Listening to Fiona Apple’s new album for the first time was the audio version of taking a heavy shunt from the side. Fetch the Boltcutters T-boned me when I least expected it and, with hindsight, that is a terrible indictment of my listening habits in recent years.

You see, Apple is a musician who had passed beneath my radar to such a degree that I now find myself almost ashamed to have overlooked her. It would be like missing one of those huge names that mean so much to me musically: Tom Waits, Leonard Cohen, Joni Mitchell, or even Lou Reed. And, yes, this album does deserve mentioning in such company. If it catches you right, you will almost certainly agree that it is an instant classic.

It is not, however, an easy album. No album can be considered easy when it includes a track like “For Her”, a song written about an abused woman, which has lines like “you raped me in the same bed your daughter was born in”. This is an album that emerges from a world of brutalised relationships, not least the one that exists between the artist and her true self. It’s an album of introspection – sometimes one even suspects more introspection that is strictly healthy – and the result is a rapid descent into the artist’s thought pool. It also breaks enough rules to be different from anything you’ve heard before. I was reminded of Swordfishtrombones in the way it changed the way I listen to music. Other emotionally fraught albums will now sound so much thinner than before.

There are no obvious singles here, no clear melodic lines that carry songs through from beginning to end. Nothing feels like it should belong in the company of a music video. It is rather, an album that is organically whole, as tracks share some degree of commonality, as your ear picks up tones and phrases that you might or might not have heard earlier. This is an album that ventures into sometimes strange, often discordant places but never once does it lose the thematic thread. Clever hooks pull you forward but rarely does the album settle into comfortable sections. It’s constantly shifting, evolving, and hitting you in whatever part of the brain turns music into shared experiences.

Albums rarely do this from the start. The first track, “I want you to love me”, should be a generic ballad but it isn’t. It’s supposedly a love song to a future lover but what gives it all manner of edge is how it arcs into philosophy and theology — “I know none of this will matter in the long run / But I know a sound is still a sound around no one” – as if trees falling in woods could obsess over the sounds they’re making. The tone it sets is heavy with echoes of Joni Mitchell where lyricism and musicality finding power in each other’s company. Above all, it’s an album comprised of driving piano phrases and percussive lyrics.

“Shameika” is one of those lyrics: a song about bullying filled with repetitive rhythms that convey the routines of loneliness and abuse. By the time you hit the third track, “Fetch the Bolt Cutters”, you’re ready to have the album’s theme confirmed. It begins with the prosaic line, “I’ve been thinking about when I was trying to be your friend”, which feels like pure Joni from Blue (specifically one of the great lyrics that begins “The last time I saw Richard was Detroit in ’68 / And he told me all romantics meet the same fate someday”) but the song soon spirals down and explores the kind of traps our minds make for ourselves – “I’ve been thinking about when I was trying to be your friend / I thought it was then, but it wasn’t, it wasn’t genuine”.

“Under the table” is memorable for the hook (“Kick me under the table all you want / I won’t shut up, I won’t shut up”) but the verses liberate it with tiny dramas that allow it to escalate into the chorus. You could say it is another track about “female empowerment” and all the slightly hokey phrases that social movements sometimes make of genuine issues, but Apple always manages to eschew trite sentiment because her liberation is that of a person who is simply awake to her power. “If you get me to go and I open my mouth / To the fucking mutton that they’re talking about / You can pout, but don’t you, don’t you / Don’t you, don’t you, don’t you shush me”.

When artists talk about liberation, it’s often the liberation of confession, yet it is much rarer than you might imagine. Apple’s success here is that she manages to convey hyper-realised moments of emotional fragility. It’s closest to Lou Reed’s brilliant, brave, challenging, but also so cruelly exploitative album, Berlin, which one critic at the time described as one of those “records that are so patently offensive that one wishes to take some kind of physical vengeance on the artists that perpetrate them”. This is nowhere near that level of brutality but it’s unavoidable that one occasionally wonders about the emotional health of the artist.

A track by track commentary would run to countless thousands of words and still leave huge gaps (an academic conference on “Heavy Balloon”, which deals with depression, would probably only scratch the surface). The thirteen tracks here will take countless listens before you begin to run dry of things to say or influences that you recognise. Yet, for all of that, it is also a refreshingly private album that isn’t afraid of leaving us with complications. The last track is “On I go” and Apple has herself described what moving on means to her. “I’m going to make music for myself, to get myself through things, and not think about what other people think about it. I don’t want to prove anything anymore.”

There’s real power in not needing to prove oneself and the result is an album that tries to please nobody but the artist herself and, in doing so, achieves so much more. Relationships are examined in states of strain or breakdown, arguments feel like they’re penned and sung at the moment they’re happening. Videos of Apple on Youtube show her playing with her pitbull, Mercy, in what is often a fierce tug-of-war. Musically, this album is like that game between dog and owner. It’s rough, combative, yet coming from a place that is ultimately tender and loving. Fight with it, challenge it, spend time in its company. It could still be an album that simply passes you by but, if you’re open to the experience, you should find that it is quite simply spectacular.