It still seems unexpected, 20 years on, this alliance of austere vocal music and wandering saxophone. Yet the alchemy between Jan Garbarek and the Hilliard Ensemble is simply undeniable.

It is somewhat misleading to describe Officium as the Norwegian jazz saxophonist improvising over early music; just as misleading as it would be to categorise the collaborations as Gregorian chant or jazz. The project is more complex than that, its charm less explicable. Jan Garbarek and the Hilliard Ensemble are in dialogue; they are equals, creating a particular texture of sound. Perhaps the wisest way to describe this is simply as polyphony, casting Garbarek’s saxophone as a fifth voice.

The collaboration is winding down after 20 years of international success, having created three albums and performed in the cathedrals from Berlin to Siena, London to New York. This is the Hilliard Ensemble’s farewell tour, with their last concert taking place at Wigmore Hall in mid-December. Tomorrow, in Cambridge, they will deliver the final Officium performance. There is a sense, in Geneva’s St. Pierre Cathedral, of this being an historic moment.

The programme follows the arc of Officium Novum: Garbarek opens alone, so discreetly many of the audience think he is warming up. However, when the voices join in, the perfect overtones reverberating among the stone vaults and columns, a transfixed silence falls. Even the oak benches cease to creak as the quartet processes down the aisle.

The concept has grown and changed since its inception, when the seminal Officium was released; going on to sell one and a half million copies. In that first offering, the Hilliard Ensemble stuck to their area of expertise – early music – and Garbarek followed. One gets the sense that the five have branched out considerably from their home territory since then, buoyed by their success and inspired by each other. Officium Novum, the second sequel after Mnemosyne, moves away from Latin and into Russian, French, Croatian, Swedish, English: an opening to the North and East of Europe. Their closing concert reflects this new variety.

It isn’t only the material that has evolved since 1994, but the whole approach to collaboration. Garbarek is not simply embroidering over existing music: he is changing its very fabric. In fact, several of the pieces in the programme are his own compositions (including the lovely “We Are the Stars”, reminiscent of Whitacre or MacMillan). This turns the concept on its head and gives it new exploratory depths.

The Hilliard Ensemble may no longer be so young, but they are masters. David James, Rogers Covey-Crump, Gordon Jones and Steven Harrold have been singing in ensembles for a long time, and this is obvious in every piece, in the very sound they create together. If the pitch should tremble, if a voice should falter, the other three rise up in support; perhaps even four, as the saxophone’s voice is so entwined with theirs. Thus, in moments when the voices are almost lost in the cavernous acoustic, Garbarek soars above, transcendent. David James’ flawless countertenor merits a mention: as the tenor and soprano saxophones’ natural companion and double, he is the keystone of this alliance. In Arvo Pärt’s Most Holy Mother of God, his voice is utterly stunning. If, amongst the others, there is occasional wavering in the lower ranges, it is quickly fixed and forgiven. Always, the sound is purified and perfected.

Meanwhile, Garbarek hovers, wanders behind the singers. At times his keening sound is wild, harsh, angular, sending shivers down the spine. Other times, his meditative voice melts and softens until it is virtually indistinguishable from the vocals. This elicits a playfulness from the Hilliard Ensemble’s performance, from meandering vocalises to sharp glottal-stopped bursts. It is not solely Garbarek who brings the element of modernity to their sound: the masters are not afraid of taking risks. At times, it is thrillingly difficult to tell if they are improvising. As they approach retirement, the Hilliard Ensemble radiates nothing but poise, warmth, and elegance – just as they have always done.

20 years is a long time for an alliance to remain so fascinating. In these final concerts, the performers radiate inspiration without a hint of fatigue, as they give life to this peculiar, beautiful blend of ancient and modern, stasis and energy, friction and fusion.