This excellent documentary doesn’t spell it out, but Frank Zappa was actually Frank Zappa’s real name (unlike, say, Ziggy Stardust) and everything about him was authentic, presented to the public on a take-it-or-leave-it basis. If anyone deserves an approving sobriquet with the “American” prefix – American Original, American Genius, American Rebel – it was Zappa, the rock’n’roll musician, freak-provocateur and contemporary composer and orchestral arranger influenced by Anton Webern, Edgard Varèse and Igor Stravinsky. This film allows him to speak “in his own words”, which means clips from his imperturbably droll, articulate performances in TV interviews over the years during which he morphed from sensually hirsute rock god to bearded patriarch, without selling out or putting on weight.

In a perfect world, “Zappa in his own words” would really mean nothing but his music and lyrics, which is where he would be truly himself – but this is nonetheless a thoroughly entertaining watch. He emerges as a radical, sceptical libertarian who derided what he saw as the occasional fascism of the left. In one edition of the TV debate show Crossfire, he even describes himself as a conservative, while making mincemeat of the plumply besuited disapprovers ranged to his left and right.

Zappa allied himself broadly with the counterculture but was obviously a pretty strict taskmaster with his own musicians, like a cross between James Brown and Leonard Bernstein. He didn’t much care for drugs, and to one interviewer he reveals he had sacked musicians for drug-taking on the road, on the pragmatic grounds that they might get thrown in jail when he needed them on stage. As for himself, he only took penicillin for “clap”.

The film makes it reasonably clear that feminism was one aspect of the 60s and 70s that maybe passed him by, as it did with quite a few male stars: he was a groupie enthusiast. And yet these assumptions are not entirely safe: the movie quotes his scabrous and outrageous song Bobby Brown, satirising the smug male inheritors of the American dream, with the lines “Women’s liberation came creepin’ across the nation...” The lines it actually quotes are “Got a job doin’ radio promo/And none of the jocks can tell I’m a homo...” - which I guess indicates Zappa’s views on LGBT issues may not quite chime with 21st century sensibilities.

He was cautious of the term revolutionary (though he did not object to “genius”), on the grounds that it was coercive and aggressive. But actually he does seem like a revolutionary, and someone who couldn’t be categorised. This film could trigger a revival in his music – and maybe new performances of his orchestral work.

•The International Documentary film festival Amsterdam continues to 27 November.