While there is a rich and varied literature for piano trio, works of quality that are composed purely for string trio (violin, viola and cello) are thin on the ground. Trio Zimmermann gave us a rare opportunity to hear some of the absolute gems from the repertoire this morning in a packed Queen's Hall in Edinburgh. The concert was so popular that not only was it broadcast live on BBC Radio 3, but even the standing areas in the upper galleries were partly occupied.

The programme began with Schubert's Allegro in B flat, a piece from 1816 that exists today as a stand-alone movement from a trio whose composition was subsequently abandoned. This single movement involves much passing of the tune from one instrument to another, rather than mere accompaniment of the violin by the viola and cello. In my book, such writing usually indicates that the intended performers were probably professional musicians, or at least competent amateurs, capable of more than repeated single notes. As an overture, the piece worked well. All three members of the trio projected clearly and distinctly. (A brace of Strads on stage may have had some bearing on this.) One impression I gained was that when playing very quietly, the pace became much more relaxed; a subito forte injected fresh energy and the previous vigorous tempo was resumed. The attention to detail such as the blending of tone, length of spiccato stroke and control of dynamics, bore eloquent testimony to the careful rehearsal that had gone into the preparation of even this relatively straightforward piece. How tempting it is to imagine the completed work and the missing two-and-a-half movements!

Composed 130 years later and just after his near-fatal heart attack, Schoenberg's String Trio took us to entirely different realms. Not only is this work immensely challenging for the listener (the man in the adjacent seat snorted with contempt and disgust once it was over, while one poor member of the audience passed out completely), it stretches the virtuosity of the players equally. The very informative programme notes suggested the strong literary links with Thomas Mann and the work's programmatic possibilities. Be that as it may, from the beginning, just about every sound a string instrument can yield was fed into the mix. I may have missed a left-hand pizzicato, but every type of harmonic, bowing technique and stopping was used. It was as if the composer were trying to recreate the sound palette that would have been available to him had an orchestra been at his disposal.

Constructed as a single movement with contrasting episodes, the opening exploded into life. Savage, hacking down-bow chords, extraordinary jumps (more like leaps of faith) from the lowest to the highest registers of each instrument, gave the first section a sense of drive and urgency. The intensity of concentration did not abate in the more lyrical central section. This contained lush sonorities and harmonies that not even my disgruntled neighbour could have found objectionable, but involved yet more spectacular interplay. The final episode was characterised by ethereal violin playing – one hesitates to talk of melody – suggestive of looseness of structure and a totally open weave of sound. Such a work is clearly not for beginners and it was delivered with passion and total commitment.

The main work of the morning was Mozart's six-movement Divertimento in E flat. It is taken as a given that despite the deceptively light-weight title, this is the single greatest masterpiece for string trio. It is a work which influenced Beethoven, but which not even he could surpass. Paradoxically, it is totally free from pyrotechnic display and based on the simplest of melodies. Composed in 1788, the trio therefore belongs to the period of Mozart's maturity, and more specifically, the final symphonies. The opening Allegro is simplicity itself: a unison E flat arpeggio, falling sotto voce towards the first forte. In the Adagio, Mozart almost reverses the trick as the cello arpeggio rises imperceptibly through the sustained chords of violin and viola. The effect is heart-stopping and magical. If, a moment ago, I affected to disparage amateurs who can only play repeated single notes, here is a piece which is full of just such writing. It is, however, in the shaping of such lines that the professional can be discerned.

The first Minuet is a tricky two-against-three syncopation, which leads on to an andante Theme and Variations, allowing each instrument its chance to shine – several times. The second Minuet is a genuine dance movement with all the lilt and grace of the traditional Ländler. The final Rondo is exuberant and joyous and this is precisely how it was performed. At times, Frank Peter Zimmermann was virtually bouncing off his seat. The viola of Antoine Tamestit positively soared – yes, we do that sometimes – and there was an exceptional sense of musical fusion. The performance was, like the Schubert, exquisitely prepared, and if in the slower passages, there was too much vibrato for the purists, the craftsmanship in execution was undeniable. Let us hope that all the youngsters who were conspicuous by their absence from the audience will be able to listen online and experience what they have missed. Never mind the athletes of the next Olympiad; where are the concertgoers of the future?