What is the best method of figuring out what to do for a solo or a breakaway? My fellow axman Rockonman and i are trying to write some stuff and its hard to find what sounds good with what we already have. any and all input is appreciated.

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the CHuCK

Take the chords name ex(E-D-C-E-D-E) Just as an example,,,
well anywaz take those chords and turn them to single notes ,take them to diffrent strings but same note or somthing like that or take them an octave higher,and give it fast licks and junk...thats my way of doing it.

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Me

First learn a scale such as the minor pentatonic which is probably the most used scale ever. Learn the 5 different positions(Octave note to Octave note...i.e=3(g)-15(g) )Then learn the relative minors. Make sure you can really move about the scale good. Then play what feels good.Remember not too fall into patterns or it won't sound like a solo, but a riff instead.

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Electric Guitars are the inspiration for cries of "Turn that damn thing down"-Gibson website

Play what sounds right with the riff, go mad, do whatever it's your own soloing style...create

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Being taught only robs you of your own creativity

First, figure out the key fo the song. After that, you should do what that Topik guy said (good advice).
Then you should take the feel of the song and take it to wherever you want to.

Use big intervals, leap in pitch. Give it lots of big bends. Play off-beat. It doesn't matter if it surprises even you, surprise can be part of inspiration. Mix up your speed. Repeat sequences of notes with minor modifications in say the timing or the identity of some notes. The structure doesn't have to be set in stone and mathematically rigid. Better to be a bit eccentric I think.

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If I couldn't laugh at myself how could I laugh at someone less ridiculous?

I think I agree with Sam. Don't overthink it...
The best stuff ever recorded was played "off the cuff"\
Also here's some advice from Eddie Van Halen.
"If you play a wrong note, just hit the whammy bar"

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Here's a hairbnd-ism for ya...
(In my best Forrest Gump voice) Life is like a box of chocolates.... it's sweet and enjoyable, but eventually has to turn to $hit....