Jack,
I would call the 'diddly di dee' type of singing 'lilting', but the marvellous thing about 'puirt-a- beul' (mouth music) is that the words DO make a kind of sense, as well as catching the inflections of the music wonderfully.

Cha tig an latha th‚id mi dhachaidh
Gus an tig na caoraich
Cha tig an latha th‚id mi dhachaidh
Gus an tig na caoraich

Gus an tig a' chaora dhubh,

Gus an tig a' chaora,
Gus an tig a' chaora dhubh
'S a h-adhairc as a h-aonais

basically it "means I won't come home till the sheep come". It's true the words are of little consequence, but they are not meaningless. We have similar songs in English; for instance to the reel "Soldier's Joy":
I am my mother's darling pet
I am my mother's darling pet
I am my mother's darling pet
I won't get married for a long while yet

I don't think any of the ones I know in English match the sound qualities of the best examples of the Gaelic puirt. Though I think 'Old Dan Tucker' might fit in this category and it's quite catchy.
By the way, as a Gaelic learner, I have sometimes been quite excited to realise what tune a lyric goes to simply by reading the words out loud and catching the rhythm.