1. American Girl (1976)

Is there any point starting anywhere else? American Girl was the closing track on Tom Petty’s first album with the Heartbreakers, the group who stayed at his side until the very end, and it became the irreplaceable set closer, the song that encapsulated the very point of Tom Petty and the Heartbreakers.

It was once said that Petty’s entire career was an attempt to rewrite the Byrds’ Feel a Whole Lot Better (he eventually just covered it), and on American Girl he created a song to rival that earlier sound of California. Petty said it dealt with one of his favourite themes: the small-town kid searching for something bigger. This American girl “couldn’t help thinkin’ that there / Was a little more to life / Somewhere else”, yet the song was no lament. For all that she was left feeling “God it’s so painful / Something that’s so close / And still so far out of reach”, the song itself was a flowering of joy.

The radio DJ Mark Radcliffe once affectionately characterised Petty as one of American rock’s great lightweights, and that shouldn’t be taken as a pejorative: if Petty was never quite the equal of Springsteen or Young or Dylan, it meant his best songs had a lightness of touch that made them as simultaneously tart and sweet as a sherbet lemon.

2. Don’t Come Around Here No More (1985)

Forgive the skipping of nine years – no Refugee? No The Waiting? No Listen to Her Heart? No Stop Draggin’ My Heart Around? Madness! – but we have only five songs, and there needs to be room for later Petty.

What’s remarkable, though, is that it is possible to skip nine years to the second song in a list like this: Petty’s reputation might have been as a straightforward, heartland rock’n’roller, but he endured because he was able to create album after album of unerringly high quality. The lead single from the Heartbreakers’ sixth album, however, was far from straightforward heartland rock. Cowritten with Dave Stewart, it added electronic effects, a sitar and synthesised bass to create a piece of updated psychedelia that sounded half pastiche and half brave step forward.

One doesn’t often associate mystery with Tom Petty, but Don’t Come Around Here No More still sounds mysterious and drugged and dislocated (the title itself was something Stewart heard Stevie Nicks say to her then boyfriend, Joe Walsh, at the end of a cocaine-addled party). It remained the weirdest – by far – singalong in the Hearbreakers’ live show.

3. Free Fallin’ (1989)

Petty shelved the Heartbreakers in 1989 for his first solo album (on which some of them appeared, of course). They must have been kicking themselves that they weren’t the full backing band, because Full Moon Fever – largely cowritten with ELO’s Jeff Lynne, who would become Petty’s bandmate in the Travelling Wilburys – turned out to be one of Petty’s strongest sets.

It opened with the song that became an anthem of liberation when Tom Cruise’s conflicted sports agent used it as his singalong in Jerry Maguire, but it’s also one of the great Los Angeles songs: Petty journeys from the suburb of Reseda (“There’s a freeway runnin’ through the yard”) along Ventura Boulevard (“All the bad boys are standing in the shadows”) before he decides he wants to “glide down, over Mulholland”.

But you don’t need to know the city and its geography to feel the sense of Free Fallin’: it’s one of those perfect rock songs in which meaning is conveyed not by any one part of it, but by the combination of lyric, melody, arrangement. It’s the place where joy, nostalgia and melancholy meet, a combination that’s incredibly easy to misjudge in song; Petty nailed every element. Standing in the midst of a vast crowd at a Petty show when he kicked into Free Fallin’, and tens of thousands of people sang along to the chorus was a profoundly moving thing. There would be tears, and it was impossible to tell whether they were tears of sadness or joy.

Runnin’ Down a Dream (1989)

Full Moon Fever’s hardest rocker also gave its title to Peter Bogdanovich’s epic documentary about Petty (if you haven’t seen it, do so – even non-fans will enjoy it). Its inclusion means no room for I Won’t Back Down – a song Petty was unsure about, but which came to be indelibly associated with him. Sorry about that, but Runnin’ Down a Dream is here on merit: that magnetic, snaking, descending guitar line that any one of Petty’s 60s heroes would have been proud of, the fierce strums of acoustic guitar in the chorus that add pepper (and which sound like an idea taken from the country-rock staple Queen of Hearts, a song Petty had to have known well).

Lyrically, it’s another of Petty’s outsider quests, he’s “runnin’ down a dream / That never would come to me / Workin’ on a mystery, goin’ wherever it leads”. It’s also the sound of something purely American: the open road. The riff unfurls like an engine opening up on blacktop, and never stops motoring. Petty’s music was almost always the sound of big skies and the heat shimmering on the tarmac; close your eyes when listening, and what you see is a vast, empty landscape. It doesn’t have the same effect when you’re driving in the drizzle on the A406 (insert your own local ring road of choice).

Wildflowers (1994)

Tom Petty just carried on, and on. Sometimes he didn’t hit the spot (I was scathing in this paper about the 2010 Heartbreakers album, Mojo). But there continued to be gem after gem. In 1996, he threw away a perfect little pop song, Walls, as the theme to the movie She’s the One, which didn’t deserve a song that good on its soundtrack. Wildflowers, the title track of Petty’s second solo album, was a song I hadn’t thought of in years, until Petty and the Heartbreakers performed it in Hyde Park in London in summer 2017. It’s a dandelion clock blowing away in the wind, a song so gentle and beautiful it seems to have been not so much written as plucked from the ether. And it contains the lyric that might serve as an elegy for Petty: “You belong among the wildflowers / You belong in a boat out at sea / Sail away, kill off the hours / You belong somewhere you feel free.”