Marin Alsop, conductor
The Rite of Spring: Stravinksy (1913)

Igor Stravinsky's The Rite of Spring is revolutionary even by today's standards. There's a brutality, an edginess, a primal quality that instinctually appeal to us, while tapping into a measure of fear. It anticipates and prophesies the looming 20th century. Like all great art, the piece is filled with paradox and ambiguity. It is the most complex music ever conceived and yet it appeals directly to our basic animal instincts. Its theme of humanity shows us that no matter how advanced we become, we can't deny our basic human nature – we remain fundamentally tribal animals. The ability to show us the past and the future simultaneously is precisely what great art does.The Rite of Spring is a snapshot of who we are, why we are, what we are, where we have come from and where we are heading. With an orchestra of 120 musicians and a score filled with huge challenges, it is a conductor's dream come true.

Edmund de Waal, ceramicist/writer
Serenade for Tenor, Horn and Strings: Britten (1943)

This piece came out of an extraordinary moment in British cultural life. Written during the war, at a moment of enormous peril, it's about Englishness, full of pastoral poetry and English astringency, yet there's a toughness right from the opening notes. The voice, poetry and horn come together in an incredible series of songs, settings of poems by British poets. Poetry is behind almost all my ceramic work, and this idea of bringing different kind of poems together in a cycle that have such a powerful connection with each other is something I try to do in my own work. I can remember hearing it for the first time as a boy in the 70s in Lincoln Cathedral and being absolutely transfixed and also bewildered – I couldn't understand what was happening. It was probably my earliest musical memory of something being completely different.

Fay Weldon, writer
The Unanswered Question: Charles Ives (1906)

Charles Ives' The Unanswered Question is short but numinous, the lyrical tonal music of the past fighting it out with an atonal future. Over an ethereal background of strings, what Ives called "The Perennial Question of Existence" is repeated in a five-note phrase trumpet phrase, answered each time by increasingly cacophonous chaos from the woodwinds. The last time, the trumpet remains unanswered and the strings fade into silence. Ives was a modernist despite himself, though no iconoclast – grounded as he was in an Emersonian belief in the benevolence of the immanent. He delighted to include snatches of popular song, traffic noise, the sound of two Sousa bands each playing different tunes in his music, and wrote to his publisher in 1905: "Please don't try to make things nice! All the wrong notes are RIGHT. Just copy as I have – I want it that way." It took a while, but today's audiences affectionately agree.

Will Gregory, member of Goldfrapp
Gesang der Jünglinge: Stockhausen (1955-56)

This work is now 57 years old, but it still sounds untarnished by age and diamond-like in its purity and sheer ambition. I like to think future generations will wonder at how a man armed with nothing but a tape machine and a few oscillators journeyed so far.

Nico Muhly, composer
Music for 18 Musicians: Steve Reich (1974-76)

This is one of the most important things that happened in music last century. It undid, in a very stylish way, the whole notion of romantic structure in music, and while it wasn't the first of Reich's pieces to explore this idea, it expands from a simple structure presented at the beginning like a concentrated paste. It employs a great combination of notated music with a somewhat free-form structure (it can last a variety of lengths), as well as needing a community of musicians listening to one another to really make it "go". It's music for, by and about friends playing together.

Rufus Wainwright, singer-songwriter
Saint François d'Assise: Messiaen (1975-83)

This opera encompasses the entire 20th century: it is very avant garde but at the same time tremendously romantic. There is an incredible spirituality at its base which gives it a timeless quality. I'm not a religious person, but I certainly appreciate it when music strives for the heavens. Also, what's more 20th-century then having a part for a theremin?

Vladimir Jurowski, conductor
The Rite of Spring: Stravinsky (1913)

The Rite of Spring is at the heart of the revolutionary process that was going on throughout Europe at the time. It's the piece where the west finally meets the east, and probably the first work in the history of European music that has been unanimously recognised as equally seminal to the development of both eastern and western music. In many ways it anticipated the cataclysms of the 20th century and the horrors of the first world war and the Russian revolution. You can hear everything in it. Its musical language might seem almost simplistic to us today, having been through the entire development of 20th-century music, but the main issue with the piece is the never-ceasing power of its rhythmic inventions. To my mind, Stravinsky's artistic achievement in this work is equal to any of the 20th century's scientific achievements. It's a cornerstone of contemporary music and hopefully always will be.

