uhhh.... not sure what you mean by "legal".
Example: the official tabs book has a copyright. The music itself has a copyright.
If someone sells you a tab which isn't in the book, it's probably not an authorized tab and the money goes to someone not associated with Acoustic Alchemy. It's a bootleg at that point.
If you perform the music, it's a good bet that someone else is paying the performance fees associated with covering music.
In the US, ASCAP and BMI collect "performance" or "for play" monies from various theatres, clubs,websites, etc. There are similar agencies in other countries.
If you're asking if the tabs that the fans have worked out are "legal".... I can only say that fans have been covering their favorite band's music for years. AA is no exception. If someone gives you a fan tab, it's a gift.
So, I think we're unsure as to how to best answer your question.
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I've Got Jazz...Do You?