Sing a song of Sixpence...

Sing a song of sixpence;
a pocket full of rye.
Four and twenty blackbirds
baked in a Pie.

When the pie was opened;
the birds began to sing.
Now isn't that a dainty dish
to set before a King?

A common nursery rhyme no? Common enough indeed that almost every child knows it, or will learn it over the course of their early schooling life, if not at the home. Yet why is it, that on hearing that nursery rhyme, or reading it, or even thinking it, I get a shiver down my spine? A shiver that has very little to do with the actual words?
Why can I see a sinister intent in the rhyme, the melody, something I've known since I was knee high to a grasshopper, but no one else can?

It's like ring a ring a rosy....
Ring-a ring-a rosy
a pocket full of posy
a tissue a tissue
we all fall down.

Describing the Black death, crimson rings are the first symptom, all over the body. A common myth was that by having a pocket full of posies, or flowers, fended off the ill-humours that caused the illness, or cured it once you had it. Then came the cold, the sneezing 'a tissue' for the sound you make...and well, the last line is obvious. 'we all fall down', we all die.

But ...why am I seeing such a sinister connotation to Sing a song of Sixpence? There is nothing, as far as I can tell, to support me in that! Sure, sticking twenny four birds in a pie and cooking them isn't exactly pleasant, even if they survive, supposedly, but its nothing to do with this...ill feeling I get. Perhaps tis just a passing fancy but still...