Martyn Brabbins, conductor
Symphony No 7: Sibelius (1924)

Of the 20th century's numerous symphonic composers, Jean Sibelius is an unparalleled genius. His symphonic utterances are so profoundly individual, and yet, despite their inherent Finnish quality, speak a universal musical truth. His seventh and final symphony is perhaps as close to symphonic perfection as a mortal can achieve. The organic unfolding of the musical argument is unerring in its inevitability. The 23-minute span – brief in comparison to most 20th-century symphonies – encapsulates a musical journey of such concentrated perfection that I feel awed and slightly terrified when I conduct it. It is perhaps not altogether surprising to learn that despite living for a further 30 years, Sibelius never felt the need to complete another symphony after this one.

Barbara Hannigan, soprano
Lulu: Berg (1934)

Berg's opera came from the end of decadent Romanticism and at the beginning of the new 12-tone world. The complex score is lush and rich with colours: lyrical, mad, sometimes jazzy, sometimes evoking Bach in its architecture. It remains vital today. Each time it is performed, it asks: "Let's look at the protagonist again, let's not make her a caricature of a harlot and manipulator." She is a person with a past who is damaged and hurt and who is doing everything she can to survive.

The opera was groundbreaking, too, in terms of its portrayal of the people and society around Lulu. Look at the lesbian character, Countess Geschwitz. The sympathy with which Berg treats her is touching: he never ridicules her. It feels as if Berg was working out so many issues for society and for the musical world in his harmonic searching.

Everyone in the opera falls in love with Lulu, and, having sung the role for performances in Brussels, I also fell in love with her. My way of gauging what are the most important pieces for me is how hard it is to let go of them when they are over. I wake up every morning and I'm still with Lulu.

Nicholas Collon, conductor
First Chamber Symphony: Schoenberg (1906)

This work plunges us headlong into the sensual, vibrant and brilliant melting pot of early-20th-century Vienna. And yet, written for a chamber ensemble of 15 musicians and lasting only 25 minutes, it rejects the grand canvasses of the late-19th-century composers and daringly launches a new aesthetic, setting a precedent for the comeback of the chamber orchestra as a vital and expressive vehicle for 20th-century music. The music explodes into life with a horn sounding a fanfare to the new century, and weaves an exhilarating journey that harks back to Brahms, yet looks forward almost to Boulez. A performance in Vienna in 1913 caused a near riot, a month before the more infamous Rite of Spring premiere.

Annie Freud, poet
West Side Story: Bernstein (1957)

It just has to be the 1961 version of West Side Story, directed by Robert Wise and Jerome Robbins, starring Natalie Wood, Richard Beymer, Rita Moreno, George Chakiris and Russ Tamblyn. The music has such an extraordinary emotional range and depth – curiosity, excitement, passion, worship, anger, hatred, terror, sarcasm, contempt, charm, grief, despair, emptiness – and yet the whole is so tightly woven; every single song is a masterpiece. Just writing these few words of admiration about this great work makes my heart beat faster and fills my eyes with tears.

Marcus du Sautoy, mathematician
Quartet for the End of Time: Messiaen (1941)

Our concept of time and space were totally disrupted by Einstein's breakthroughs at the beginning of the 20th century. No longer was there a single timeline, or a fixed frame of reference. Time could go at different speeds. Space could contract. For me, the Quartet for the End of Time captures some of the spirit of that scientific revolution. The story of its composition reflects one of the major historical events of the century: the second world war. But it is the music that resonates with this new view of the universe. The opening movement exploits the mathematics of two prime numbers to create a sense of destabilised time. The piano part plays a 17-note rhythmic sequence against a 29-note harmonic sequence. The two different primes create a sense of two different timeframes that never quite get in sync.

Alex Ross, critic and author of The Rest is Noise
Six Pieces for Orchestra: Webern (1909)

In the history of painting and literature, the shattering of artistic norms at the threshold of modernism is celebrated almost as a sacred moment: the explosion of abstraction in Picasso and Kandinsky, the eruption of interior consciousness in Joyce and Woolf. In music, the incursion of the alien is nowhere more intense than in Webern's Six Pieces for Orchestra, composed in the wake of Schoenberg's break with tonality. At the end of the fourth piece – a tenebrous funeral march, written in memory of the composer's mother – massed percussion creates the first great sonic maelstrom in musical history. Wisps of lyricism surround that central crisis, like circling birds. "Everything hovers," as Webern once said. These, too, are sacred emblems: radical icons of a nameless new religion.

