Singing a dance tune is usually called lilting or diddling, although I never come to tears singing a dance tune, except, maybe THE BLACK ROGUE, and then only tears of laughter.

I got some information from a recording of Cathal McConnell and Len Graham For the Sake of Old Decency:

THE BLACKBIRD is a dance tune which can be played as a set dance(which I will talk about later), a slow air, a hornpipe and a reel. There's also a song to it.

This is more or less verbatim what Len Graham says about the song THE BLACKBIRD before he sings it:

"THE BLACKBIRD doesn't really refer to a feathered species, but it's more to a political, I should say character from history and I'm sure you've all heard of Bonny Prince Charlie. Well, the father of Bonny Prince Charlie who was known as the Young Pretender was known as the Old Pretender, so the Blackbird was an allegory for the Old Pretender and this cause was, of course a very popular cause in Scotland and in Ireland. This is an Irish song..."

I won't include the words to this lovely song here, but the melody is the same as the hornpipe and the slow air that Cathal plays.

THE BLACKBIRD and RODNEY'S GLORY are both set dances. I don't have any information about RODNEY'S GLORY, but I am glad to look it up, though it may take some time. I got the following information from Breandán Breathnach's Folk Music and Dances of Ireland:

"Set or long dances are solo dances, usually with a jig or hornpipe rhythm. They deviate generally from the usual form of the dance tune in having one part, ususally the second, longer than the others, and sometimes the parts maybe in different times. Each tune has its own particular dance which, following the usual Irish custom, has the same title. ..they required an expert to perform them properly, and this skill was exibited much better on the kitchen table than it would have been on the clay floor of the house.

Brían