Given that my father was György Ligeti, it wouldn't come as a surprise that I was exposed to the sounds of unconventional musics from a young age, even if I didn't start learning or playing music systematically until much, much later. So I'm not sure I can identify any specific piece that opened the door to new music for me, but Claude Vivier's Lonely Child has opened other doors. He's a fairly under appreciated composer (maybe not in Canada, but internationally) who I love and my father loved, too, and we agree that Lonely Child might be his greatest work. And he has become quite influential on my composing, mainly by showing me ways to break out of my own clichés and routines.
Like my father I love polyphony, and much of my music has been metrically complex and built upon a simultaneity of several musical strands, phrases, rhythms, or tempos. By contrast, Lonely Child couldn't be any less polyphonic. Here voices move in rhythmic unison, demonstrating how interesting exactly that can be and allowing me to access a ritualistic expression in my own music.
Perhaps even more intriguing are Vivier's harmonies. I've long experimented with microtonality, but mostly using electronics; I was unsure how to do this with conventional instruments given how much musicians work on not being "out of tune". Vivier was a sonic realist who incorporated microtonality without becoming caught up in mathematical dogma. The intonations he asks for are approximate, a compromise between musicians' habits and being just close enough to the alien in order for it to shine through. It's an exemplary way of reaching the unknown while allowing musicians to remain comfortable.
I'm a pretty free-thinking person and composer, but Vivier has freed me up quite a bit more.