For its concert on Sunday afternoon, the Philadelphia Orchestra under Simon Rattle performed symphonic works which, the programme notes claimed, “invite us to think about the possibilities of hidden musical meaning”.

Over the years, speculation has been rife on the famous F-A-F motif of the opening chords on woodwinds in the first movement of Brahms’ Symphony no. 3 in F major, thought to be a musical code for the motto “Frei aber froh” (free but happy). The temptation to present this terse motif dramatically to achieve maximum impact must be hard to resist. Yet Simon Rattle and the Philadelphia Orchestra handled it with restraint, thereby maintaining a carefully honed balance between the opening and the rest of the movement, which hangs together much more coherently.

The F-A-F motif, apparently borrowed from the other work on the programme, Schumann’s Third Symphony, is the theme that pervades and unifies the work, emerging throughout in different guises. It is the ability to highlight this apparent unity that struck me most about the Philadelphia Orchestra. Whether it be in keeping an even tempo; in drawing out the variations on the F-A-F theme; or in bringing to life the rather narrow tessitura of the material – the orchestra took pains to present the symphony as a coherent and consistent entity.

That is not to say that the orchestra sacrificed the details. The mellifluous passages for clarinet in the Andante and the theme for cello taken up by the horn in the third movement stood out as examples of plenty of attention being given to details. It was also not lost on the orchestra that the work depicts the germination of a small musical idea into a fully-developed storm which, after whirling around repeatedly over a wide terrain, spends itself and peters out quietly. Just as the orchestra avoided making a dramatic entry at the start, it was also content to go out in a whimper with a much powered-down repeat of the emphatic opening chords.

By its very nature, atonality is particularly suited to the expression of amorphous and indescribable anguish. Sandwiched between two unashamedly Romantic symphonies, Webern’s Six Pieces for Orchestra brought this to the fore. The work records the composer’s response to the death of his mother. In sharp contrast to the luxuriance of the other two symphonies, orchestration in the Webern pieces were sparse but poignant. Lone statements on woodwinds, sustained passages on horn and a trombone crescendo help accentuate desolation in the first two pieces. In the fourth piece, which according to the composer is a funeral march, a sharp statement by the piccolo follows a soft rumble in percussion that eventually builds into a crashing explosion. The bassoon, plunging the depths of the lowest register underneath the flute and clarinets, suggests the onset of tranquillity, and the harp has the final say in bringing the suite to rest. Simon Rattle and the Philadelphia Orchestra’s approach to the Webern pieces was measured but effective, delivering the emotional content with well-controlled and suggestive atmospheric concoctions.

Written during a stressful period in his life as music director to the city of Düsseldorf, Schumann’s Symphony no. 3 in E flat major, “Rhenish” is surprisingly upbeat, apparently inspired by a sojourn to the Rhineland. The five-movement structure of the work harks back to Beethoven’s Pastoral Symphony, but it is not overtly programmatic. Nevertheless, suggestions of extra-musical ideas are discernible, such as the apparent depiction of a solemn church ceremony in the fourth movement, and the simple elegance of rustic country scenes in the Scherzo.

Hardly had Simon Rattle steadied himself on the rostrum than he launched into in a brisk tempo, leaving us in no doubt that he thought the work was a joyful celebration of life, full of unbridled energy and imbued with a strong sense of forward motion. The audience clearly endorsed this approach, giving the orchestra a standing ovation.

It is fascinating how the same territory – the Rhineland – spawned a similar musical idea that developed into such divergent material in the Brahms and Schumann third symphonies. Simon Rattle and the Philadelphia Orchestra provided much insight into the differences between the works, but at the same time helped us understand how each in its own right is a well-conceived unit of musical expression.