I know its called the "Egg Song" here on BYC, but my understanding of chicken talk is its the "I am upset" song. Some hens get upset when they lay an egg, some get upset when they get kicked out of the nesting box by the next hen. The roosters sing it when they get upset about something too. It announces any upset in the coop. If you hear it from a lot of birds - you better check the coop - there could be a predator (or it could be a cat..)
If you really want to mess with KFC - start the "I'm upset song"Bak Bak Bak Bagawack!
When we first got them I didn't know about egg song, I just knew someone was making a strange noise. I kept going in to check-nothing-just a pullet making noise. The next day I heard it again and found my first egg. It is not uncommon here to have 4 boys join in the song along with the hens. When they get going they can outdo most roosters crows in volume and duration. I warn people that hens are not always quiet but until they hear it themselves they don't believe me. The ladies do wait until the sun is up most days.
My boys usually start their alarm calls with a growl of-sorts. My barred rock "quarks" a warning. They gots lots of practice today with all the crows and starlings flying over them
My ladies woke me up at 6:00 this morning! I know what you mean!