Although I’ve never been a big fan of Joe Satriani’s music, one of the things I’ve always loved about him compared to his contemporaries like Steve Vai, Yngwie Malmsteen, and Tony MacAlpine, is that he has a bit more training in off-the-beaten-path music theory than the more neoclassical and modal theory that the rest of those guys thrive on.
Part of the reason for this is that Satch studied for a brief period of time with one of the unsung giants of jazz piano, Lennie Tristano. Tristano has always been less-regarded than players like Bill Evans, partially because he spent much more of his life teaching and performing than he did recording (although the several recordings which do survive are all tremendous – including several “all star” sessions from the late 1940’s featuring Charlie Parker, who actively sought out Tristano to play on a session).
I’m not sure how far Satch got in his lessons with Tristano; surely not enough to call himself a great jazz improviser, but enough that I think you can hear a pretty profound impact of this music on his rock improvisation and melodic composition.
You can get a taste of how he thinks about melody in the following guitar lesson below, courtesy Guitar World. This lesson should be helpful if you are thinking about moving away from playing chord-tone driven solos and melodies. Check it out below: