There are revolutions and there are revolutions. In the language of the early 20th century and its musical developments and the way they are sometimes told, you might think that – wherever you were in Europe between 1900 and 1914 – it must have sounded like creative explosions were going off in all directions. Mahler – boom! Schoenberg – ouch! Stravinsky – kapow! Debussy – sacre bleu! Ives – dang! Strauss – mein Gott! But if you take a cross-section of musical culture at any point in the early 20th century, you will surely find that there is no clear sense of what was, or was going to be, important among contemporary audiences and critics. They had different priorities to the way history has ended up telling the story of early 20th century music, and what programmers now deem to have been the most influential pieces and composers.

Take Schoenberg's Second String Quartet, which the Diotima Quartet will play tonight at the Queen Elizabeth Hall. It may mark the moment the composer gives up on key signatures in the final setting of poems by Stefan George, but its influence, outside a tiny circle of pupils and admirers, was negligible. Musical culture did not change on 21 December 1908, when the piece was first performed in Vienna. Composers did not suddenly start composing without the musical anchors of tonal centres, and, again, outside a miniscule musical coterie, the idea that this piece would herald a new era of atonal sound, fury, and experimentation would have seemed crazy. It certainly did to the critic of Signale in Berlin, who wrote after the first performance: "If I nevertheless abandoned my customary reserve, I only proved by it that I suffered physical pain, and as one cruelly abused, despite all good intentions to endure even the worst, I still had to cry out."

But critics were saying the same thing about Reger and the "astounding aridity and poverty of invention" of his decidedly conservative, to our ears, Sinfonietta in A Major; about Debussy, whose opera Pelléas et Mélisande "eliminates the melodic element, and this marks a step backward", and whose La Mer "avoids all that might resemble a melody"; about Scriabin, with his "formless melodies" and "acrid harmonies". Schoenberg did not have the last word on critical opprobrium, and his supposed "revolution" was simply not heard as such at the time. Rather, Schoenberg's music was just one far-out option among many.

But none of them were revolutionary in the sense of, you know, inspiring revolutions or marking a complete break with the past (that came later in the century). In fact, the most radical thing about Schoenberg's Second String Quartet when you hear it today is precisely that there isn't a big musical signpost saying: "No key signature ahead – beware!" The whole point is that you're not supposed to hear when that happens. Throughout the piece, Schoenberg wants to create a seamless transition of melodic ideas, febrile harmonies and fluid modulations, so that – when you arrive at the final movement – you don't suddenly think "Atonality, here we come"; rather, thanks to the internal logic of the music, you're prepared, both musically and emotionally, for the visionary meditation of Entrückung and its "air from another planet". (Air, however, that never loses sight of the gravity of tonal centres, even if the music seems to float above them rather than settle in a particular key.)

Schoenberg himself never liked the term "atonality". "To call any relation of tones atonal is as little justified as to designate a relation of colours aspectral or acomplementary," he said. "Such an antithesis does not exist." In fact, one way of thinking about Schoenberg's quartet is a post-Brahmsian play of musical motives allied to post-Wagnerian sensuality, with a healthy dose of the old-fashioned romantic ideal of subjective expressivity: not really that new at all, in other words.

A 1913 caricature from Die Zeit: The Upcoming Schoenberg Concert. Photograph: Imagno/Getty Images

My suggestion is that you don't listen to the Second Quartet expecting a musical explosion. Rather, you treat it the same as you would any other string quartet (well, any other quartet with soprano soloist – like, say, Brian Ferneyhough's fourth) and relish the chance to visit Schoenberg's planet of heightened expression.

There was, however, one composer who really did create a new way of thinking about music – well, "new" in the sense of fusing aspects of 15th-century pitch and rhythmic structures with contemporary languages – and you can hear his music on 29 January with the London Sinfonietta. Anton Webern, Schoenberg's pupil, inspired an artistic avant-garde after his death in 1945, when composers such as Boulez and Stockhausen realised what was going on underneath the often quiet, crystalline (and always short) surfaces of his music. Webern wrote music in which the recent, romantic past is hardly referenced at all, music that makes Schoenberg and Berg seem like old masters rather than young firebrands: all right, if you insist, a (reluctant and posthumous and metaphorical) revolutionary … More on him later, during the The Rest Is Noise!