IV. Blackbirds

[Gilberto]

1.

Sing a song of sixpence
Blackbirds fill the sky
Trust to any other sense
But open not an eye

2.

Shadow plumage blocking sun
To make a night of day
Don’t try to look at them, just run
And try to get away

3.

Autumn leaves and feathers fall
The blackened sky descends
You mustn’t look at them at all
Or else the story ends

4.

Do your best to keep your feet
When blackbirds start to sing
Else you’ll make a tasty treat
To set before their king

[professordave]

This is my favorite quatrain because it's so visually appealing. A "black bird" could easily be interpreted as a raven, which is a well-known harbinger of death. Crows get a similarly bad rap (it ain't called a murder of crows for nothing).
Everything about this quatrain concerns imminent death. The blocking of the sun (giver of life), the falling autumn leaves, and the black birds.
This quatrain also gives warning to using your visual sense to spot this danger, but it does indicate that listening for this danger is a better option.
My interpretation: At some point in the near future, a predatory race of interstellar creatures will descend on Earth to feed. They will either have black wings or fly in fixed wing spaceships. Their main weapons are aimed at permanently or temporarily blinding their prey and then feeding on the blind creatures at their leisure (Day of the Triffids anyone?). You can hear them coming by the loud whistles they make when speaking. Best defense: hide until they leave.

[Gilberto]

That's what all my quatrains are about!

Here's an alternative on the same theme: The whole thing is about being lost in the dark. Maybe about a solar event itself. The blackbirds blot out the sun like an eclipse. The aversion to looking may refer to the fact that you won't be able to see in the darkness, or it could be a warning against the rays. Even in an eclipse you can be blinded by the rays of the sun. Night and day become one (or at least equal) during the autumnal equinox. Maybe it's something to do with that.