The Schengen rules do not distinguish between "business" and "tourist" visas.
What you have is a uniform short-stay visa for multiple entries. It is valid for an unlimited number of subsequent trips to anywhere in the Schengen area, as long as the purpose of each of the trips is legal (e.g., you can't work).
Note that if the visa displays a "duration of stay" less then 90 of days, this is the total number of days you can be present spend in the Schengen area, summed over all your trips.
If the "duration of stay" is given as 90 all you have to comply with is the general 90/180 day rule. (However, in case of a 6-month visa where you haven't had any visa before, that works out the same as max 90 days over the entire 6-month visa validity).