Richard D. James, better known as Aphex Twin, the UK’s (arguably, but not that arguably) most innovative electronic music producer ever, has said he was suprised his record label Warp wanted to release a new album by him – the first Aphex Twin album in 13 years. I don’t know how he can have got that impression. Warp was so enthusiastic that it floated a green blimp over London with the Aphex Twin logo on it. I was so enthusiastic about it that I bought the album from an actual shop the day it came out; almost everyone I know has heard it; last week it was the eighth best-selling album in the country, which is unusual for a piece of avant-garde electronica.

I’ve listened to Syro every day for the last week, and I mean properly listened. I’m still figuring it out. One reason it’s difficult to get the measure of is that it isn't what it sounds like: it’s a complex piece of musical modernism disguised as cheeky electro-funk. Perhaps this is why several reviewers have sounded a bit underwhelmed: yes, the album is very very good, but not a ‘major statement’. It’s true that Syro doesn’t constitute much of an advance stylistically on the acid-breakbeat tracks that James released as AFX between 2005 and 2009. And you don't get the sense from it that you’re right at the technological bleeding edge, as you do with, say, Florian Hecker (though the track titles, which are derived from bits of equipment used in the record’s construction, reflect James’s technological fanaticism). Nevertheless, in terms of its manipulation of rhythm, harmony and line it’s astonishingly refined.

Most dance tracks are built from loops, but no two bars of Syro are the same. Not even two bars of beats. Whether James is wrily vindicating chill-out room breakbeat, or channelling early jungle, there’s always something moving in the rhythm to hold your attention – a little flam here, a cow bell, a spun back snare. The lengths of the drum samples the beats are built from keep changing: they’re not Lego bricks, they’re oil paints.

But it’s James’s experiments with tonality that elevate him from a next-level dance producer to a composer of genius. On the first track there’s a vocoder line, but it isn't used as a riff, it’s involved with half a dozen synths in an intricate maze of polyphony. It recycles parts of itself, and creates variations on others. Then it disappears for a couple of minutes and returns, not as a melodic line but as backing vocals. The chord sequence that opens the track wouldn’t be out of place in a Ligeti string quartet. Misfit harmonies cohere into a phrase that shouldn’t work but does; then the mood changes from edgy to pretty, with the introduction of a chiming, melancholic lead line; then the paint is combed through, swirled around, and the mood changes once more.

On a traditional house tune there’s usually one bassline. On most tracks on Syro there are three or four. They dance round each other and complete each other’s sentences. They meddle with the beats, jostling kick drums for space. One bassline will change direction, forcing the others to follow it: they are constantly editing and re-editing each other. They don’t even know they’re basslines: occasionally one will revolt and spiral up into a higher register; while lead lines can trundle downstairs to join the knots of wriggling bass.

In a recent interview with Philip Sherburne for Pitchfork, James spoke about his desire to get away from ‘equal temperament’ (using a chromatic scale that consists of twelve equal semitones): ‘I've always liked these weird scales and tunings. I've been using my own scales for quite a long time now.’ Syro often sounds like several temperaments run together: riffs, scales, arpeggios sometimes complement each other and sometimes shift out of coherence, before settling down into another weather system of complementary harmonies. The chord sequences are sometimes jazzy – Bill Evans-y 9ths and 13ths – and sometimes distorted reflections of conventional hardcore piano riffs. Sometimes they’re just completely off the wall. ‘If you hear a chord that you've never heard before,’ James has said, ‘you're like, "huh".’ There are definitely a few of those.

And this is an album that’s also capable of erupting in one of the most glorious day-glo Italo-disco tunes ever made. An album in which an ensemble of autotuned vocalists sings ‘mouse orgy’ at you for a couple of minutes. An album that exhales a profound affection for dance music history and that has had me, on several occasions, shuffling helplessly round my sitting room on my own like the last drunk on the dancefloor at a wedding. It breaks down received musical hierarchies, creating a soundworld in which the fugal strategies of Bach are as valid, as ripe for imitation, as the wheezy synths of G-Funk. James is like a spider grinning at the centre of a web that contains all of music history, asking himself what would happen if Hindemith and Warren G smoked a joint together. Or can a piece be happy, sad, funny, funky, creamy, cubist, romantic, hyper-intelligent and super-dumb all at the same time? And twitching his threads accordingly.

The fact that it’s easy on the ear shouldn’t be cause for disappointment; it’s remarkable that music this good can be this fun: Syro’s unassumingness, its grooviness, its libidinous cheekiness, delight the ear as they challenge you to pay closer attention. But anyone who wants the ‘statement’ needn’t wait much longer. Syro, James has said, is a way of kissing goodbye to a certain style before the real work begins. He has workshops full of robots at his studio in Scotland working on something new, the likes of which we’ve never heard before: ‘I've been doing loads of electro-mechanical stuff with drum robots and things like that. I've got four MIDI pipe organs and a Disklavier controlled piano and computer-controlled percussion. I've done loads of stuff with those, and none of that's on Syro.’ Bring on the blimps. Bring on a fleet of blimps.