The only bird I know who changes a call (according to rhyme at least) is the cockoo
"The cuckoo comes in April, he sings his song in May, he changes his tune in the middle of June, in July he flies away"
According to an RSPB forum
"The cuckoo changes its call in speed and tone as the breeding season progresses. In the early part of the Spring it is faster and higher and later on it is slow and drops in tone. Great to hear at any time though and something to treasure in your memory for the winter months."

I'm not a bird expert and haven't noticed this for myself. You would think that if true for one bird it might be true for others. But that doesn't seem to be what the song is talking about.