How would you describe the differences between Indian and Western music, especially as it relates to the sense of pitch?

Indian and Western music differ considerably in terms of pitch because Western music adheres to the concept of absolute pitch, while Indian music predominantly focuses on relative pitch. Absolute pitch means that a note is represented as an absolute frequency, so if someone says "A2", that pitch can be mapped back to an exact frequency, and therefore can be reconciled among many different styles of music and instrumentation. 

In contrast, much of Indian music (both classical and non-classical) uses the concept of relative pitch, which means that the musician sets a tonic note (their base note) and that pitch is the starting point for all other notes. For example, if one musician were to say that a specific pitch were "sa" (one of the 7 notes in the Indian music scale), another musician would not be able to reproduce that note, since they wouldn't know where the first musician set their tonic. However, this has other advantages,  because a tune is defined in terms of relative pitch and can be reproduced easily among different musicians and instruments without the worry of an absolute frequency which cannot be reached by a specific musical range.