You'll find the timeline helpful.
Schoenberg's aim at the beginning of the 20th century, was to break the stranglehold of classical music harmony and to free music so that it could develop unfettered by the past.
His method was to eliminate any sense of key, of familiarity, of knowing where one was in the music, to cast the listener adrift and send them into unknown territory. He created a totally chromatic expressionism.
His method of tone rows and serialism was his way and he developed this atonalism with his two main composer pupils, Alban Berg and Anton Webern, in what has become known as the Second Viennese School.
Music Concrete and Experiment
Music concrete was a way of composing by incorporating and expressing real sounds - the sounds of the street, the city, the natural sounds created by any means, including musical instruments, but no longer limited to them. The original exponents were Pierre Schaeffer and Edgar Varese who paved the way for experimental music of all kinds.
The technique, developed at the end of the 1940s, was to record sounds, alter them in any way desired and then edit them into a montage.
Electronic and Rock Music
Music concrete was already using recording methods and electronic means to alter the music, however, it was rock in particular that paved the way to applying technology to music composition. This was clearly applicable to both genres and since the 1960s there has been crossover between rock and contemporary classical, both in the technology and collaboration between the creators of new music.
The electronic synthesiser began to enter the composer's armoury and to appear onstage alongside drum kits and electric guitars.
Terry Riley achieved fame by exploiting a crossover between his minimalist music and the huge market available through rock, namely with his "Rainbow in Curved Air" and "In C". Composed in 1964, "In C" was written for any combination of instruments.
A difficulty with experimental music is that it alienates audiences and thence the funds for investing in further development. Often, contemporary composers simply weren't interested in pandering to an audience.
A change occurred with the advent of minimalism, characterised by simple harmonies again and repetitive rhythmic figures that shifted bit by bit to create original but accessible music.
Composer, Michael Nyman, coined the term "minimalism" applied to music and its best known exponents are Terry Riley, Philip Glass and Steve Reich. They rescued contemporary classical music from oblivion.
Synthesised music has continued to be "the norm" and now in the digital age composing techniques have moved on from pen and paper to laptop and software.
A laptop can be equipped with not only fully flexible composition software but a comprehensive recording facility with Digital Audio Workstation, having the ability for anyone to make their own music concrete, then play it to the world via the internet.
The spirit of music can now be anything, anywhere, any time.