Pandit Bhatkhande was one of the great systematizers of classical (north) Indian music. He humourously described the meaning of the word "Pandit" as one who knows a fair amount of theory but is just passable in terms of performance. I thought the humour could be extended to encompass my far greater ignorance in both directions! The theory of Indian music has been so poorly documented that there is some point in documenting it even without much knowledge.
It is well known that Indian music is melodic. Western music, too, used to be melodic, just as early Christians held beliefs very similar to karma-samskara in Hinduism. However, Western music got tied to a particular instrument: the piano. Then it separated the performer, who performed somewhat mechanically, from the artist who creatively composed the music. (If you are asked to think of a great name in Western music you might think of Beethoven or Bach or Mozart, who were all primarily composers, not performers; few people remember great pianists.) This led to the equal tempered scale widely used in Western music today. It also led to the greater reliance on harmony (in the technical sense of a number of notes being struck simultaneously). In Platonic terms, it is not clear that such music is good for the soul!
Here is a comment on a key difference between Indian and Western music in the context of the philosophy of mathematics. (Recall that Plato thought both mathematics and music were good for the soul, and also recall Whitehead's comment that Western philosophy is a series of footnotes to Plato.)