Not really they're 2 different ways of looking at music.
Our Indian system, you could say is based on intervals. A lot revolves around vocals in Hindustani Classical, hence most of the instruments do not necessarily have one standard tuning.
Western classical music however, has named the frequencies hence there can be only one C. This, you could say, standardizes all instruments. Maybe it's because western classical music evolved with complex arrangements for multiple instruments.
Staff notation provides a very standardized way of reading music. If 2 people play reading the same notation it isn't possible for them to be playing in different keys.
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