I want to find more songs like these but don’t what they are called.
It’s an old style of singing you can sometimes see in 50’s movies, with Rosemary Clooney, etc.
The leads sing a duet, but first one sings, then the other, then they both sing their own songs at the same time, overlapping.
One is Baby It’s Cold Outside
I really can’t stay - Baby it’s cold outside
I’ve got to go away - Baby it’s cold outside
This evening has been - Been hoping that you’d drop in
So very nice - I’ll hold your hands, they’re just like ice
My mother will start to worry - Beautiful, what’s your hurry
My father will be pacing the floor - Listen to the fireplace roar
So really I’d better scurry - Beautiful, please don’t hurry
well Maybe just a half a drink more - Put some music on while I pour
:
:
Another is (I Wonder Why) You’re Just In Love [sometimes called “I Hear Singing”]
I hear singing and there’s no one there - You don’t need analyzin’
I smell blossoms and the trees are bare - It is not so surprisin’
All day long I seem to walk on air - That you feel very strange but nice
I wonder why, I wonder why? - Your heart goes pitter-patter
Isn’t that more like “call and answer” type songs?
Would the term “syncopated” apply?
Or “point-counterpoint” ?
( Excuse my ignorance, but I never studied music, I just want to find more of these songs. )
Would that be like McDonald Eddy and the* Indian Love Call*? Haven’t heard it in so long I forget the words.
A Google search on call and answer seemed to only have Barenaked Ladies. (Which I hope is a band I’ve never heard of.)
Here’s that song, but I don’t recall that they sang at the same time, stepping on each other’s lyrics so to speak.
INDIAN LOVE CALL - Nelson Eddy & Jeanette MacDonald
When I’m calling you - oo-oo-oo …
Will you answer too - oo-oo-oo …
That means I offer my love to you, to be your own
If you refuse me I will be blue and waiting all alone
But if when you hear my love call ringing clear
And I hear your answering echo, so dear
Then I will know our love will come true
You belong to me, I’ll belong to you
I doubt that is a round. A round is a piece of sung (if unsung then it is a cannon) music where singers sing an exact melody starting at different points in the piece thus making harmony off the single melody. “Row, row, row your boat” and “Frere Jacque” are both examples.
As others have said, what your example shows looks more like a call and response. Ie, one person signs the first part and a congregation or another sings the “response.”
Here is a link to a bunch of other rounds with music and free midi files. The site in the link is non-profit and all the rounds that it contains have gone into the public domain. The numbers in the sheet music show when the other singers should start.
Funny, I was just about to start a thread asking what rounds (by dorkus’s definition) dopers knew of in modern pop and rock music.
The one I heard was Dog Paddle by Modest Mouse, and I thought it was interesting to hear a technique usually only applied to children’s and drinking songs in a rock number, and wondered if there were more.
imperfectionist, FYI, “Call and Answer” is a song by the band named Barenaked Ladies. Sorry to break it to you. 
And a great song at that, saramamlana,
And it’s not really a type of song, but it is a song that contains a musical writing technique, contrapuntal writing (point-counterpoint) as pointed out by someone else. The writing technique goes back to Bach, and even further into medieval (sp?) music. The difference is that now lyrics are being put to the music…
c. sounds exactly like what you’re describing.
http://www-personal.umich.edu/~msmiller/counterpoint.html has some information about different types of counterpoints. I don’t think any of those described are exactly what you’re looking for, but I think the answer to your question is definitely counterpoint.