Patricia Kopatchinskaja, violinist
Violin Concerto: Ligeti (1990)

Ligeti's Violin Concerto is the best violin concerto after Beethoven. Ligeti is one of the most impressive figures of recent times. Like a scientist in a laboratory, he never did anything routinely, but for every single piece he invented new methods and solutions. While his fellow Hungarian Bartók used the eastern European folklore as material and inspiration, Ligeti uses anything he can find – for example, in the violin concerto there are several okarinas, instruments that are more than 10,000 years old. He wants them deliberately out-of-tune, which produces an exhilarating effect. He also uses elements of the Notre-Dame choir school of the 12th century, Hungarian folk melodies and complex Bulgarian rhythms. The orchestra consists of only two dozen musicians, but they do not provide just an accompaniment – everybody is challenged to their musical and technical limits, as is the soloist. This might sound very intellectual, but Ligeti is like a child at play, with humour, cheekiness and temper tantrums. And if everybody meets the challenge, this concerto becomes a big spaceship: complicated, luminous and nonsensical, taking off and flying to Neverland.

Mark Elder, conductor
The Rite of Spring: Stravinsky (1913)

I have to choose the Rite of Spring. Due to its ritualistic subject matter, aAs the chosen girl dances herself to death, Stravinsky found a musical language that broke all the barriers in terms of what an orchestra can sound like. The severe pagan ritual that the music describes so eloquently demanded a new sort of beauty. The ballet's birth in Paris in 1913 after weeks and weeks of tense rehearsals was a famous disaster. Yet it wasn't only the unfamiliarity of the musical style that was found so shocking but also the extraordinarily unexpected and crude choreographic style that Nijinsky designed. It was only later as the piece began to be heard in the concert hall that audiences could begin to appreciate how powerful, elemental and beautiful this score is. To me there are two overwhelming elements in the Rite's achievement: its use of rhythm and its astonishing orchestral colours. It has had an enormous impact on musicians and should continue to astonish 100 years after its premiere. The complex rhythmic structures that occur throughout its 35-minute length released a rhythmic freedom in Stravinsky's music, and for other composers too. Indeed, it's difficult to imagine the soundworlds of some of the later giants of the century – Harrison Birtwistle, Steve Reich, György Ligeti or Pierre Boulez – without the Rite's intense and courageous influence.

Gillian Moore, head of classical music at the Southbank Centre
Amériques: Edgard Varèse (1918-21)

My contribution to the soundtrack to the 20th century would be Amériques by Edgard Varèse. This is Varèse's New World symphony, written shortly after he arrived in New York from Europe. But where Dvorak's late-19th-century America sang folk tunes and spirituals, Varèse, just 25 years later, was dancing to a new music of the machine age: the clanking of overhead railways, the hooting of foghorns on the Hudson river, the wail of police sirens all find their way into this huge urban symphony. But, even with its supersize lineup (130 orchestral musicians), it's not all sound and fury: there are sinuous melodies, seductive jazz-tinged dances and a nod or two to Debussy and Stravinsky.

Shara Worden, singer with My Brightest Diamond
Symphony No 3: Górecki (1976)

While the 20th century held wondrous feats of innovation and discovery, the invention of the internet and trips to the moon, as well as new musical languages created by composers such as Debussy, Schoenberg and Stravinsky, we also see it as the century in which we learned how to destroy ourselves with the invention of the atomic bomb. For this, I would like to offer Górecki's Symphony No 3, Symphony of Sorrowful Songs, perhaps not as the greatest piece of music from the last century, but as a meditation upon the value of all life, and the imperative that we restrain ourselves from making the same grave errors in the coming centuries that we made in the last.

Oliver Coates, cellist
Mortuos Plango, Vivos Voco: Jonathan Harvey (1980)

This masterpiece of organised sound is derived from a spectral analysis of the tenor bell at Winchester Cathedral. Harvey forged the sound of the bell with the pure treble voice of his son, then a chorister in the cathedral choir. The effect is heartbreaking. The purity of Harvey's concept synthesises the heavy tolling of history with his optimism for the future.

