In 1993, by some strange musical alchemy, a creative partnership was born that has gone on to bear some remarkable fruit. On Officium, stylish jazz and classical label ECM brought together The Hilliard Ensemble – a vocal quartet known for the precision with which it had tackled and animated austere soundworlds from Perotin to Pärt – and Norwegian jazz saxophonist Jan Garbarek. The resultant album, of early vocal music overlaid and intertwined with plangeant, improvised saxophone, proved not only original but enormously successful. ECM went on to repeat the trick with Mnemosyne and, most recently, Officium Novum.

In this concert presentation, part of the City of London Festival, another distinctive voice joined those of the performers: the vast reaches of St Paul's Cathedral. The Hilliard Ensemble are known for their acute understanding of the way a venue can influence and shape a performance, and they clearly relished the chance to exploit the cavernous acoustic. Their immaculately-tuned harmonies swirled up into the dome and were met by the extraordinary dynamic range of Garbarek's saxophone.

Officium Novum translates as 'the new office', and there was a quasi-liturgical sense of drama to this performance, which unrolled in one uninterrupted 90-minute span. The music consisted of Armenian devotional music, in early 20th-century arrangements, alongside Perotin, Pärt, and original compositions by Garbarek, who linked together all the pieces with his trademark modal noodling. An extraordinary atmosphere was created right from the outset, as the singers emerged, wordlessly vocalising, from the four corners of the cathedral, and proceeded to slowly converge on the stage. This sense of ritual carried on throughout the concert; the singers often moved about in the same solemn manner, splitting up, recombining at the side or in the middle of the nave, and weaving between the blocks of seating, sometimes with Garbarek in tow, and singing all the while. The ensemble is clearly now so comfortable with their unique collaboration that the whole concert was perfectly well-drilled; the flow was never broken, and accordingly the all-important atmosphere was not compromised. The effect was rather like watching an unfamiliar liturgy play out with a centuries-old certainty – an impression reinforced by the inclusion of the Armenian 'Sanctus', the Christian church's hymn of praise, Surb, surb, sung from the south transept.

Such was the contiguous nature of the performance that it was sometimes hard to detect when one piece had ended and another begun. However, certain moments of clarity emerged from the sometimes blurry texture. Particular highlights included Garbarek's riff on Perotin's Alleluia nativitas, which drew on the repetitive qualities and rhythmic vitality of the 12th-century music (and was somehow not lost in the building), and Arvo Pärt's beautiful and haunting Most Holy Mother of God, written for the Hilliards and wisely left to them by Garbarek.

With all the sonic beauty and musicianship on display it would perhaps be rather curmudgeonly to complain of the non-provision of texts to the audience, though this may have ameliorated the acoustic's smothering effect on diction.

As a concert experience, a night in the company of Jan Garbarek and The Hilliard Ensemble is difficult to classify. Part performance, part installation – maybe 'meditation in sound' is more apt. Easier by far to pin down is the level of thorough-going musicianship demonstrated in the way that the performers listened and reacted to one another. In St Paul's Cathedral was celebrated the intriguing interplay between two very different musical and performing traditions. Witnessing it was an elevating experience.