The effects of modernism on music are very controversial among musicians; some think that it is an important set of innovations, but others (like me) think that in general it is just are reversal of what music is supposed to be--rather than clearly presenting some meaning or thought, it deliberately obfuscates them behind layers of gimmicks and untraditional techniques, disguising an essential lack of inspiration or compositional skill.
The composer most closely associated with modernism is probably Arnold Schoenberg. He came up with a "12-tone scale" in which every tone is treated equally, as opposed to traditional 7-tone scales which eliminate 5 tones. Here is a recording of his Variations for Orchestra:
I can't stand this kind of music. To me, his twelve-tone scale can only express extremes of anxiety and fear; it seems like his music is defined entirely by its limits and can't convey any subtleties or beauty. I think that the reason Schoenberg is famous is maybe the same reason people read Finnegan's Wake--you get academic cred for claiming to see meaning in something that is, in fact, completely and intentionally devoid of it. I think Schoenberg admitted to a measure of this; he wrote "If it is art, it is not for all, and if it is for all, it is not art"--not only is this classist, but he is essentially saying that music people can enjoy is not worthwhile. I think that this exemplifies his reversal of the traditional criteria for good music. It is definitely new, but I don't think that makes it good.