There are birds that trill around during the day, and I finally figured out what they are.
Canaries. I should have figured.
So, the wild canary is indigenous to the islands in the vicinity: the Azores, Madeira, and you guessed it - the Canary Islands. The birdies are named after the islands, but it turns out the islands are named after dogs. Folks there kept a load of dogs, and the Romans took to calling it canaria - of the dogs.
Lots of people here keep pet canaries out on their terraces. It must be strange, being locked up in a little cage and hearing the wild version of you twittering around. Quite tormenting...