Steve Mackay, the saxophone player, died in October. I found out just last week, after falling into a YouTube hole marked 'Stooges', though his death was covered not only by the music press but by the Washington Post and the Guardian. This is slightly surprising; Mackay did many things with his life, but he's known for playing on a few tracks on one album, which came out 45 years ago. Then again, the album is Fun House, and one of those tracks is '1970' – mind-blowing, earth-shattering music, which really was made to shatter the earth: 'What the Stooges put into ten minutes was so total and so very savage,' Iggy Pop wrote in his memoir, I Need More, 'the earth shook, then cracked, and swallowed all misery whole.'

Mackay's playing on that record alone does a lot to redeem the reputation of the much-maligned rock saxophone. Why maligned? Because of Johnny Colla of Huey Lewis and the News, and Andy Hamilton, who plays the solo on Duran Duran's 'Rio'. And because of the 'sexy sax man', Tim Cappello (who, actually, turns out to be kind of awesome). The general impression in these cases, and not a few others, is that rock saxophonists are superfluous members of bands that are already playing superfluous music.

But the saxophone is central to rock, and not just because of Bruce Springsteen's 'Big Man', the late, great Clarence Clemons, or the equally great Andy Mackay of Roxy Music, or the epically great 'honkers and shouters', like Louis Jordan and Illinois Jacquet, who emerged from the big bands in the 1940s, and came up with rhythm and blues in the first place.

Take Keith Richards, who may or may not have nicked the riff for 'Satisfaction' from Martha and the Vandellas (there's somedisagreement over which song he would have nicked it from). What's more certain is that he played it, through a fuzzbox, as a placeholder on what he thought was a demo recording, to indicate where the horn lines would go. Years later, he said that Otis Redding's cover of 'Satisfaction' was closer to what he'd had in mind than the Stones' own recording.

Or take the riff that Dave Davies played, ten months earlier, on 'You Really Got Me'. It, too, was a horn riff transposed to guitar (supposedly, Davies slashed his amp to get the fuzzed-out effect). Other guitarists – Link Wray, Paul Burlison of the Rock and Roll Trio, and many more – had also damaged their amps, intentionally, to get fatter, fuzzier, sleazier sounds, which approximated a saxophone. The tradition goes back to 'Rocket 88’, recorded in 1951 and often cited as the 'first rock and roll song'. Willie Kizart is supposed to have played his guitar through an amp that fell off the roof of his car on the way to Sam Phillips's studio.

Above all, there's Lou Reed's beautiful, insane solo on the Velvet Underground's 'What Goes On', which was made by laying three or four guitar lines on top of one another. The result sounds surprisingly like an Ornette Coleman sax solo (which was, in fact, the sound Reed was looking for). But then Ornette Coleman solos are more or less what Steve Mackay was playing with the Stooges. Is it so strange that, at the extremes, jazz and rock should fit together so nicely? A shitty thing about standard histories of rock and roll – ones that tell us that the music is half country and western, half rhythm and blues – is that they always slight jazz. (To do otherwise would be to suggest that rock and roll was being played, by black musicians, well before Elvis Presley followed Willie Kizart into Sam Phillips's studio.) But the truth is that electric guitar solos are directly descended from saxophone solos via Charlie Christian, who defined his instrument (which was once seen as a joke among jazz musicians, much as the saxophone's a joke in rock) by being the first guitarist good enough to cop saxophone riffs in cutting contests.

Someone should write a book about it. Meanwhile, now that I'm listening to it, the sax solo on 'Rio' is cheesy, but great.