If anyone is even remotely familiar with Weezer's work, than you may have heard how Rivers Cuomo is able to take a guitar solo and voice it in such a way that's similar to the way the singing sounds over the chorus or verse, giving it a very recognizable sound. Instead of just melting a face, he plays off the chords he's singing. At least that's what I gather.

First of all, is there a word for this? When someone voices a solo as if they were singing the words?

Another very good example would be the solo in Smells Like Teen Spirit.

Secondly, how can I more easily transpose a line I sing over a progression into a solo or fill?
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Figure out the notes and rhythms that the vocal line follows and use that as the basis of your melody in the solo. For some good examples of this, hit up the Beatles. That idea is actually rather interesting to me as well, although I play metal, not rock. The short and sweet is to take the vocal melody, play that and do some variations to make it more solo-y.
He's just playing his vocal melody on guitar, if you want to work out how to do it record yourself singing a perticular line, grab your guitar and pick out each note you sing and transcribe it to guitar its all the same notes just different ways of making them.
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Transcribe the vocal line
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Thanks guys. It's a real interesting style of soloing to me. I figured as much as you guys had said. I just wasn't quite sure if there was a method beyond transcribing the vocal parts myself, by ear, to guitar.