James Blake, songwriter
Three Elegies for Nine Clarinets: Gavin Bryars (1994)

This piece is, for me, a celebration of the timbre of the clarinet. Taking a magnifying glass to this instrument, we can enjoy in detail the clicks and breath, and even multiphonics that make the clarient so sonically rich. Three Elegies also celebrates restlessness in harmonic progression. Just as you relax into a chord, one clarinet arrives to challenge it, and the others tend to yield. I like the way the nine instruments all play a distinct role, at times pairing up and at other times swinging into pendulous sync. Here Bryars is not afraid to "change scene", as in film.

Michael Clark, dancer/choreographer
The Rite of Spring: Stravinsky (1913)

There really is no other choice. Not only did Stravinsky fearlessly dare to venture into a new, undiscovered sonic landscape, anticipating what we would spend the rest of the century trying to catch up with, he also the world a piece of music that could only be completed by dance – the sacrificial dance. Through total disregard for most of the established conventions of 19th-century classical music, his radical use of tonality, dissonance, metre, stress and, most of all, rhythm (he elevated rhythm in itself to the dignity of art), Stravinsky created music that sounded like what people were feeling. Stravinsky foresaw the real conflict of war and revolution, life or death confronted on a daily basis – the willingness to die for one's beliefs. The notion of self-sacrifice for the greater good: art. This work is the soundtrack to the 20th century, a map of the internal, psychological world we were to inhabit for the forseeable future. A bleak terrain. A battleground of contradictory impulses, ideologies and desires.

Simon Callow, actor
Il Tabarro: Puccini (1918)

Puccini, something of a musical magpie, and not exactly progressive, nevertheless had his finger on the pulse of the 20th century to an astonishing degree – sentimentality, cruelty, hedonistic abandon, alienation. Many of these elements are to be found in his works – Madama Butterfly, Turandot, Tosca – but for me his one-act opera Il Tabarro, part of the Trittico, gives us as concentrated a dose of 20th-century blues as you can find: even the love-making in the big duet is edgy, tense and unfulfilled, and the scattered, fragmentary scene of people supposedly having fun is dry and grim, while the great tenor aria is an almost unbearable cry of pain on behalf of the underclass.

Jeremy Pritchard, bassist with Everything Everything
Koyaanisqatsi : Philip Glass (1981-82)

This was Philip Glass's score for the Godfrey Reggio film of the same name. Koyaanisquatsi translates from Hopi language as "Life Out of Balance". It seems apposite for the 20th century: cinema itself is the quintessential 20th century medium, and this film depicts the exponential acceleration of technology and human development, and the gradual ecological and spiritual erosion, and loss of control inherent in that. There is no dialogue or plot, just a kind of scintillating multimedia tone poem. Glass's compositions for massed brass, voices, organs and synthesisers are by turns tense, portentous, frightening, gloriously exhilarating, curiously beautiful and utterly desperate, reflecting Reggio's various plateaus; cave paintings, clouds, the frenzy of mass-production, a nuclear plant on a pleasure beach, the thronging streets of American cities, the slow motion explosion of the Atlas-Centaur rocket in 1962. The whole piece has a century-wide feel to it.

Jude Kelly, artistic director, Southbank Centre
Quartet for the End of Time: Messiaen (1941)

"There shall be time no longer" . This haunting phrase from The Angel of the Apocalypse is inscribed by the composer, Messiaen on his score for a piece that grips and shakes me whenever I hear it. Messiaen was among the thousands of French soldiers rounded up by the Germans in 1940 and transported to Stalag VIII-A, a Prisoner of War camp near Dresden. A catastrophe of civilisation was unfolding across Europe and this musical response, written and performed in the camp by four survivors is hauntingly elegant, agonisingly tense but shot through with love and pity. How can the barbaric, the merciless, the unfathomable be expressed? Messiaen finds sounds, form, and pattern that vanquish any thought that the soul can be destroyed. The beauty of this music stands regardless of its origins but its particular history also reassures us that art offers a way to transcend despair.

The Guardian is a media partner for the Southbank Centre's year-long The Rest is Noise festival, which starts on 19 January 2013. Details: therestisnoise.southbankcentre.co.uk