Right, it doesn't involve playing notes together the same way it's done in Western music.
I guess I misinterpreted what you were saying -- the Indian notes are still derived by looking at notes which sound harmonious when played together, roughly the same way Western notes are derived. They are not usually played together on the same instrument like you would with a piano or a guitar. Harmony between vocal parts is not uncommon as is harmony with background instruments like the tanpura. But yes, Indian music doesn't have harmony in the same sense as Western music. But the origins of the notes are very similar.
I spent a lot of time studying this myself because I was fascinated with the fact that these 12 notes in particular seemed ubiquitous in many music systems, and that there wasn't any immediately obvious reason as to why these notes sounded pleasing. Ultimately learned some music theory in the process (I've studied Indian and some Western music, so a lot of it was stuff I already knew, but not in concrete form), but never in a very structured fashion -- more along the lines of asking people and reading snippets.
Put this book on my list, sounds like a structured way to learn something I've been super interested in for years.
I guess I misinterpreted what you were saying -- the Indian notes are still derived by looking at notes which sound harmonious when played together, roughly the same way Western notes are derived. They are not usually played together on the same instrument like you would with a piano or a guitar. Harmony between vocal parts is not uncommon as is harmony with background instruments like the tanpura. But yes, Indian music doesn't have harmony in the same sense as Western music. But the origins of the notes are very similar.
(I'm talking about classical Indian music, btw)