On an ever higher note

I finally remembered all the lyrics to this song, which goes to a higher and higher pitch with each repetition, until the singer can go no higher:

Had a little dog,skinny as a rail;
Had a lot of fleas all over his tail.
Every time his tail would flop,
The fleas on the bottom would hop on top.

Melodically, the flea song resembles another, probably much older, song that uses the same raised-pitch device. This one has never been in any part forgotten:

Have you ever been in the land of gin
Where the river of rum flows by,
And the little gin rickies grow in the trees
And the highballs grow on the ground.

At least, that's the way I learned it.