Berlin Staatskapelle / Barenboim, Royal Festival Hall, London

Thrilled, enlightened, refreshed – and this after two nights of Brahms. The old stalwart of the symphonic repertoire has gone so far out of fashion that performances of any symphony, let alone all four, are hard to find. Last week's cycle came with a visit from the Berlin Staatskapelle and Daniel Barenboim – themselves responsible for part of the recent surfeit of Beethoven cycles, so perhaps they owed London a change. Or perhaps they had something worthwhile to say about the music. They were rewarded by packed, probably surprised, and by the end excited and noisy houses.

The Second Symphony soon set the tone. Apparently easygoing, it got slower for a while before gathering pace as the music grew argumentative. Alertness, constant minute fluctuations of pulse and a tendency to press on, then drop back, became the dominant features. The wide range of tempos stemmed from a response to musical tensions and always added up to a coherent whole. It's hard for musicians to achieve this without sounding contrived, and for the first of several times over the two evenings the comparison that came to mind was Wilhelm Furtwängler, the great German conductor of the mid-20th century.

In a similar way the sense of freedom, even risk, galvanised the listeners. It worked against a background of secure technical control and an ear for the peculiar way Brahms orchestrated his music to bring out the way it functions in glowing colours. Those melting moments always make a formal point. The rare interventions of the trombones in the Second, which produced a real arousal factor here, are a classic case of showing the muscle under the skin. Barenboim constantly played on this colouring with the intimacy of a confident understanding of its purpose.

The character of the orchestra was a big factor. Set against the glamour of the Berlin Philharmonic this is Berlin's forgotten band, based at the former east side's opera house and working hard in the theatre most of the year. All that exercise keeps it fit and very traditional in tone: more like the Leipzig and Dresden orchestras than the Philharmonic, and in many ways preferable for its fine individual timbres and lack of bloat in the overall sound. It uses extra woodwind instead for the big moments, and the result is to give Brahms a Schubert-like brightness, oddly similar to the effect of using period instruments, for all its supposed inauthenticity.

As the Second continued, the restless and long-range phrasing made the Adagio especially illuminating. A similar style gave the Fourth and Third a series of memorable moments within a well-judged wholeness. Both of these symphonies' finales were high points. In No 4 a solemn, suddenly grim stance evolved into passionate drama and an astonishing, unstoppable surge of acceleration. No 3 had the most epic performance, steady-paced and raging, then responding fully to the music's unexpected achievement of serenity.

That left the First for last. The risk of an anti-climax was there, in that this is the most loosely composed of these otherwise intensely close-knit works. It's always hard to make a running order for a Brahms cycle as three of the four symphonies are so loudly conclusive, and putting No 1 here makes the end of its first movement sound like a trial run for the conclusion of No 3.

Barenboim's solution was to make No 1 a contrast to the others, expansive and tending to broaden. It came near to undermining the music's tension at times, but it gave extra momentousness to the Andante's evolution towards its violin and horn duet. As for the huge end of the finale, fast then slowing, this one blown-up feature of the cycle arrived quite properly as Brahms, for the only time in his symphonic life, reached out just beyond his grasp and made the music big for the sake of big.