have reinforced a trait that was correlated to fitness ("evolution of appreciation of art as a by-product" hypothesis).

It is also possible that sexual selection may have selected for art appreciation without art appreciation being correlated with fitness but just because it asks for a big brain and lots of energy (brains consumes lots of energy) and being able to appreciate arts means that the individual has extra-energy to spare and is therefore very fit (handicap principle).