I've programmed plenty of concerts and events in the past but this weekend's Occupy the Pianos is the first festival I've curated. As I structured the programmes for the three-day festival, a trend emerged, and I found that I'd chosen to present almost a canonical succession of piano work by pioneers of the American 20th Century. Which begs the question, what continues to breathe life into these radical pieces, and why do they deserve attention?

Julius Eastman, active in the 1970s in New York music, was black, gay and proud both ways. His music's simplicity, in the refined and fussy world of classical music, makes a statement in itself. As do the titles - Crazy Nigger, Evil Nigger, Gay Guerrilla - defiant and outspoken as Richard Pryor. This music has been largely unsung, or only sotto voce till now, and it has been thrilling to get to know Gay Guerrilla, one of the pieces I'm performing this weekend. It is a half-hour canvas, an open score of single tones and chords for multiple pianists, with parts perfectly accessible to amateurs, giving freedom in its interpretation yet tightly controlled. Culminating in a pile-up of the chorale A Mighty Fortress, it is also a bracing shake of the fist, radical still in its accessibility and fierce identity.

Radical artistic ideas can quickly become a (laughing) stock-in-trade, cheapened by misuse and overuse. Take minimalism. Starting as urgent, new and a breath of fresh air in the self-regarding hothouse of new music, it is today co-opted as figurative, or actual, soundtrack. Simple musical ideas represent a kind of shorthand for emotional states, where generations of composers had developed them into something vastly more subtle. As soon as a movement is established, its tone and accent can wear thin on the ears: the Next Big Thing becomes the Done Thing and is then over, passé.

Sometimes a trick of history can render a radical unfashionable. George Crumb, big in the 70s, created a music of Zeitgeist-harnessing power: mystical, ethereal, sometimes savage, covering themes from astrology, nature and myth. These were perhaps a means of escape from the Cold War and Vietnam (also referred to in his electric string quartet, Black Angels.) On the piano, Crumb's innovations are referred to as "extended techniques" - other ways of playing the instrument: on the strings, body or frame, or using tools to change the sound. These sounds will be familiar from film and TV, where muted thumpings and out-of-tune tinkling denotes "scary". Perhaps for this reason they fell out of fashion with composers of concert music, who also disdained the whiff of patchouli. Many composers, me included, are now re-embracing these sounds, maybe because conventional piano sounds are so loaded with history and memory.

Today, it's become a commonplace to point out that the US music scene of the 20th century was awash with pioneers: inventors of new modes of listening and tunings like James Tenney and Harry Partch, creator of rhythmic complexity and player-piano king, Conlon Nancarrow. Their music maintains maximum freshness and directness, be it complex or simple. The avant-garde went underground, slowly winning the hearts of fans, composers and specialists. I remember Nancarrow being championed in the 80s by Ligeti, and now he is name-checked by young composers as a major influence.

Radical thinking... pianist and curator Rolf Hind

John Cage and Julius Eastman knew each other in New York but had a spat when the latter interpreted a seemingly "free" score of Cage's "wrongly" (too much sex) which perhaps merely goes to show the creative tension that exists between two urges: to control or allow everything. In the public consciousness, John Cage is often seen as the prophet of Anything Goes. He posited the most radical alternatives to our conventions in music. Chance and the I Ching, technology and Finnegan's Wake, the rasas of Hindu art and the riddles of Zen. In some pieces, like the tiny piano work Seven Haiku, this teasing leads to a written riddle: the music is so detailed, the calligraphy so exquisite, yet the instructions cancel each other out. It's Zen brought to life as score-art and sound, and continues to fascinate.

Sometimes, as in his pieces for prepared piano, the radical new art finds its voice for the simplest reason. Cage only had a piano at his disposal in the 1940s. He wanted an entire percussion orchestra, so he started treating it with various objects. The resulting hybrid still sounds extraordinary, opening up undreamt of areas of expression.

Back in the 20s were other fashionable radicals of the Machine Age: George Antheil and Henry Cowell. Both lived as wildly as they wrote, with Cowell spending time in prison for sex with a 17-year-old male and Antheil holding the patent for a Secret Communications System which he developed with the actress Hedy Lamarr. Cowell was the first to thoroughly investigate the new uses of the piano, a precursor of Crumb. Antheil, the teen Bad Boy, thrilled audiences with violent machine-age outpourings. An outsider, the newly immigrant Frenchman Edgard Varèse combined these trends in an evocative blend: his Amériques, a score full of percussion and noise that depicts the violent beauty of Manhattan Metropolis.

The Founding Father of this US radicalism is Charles Ives, a composer who hardly heard his own work. Indeed he maintained a career in life insurance and wrote his visionary music on the side. His monumental Concord Sonata combines the many literary and popular influences of his America: ragtime, popular song, hymns; literature, both domestic and everyday (the Alcotts), and wild and visionary (Thoreau). Later audiences identified this urgent attempt to forge a cultural identity where one was needed, a radicalism that still thrills today.

The magic of Ives' story is that he credits his father, George - a bandleader - as a huge musical influence. Ives Senior recognised back in the 1870s that most audiences exposed to more than a C-G-C pattern "had to be carried off on a stretcher" - as Ives himself put it. He explored tuning systems, foreshadowing Partch, as well as many other musical experiments, and encouraged a current of questioning, a fanatical disregard for the nice or conventional, which flowed into his son. It's good to know, or to hope, that such radicalism is always Out There, when any citizen interrogates reality to create culture.

• Occupy the Pianos Festival, curated by Rolf Hind, is at St John's Smith Square, London, from 30 May to 1 June 2014.