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Two reasons for having a higher bridge. One is that there is less risk for the strings vibrating against the fingerboard. Second would be that you get more downwards pressure on the top from the bridge when it is higher. This creates more power. That being said, you want the strings to be easier to press down and a violin that can produce a large sound with low strings.
"with low strings"? So is it better to have a slightly higher bridge?
I am in process of fitting a new bridge and now wonder if I should allow a little more height. Is there a guide as to specific dimensions and proportions that should be considered?
@Ripton: Yes there is a book / guide.
USEFUL MEASUREMENTS FOR VIOLIN MAKERS by Henry A. Strobel.
This is the book that violin makers and luthiers consider, holy.
If you prod around, I think you can find a "PDF" of dimensions for what you're looking for. Check Pg.10 for measurements and Pg.22 for diagram.