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Brahms's ubiquity on concert programmes means he's a composer who needs more rescuing than most from the accreted myths not just of performance practice, but of how we think about the man and his music

Conductor Riccardo Chailly and the Leipzig Gewandhaus Orchestra are rethinking Brahms this week and next at the Barbican in London with their complete cycle of symphonies and concertos, performances that are trying to strip away decades of preconceived ideas about how to play this too-often taken-for-granted music. It's precisely Brahms's ubiquity on concert programmes that means he's a composer who needs more rescuing than most from the accreted myths not just of performance practice, but of how we think about the man and his music; hoary old ideas like the beard, the self-pity, the (supposedly) buttoned-up academicism and historicism. But even without a great orchestra and concert hall at your disposal, we can all approach Brahms from different angles than the ones we're used to. So forget the beard, ditch what you think you know about the 19th century's "leviathan maunderer" (one of Bernard Shaw's most lacerating Shavianisms) and here's five unexpected reasons to embrace Brahms.

1. Brahms takes five: here's a whole piece with five beats to the bar. This piece - the second of his op 112 set of six songs - is a tiny, brooding night-terror for four voices, setting Kugler's poem of nocturnal phantoms and lachrymose visitations. The strangeness of that five-beat metre and the churning, uneasy piano part makes for a brilliantly dark piece of world-painting.

2. Brahms the lover: in his Second Sextet for strings, Brahms transliterates the letters of the woman to whom he was engaged in the late 1850s, Agathe von Siebold. The first movement enacts a kind of emotional catharsis, turning her name into music - A-G-A-H (German spelling for B) -E - at one of the music's most passionate climaxes. Their engagement was broken off when Brahms couldn't face the idea of being an unsuccessful composer - it seemed at that time that was to be his fate - and having to be pitied by his wife. A strange world, mid-19th century marital politics... In any case, Brahms both commemorates Agathe in this 1864 work, and consigns her memory to the past. The Second Sextet is simultaneously one of Brahms's most complete chamber works, but it's also his most passionately personal.

3. Brahms the German nationalist: the German Requiem, the largest single piece Brahms wrote, is a remarkable piece for its humanism, its fusion of historical models from Schütz to Handel, from Bach to Schumann, and for its combination of grand, public scale and emotional intimacy. Brahms composed this huge choral work knowing that it would be a monument of late 19th century German culture, fulfilling one of Robert Schumann's predictions about the kind of composer he would become. The Requiem was premiered in 1868, the same year as Wagner's Die Meistersinger von Nürnberg; they're both competing visions of what a contemporary German culture could be, on the eve of Bismarck's unification of the country. Brahms's is liberal, conciliatory in its relationship with the past, humanist and anti-ideological; Wagner's - well, isn't...

4. Brahms the pleasure-seeker: the Liebeslieder Waltzes are Brahms at his most unbuttoned, they are a transcendence of the gemütlich Hausmusik of German amateur music-making in the 19th century into little jewels of pure vocal joy.

5. Brahms the postmodernist: the finale of the Fourth Symphony is a passacaglia, built on one of the strictest musical forms there is, with a repeated eight-bar theme that ties you in as a composer to a mere handful of options of key, harmony, and expressive possibility. Or so you might have thought. But Brahms closes off his symphonic cycle with a piece whose emotional intensity comes precisely from its formal constraint. What you hear in this music is a continual friction between implacable structural rigour and sheer expressive power. (For some, anyway: Thomas Adès, for one, hears this piece as a musical sham!) It's a forerunner, in a sense, of the kind of neo-classical historical objectivity that Stravinsky would attempt, but all of that historical referentiality paradoxically means that the finale of the 4th is also Brahms at his most personal. No-one else in the 19th century could have conceived this music's white-hot concentration and compression - as Chailly and the Gewandhaus will surely reveal next week.