Dantes associations do not appear to be correct, according to this link. 

the Moon resembles Grammar
Mercury may be compared to Dialectics 
Venus may be compared to Rhetoric 
the Sun may be compared to Arithmetic 
Mars may be compared to music 
Jupiter may be compared to Geometry 
Saturn may be compared to Astrology

I did not mean to say that they were right or wrong in any objective sense, but that the associations attributed to Dante in the article differ from those found here: Convivio, by Dante Alighieri.