This must be the best artistic representation of synaesthesia I've ever seen. It's a visualisation of John Coltrane's "Giant Steps."
Synaesthesia, besides being one of those words you can never be sure you've spelled right, means the experience of sensory overlapping. Tasting colours, seeing sounds, etc. For some reason, some very few people experience aesthetic experiences in this way, particularly music. They will often describe the colour of notes, or the way it feels in a tactile sense. It's an interesting phenomenon, because it raises the question of whether art is in some very real way a transgressive phenomenon to our sensory apparatus. I'm not at all sure that it is, but it's an interesting question.
Synaesthesia, as far as I recall, is a phenomenon which in addition to being found in music lovers, is mostly found in the schizophrenic, autistic, dyslexic, left-handed and in frequent users of recreational psychotropic pharmaceuticals. So what is it music does? I don't know. I doubt that anyone does. But it's powerful stuff, that's for sure.
The visualisation of "Giant Steps" works for me because, though not a synaesthetic, I would sometimes, when I was younger, visualise things mentally when listening to instrumental music, in something approaching synaesthesia. I think it was a way for me to translate what I was hearing into some sort of language. After a while, maybe because I started to "get" the language of instrumental music, I stopped doing this, but this video brought it all back. Something about the flow in it seems to adequately capture those visualisations.
"Giant Steps," incidentally, is impossible to play, let alone improvise over, on any instrument.