Too often is the word 'art' wielded when assessing the merits of pop music. A great deal of that which graces reviews pages is simply a matter of mechanics and mathematics, influences coming together in carefully arranged equations to produce a palatable result. This is probably still a creative act and often yields magnificence, but to brand the ubiquitous white noise that makes up the new releases merry-go-round as art is inaccurate, especially compared to music like Jesca Hoop's.

For Hoop is an artist in every possible way, from the mad chaos of her videos to the unsettling starkness of her lyrics. Even now after three albums, there is a staggering originality to everything the California-raised, Manchester-based singer touches. Her previous LP, Hunting My Dress was as electric as it was moving in its weird and audacious poetry and strange, mystical songs that hinted at Celtic music as well as the pop of Kate Bush and the melodic gifts of the McGarrigles.

Now firmly established as a Mancunian having moved to the city in 2009 on the advice of Guy Garvey, Hoop's third album is another curious and uncategorisable beast. On first listen, it appears she has gone down a more energetic, mildly power pop-inflected route that first manifested itself on Hunting My Dress's 'Tulip' – opener 'Born To' is along these lines.

In actual fact, there are more soft ballads than first impressions suggest ('Pack Animal', 'D.N.R', the title track), the intricate architecture of which proves this is an area in which she has certainly evolved. However, these songs are dwarfed by those where Hoop assumes her Paganish, fevered persona that seems supernatural in its unflinching and inhuman power. 'Peacemaker' sounds like a cross between St Vincent and midnight calls to prayer in Marrakech.

'When I'm Asleep' is a milder version of the same, while the genre gymnastics are completed by the acute pop of 'Hospital (Win Your Love'). Musically Jesca Hoop has created something of familiar warmth and urgency, with a grasp of pacing, harmony and melody that more fabled songwriters (Garvey?) can only hanker after.

But it is lyrically that The House That Jack Built is a masterpiece. Her words are always confronting in one way or another, be it direct paeans to lost parents (Hunting My Dress's 'Angel Mom') or the more abstract imagery of 'Peacemaker' with its “sex and make / milk in your baby / swords enraged / fuck me babe / pray abstain girls reign".

Indeed, the sexuality of Hoop's lyrics is in part responsible for the frantic edge to songs like 'Peacemaker' and 'The Kingdom' from Hunting My Dress. But this sometimes-Amazonian and fierce mood, lustful and primitive, is balanced against several songs that explore the pigtails-and-treehouses innocence of childhood. 'D.N.R' is one – another sombre tribute to a deceased parent, this time her father – as is 'Pack Animal'.

And the combination of the two extremes is at the heart of Hoop's art. The little girl and the stampeding, psychologically fraught sexuality are irrevocably part of the same essence, with no perceived morality to separate them, both simple expressions of nature. In this way, The House That Jack Built is a celebratory exercise in existentialism.

The only time when these seemingly disparate aspects of self are at rest are, according to The House That Jack Built, when you are asleep. Album closer 'When I'm Asleep' features the refrain 'When I'm asleep / I'm not anyone / you're not anywhere', unconsciousness allowing a blissful period where identity doesn't exist. Hoop is clearly interested in this idea: she writes a blog called You Are Innocent When You Dream (named after the Tom Waits song, who once employed Hoop as a nanny for his children, as is mentioned ad nauseam), where she regularly posts whatever she has dreamt. This may explain the dark surrealism that has punctuated all three albums.

So with sex, childhood and dreams all on one album, Freud would surely have a few words for Hoop. But given that this is one artist who seems to follow nothing but her own muse, there is little chance she would listen. Which is good: let nothing interfere with this astonishing creative force.