I'm having a lot of trouble trying to harmonize to the lead singer in songs.
I've tried harmonizing to single notes on the piano but it doesn't really help
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Usually you'll want to harmonize with a melody with a similar pattern, within the same scale (or a mode of the scale, see here, it's for guitar but can be applied to vocals I guess), forming intervals between the harmony and the melody. Remember that the harmony is meant to be an accompaniment, so it might not sound good on it's own, but it should with the main melody.
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Best advice I can give here is to really train your ear on harmonizing. Once you get your mind set on how a proper vocal harmony should sound, it should be a lot easier to perform.

A good exercise would be to listen to a ****ton of The Beatles and really try to separate John from Paul. Songs from the first part of their career are usually easier to do this (Please Please until Rubber Soul).
"...I cried. Just for a second. Then I thought, 'I must rock.' "
- James Iha

Rock on y'all!

Listen to a lot of Billy Talent too, Ben and Ian harmonize almost everything.
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How was Confucius death metal?
You've clearly never read any Confuscius.

As I wait on the edge of the earth,
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Crosby Stills and Nash...their harmonies are like butter. Learn from them
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Oh, and besides The Beatles I would add Alice In Chains too. Two singers, very clear sounding.

However, I first mentioned The Beatles for some reasons: John and Paul's voices are very distinctive; recordings on the beginning of their career didn't have much effects at all, so it was almost like how they would sound live (therefore how you should strive to sound live); Beatles pre-Sgt. Peppers did not use overly complex harmonies, so all in all it should be a good easy starting point.

If you want to take it to the next level, go for the Beach Boys, most specifically Pet Sounds. Also, Queen would drive you insane.
"...I cried. Just for a second. Then I thought, 'I must rock.' "
- James Iha

Rock on y'all!

Interested to see how this thread rolls out. I can't figure out harmonies either.. mind you I've only ever given them a go while playing Rock Band 3 with friends.. but I figured it was a good way to try to get some sort of very primitive practice on them.. anyway I suck.

I figure harmonizing should be something I learn to do, it can't hurt either way.