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Chatting with Rolling Stone, Joe was asked about what it was like to be teaching the likes of Steve Vai, Metallica's Kirk Hammett, Larry LaLonde of Primus and Testament guitarist Alex Skolnick.
"I always thought I was the luckiest guitar teacher ever," he replied. "I did have just a lot of great students. You'd have Larry come in, and he would say, 'Man, listen to these songs we're writing. How do you play over that? What kind of a solo can I do?' He was such an interesting student, as were Kirk and Alex.
"They had great technical facility, which made teaching them really great because you could show them something and six days later they had it down," the guitarist added.
Asked about the experience of giving Vai guitar lessons, Satriani commented, "You couldn't make a Steve Vai [laughs]. That's a one-in-a-billion type of personality that comes out together with an incredible talent facility. You grow it; you help them grow it. Hopefully, it matures and they don't hit any roadblocks along the way."
Finally, Joe focused on Kirk, saying, "He had a very interesting thing going on. He was in Exodus at the time we started lessons and, then all of a sudden, he got into Metallica, and they were making a record and they were on tour. So he would come in with stuff that was going to be on the Metallica records.
"He had a real need to get things figured out. He was totally into Michael Schenker and Hendrix and stuff like that, but it didn't really apply to what he was writing with James [Hetfield] and Lars [Ulrich], and I really was there to show him the possibilities and then sit back and watch it turn into something.
"He loved it. He would say, 'Lay it on. Give me as much information to choose from as possible,' and then he would go on and make his own decision about it and how to apply it. And the guys in the band must have encouraged it as well, because all that stuff wound up on the records and it was so cool to hear it," Satch concluded.