"Show us in Paradise," The Protector says to The Boy in the foreboding opening scene of Written on Skin, a new opera by gay composer George Benjamin that had its premiere at the Aix-en-Provence Festival on July 7. "The Protector" is commissioning an illuminated manuscript depicting his possessions – including his wife and her "still and obedient body." This being opera, you know it's only a matter of time – in this case not much, at least on the clock – before everyone is instead in Hell.

Our century's finest opera and Benjamin's second (and, at 95 minutes, first at full-length), Written on Skin is already headed for a half-dozen of the world's opera capitals in this searching, uncompromising, and tirelessly inventive production by Katie Mitchell. Against odds, there's not a hint of cliche in Vicky Mortimer's multi-tiered sets and mixed period-modern costumes. As if that weren't good enough, the premiere performance is already viewable free on www.medici.tv (you only have to register), so pointedly directed for television (by Corentun Leconte) that you have the best seat in the house.

It's fitting that the opera opened at Aix, because its story derives from the legend of the 13th-century Provencal troubadour Guillem de Cabestany, though librettist Martin Crimp, Benjamin's frequent collaborator, has given it a contemporary (and timeless) spin while preserving its elemental, raw power. His words, all clearly audible in this intricate score, brand themselves on the listener's mind.

We know the illustrator only as The Boy, played by countertenor Bejun Mehta at his most luscious; and The Protector only as The Man, sung by Christopher Purvis, Britain's greatest acting singer, channeling a volcanic power that rises in the imperious character and ultimately gets away from him. The Man, observes the Boy, is "addicted to purity and violence."

There's a lot of "says The Boy," "says The Man," and so on, as the three principals all sing that continuity as well as their own lines, the effect of which, counter-intuitively, is anything but distancing. It also helps underline the opera's pivotal transformation. The Woman is virtually mute when we first see her, trapped barely out of childhood in a marriage Sieglinde or Judith in Bartok's Bluebeard might have envied, and kept illiterate (pivotal to the story) and barefoot. Through forces The Boy and his art unleash, she reclaims herself as Agnes, Barbara Hannigan's enactment of which is as powerful a performance as I have seen on the operatic stage. It costs Agnes her life, which in this case looks unmistakably like freedom.

In exploring the death-dealing powers of Eros, this opera sits directly in the line that goes from Tristan through Lulu by way of Strauss' Salome and Elektra , the last two of which it resembles in the inexorability of the score over a devastatingly short span. Without a trace of gratuitous sensationalism or an instant of nudity, this is the sexiest opera I've ever seen. The kisses The Woman lavishes on The Boy after challenging him to draw "a real woman," and the ones The Man lays on The Boy – which we've seen coming since he swore, before there has even been a marital transgression, "I love The Boy" – are no "stage kisses," and it's a tribute to this astonishing trio that they can render these moments and still sing. In TV close-up, the scenes are scorching. "Love's not a picture," Agnes calls out, "love is an act."

Perhaps the most remarkable thing about Benjamin's score is how singable it is. It's not tuneful in any platitudinous way, but every note and interval in the vocal score seems foreordained, and the fusion of word and note in the score helps the singers achieve the same. Benjamin's compositional voice – individual and hard-won, saturated yet pellucid, inviting and ensnaring – has matured into something almost frightful in its transparency to its own larger purposes. It's stealth art. You forget you're in the theater, hearing music.

When The Boy first shows The Woman his book, the score is shot through with the textures of "early music," but without crass borrowing and only whiffs of gamba. All sense of the contrived or the derived has been seared out of it like fat.

That's not to say that this bold, original music doesn't leave traces. There are hints of Berg in the opening measures, and as the score hurtles inexorably forward, Lulu, Debussy's Pelleas, and greats gobs of Britten are in its rear-view mirror. But unlike Agnes' horrid last meal, they're completely digested in Benjamin's formidable brew.

The little we see of Benjamin in the pit, conducting the ace Mahler Chamber Orchestra, is telling. Not quite a microbeat, his is devoid of big, overpowering gestures – just a knowing plunge into the heart of the matter.