I am not sure, but 13 does sound about right. If you really want to know, find a copy of the Atlas of Middle Earth, it has a geographical distribution of all the languages of Middle Earth. I counted: dwarwish, quenya, adunaic (nemenorean), sindarin, westron, dunlending, rohirrim, the black tongue, orcish, druedain,[that's ten] (and what about the languages spoken by easterlings, variags, and haradrim?) I am sorry that I don't have the Atlas on me, but if anyone does, please, please check it up. I am sure they have it. By the way, there are definitely different dialects spoken as well. Such as beorning (Related to rohirrim) and the three groups of hobbits had their own language before they adopted westron. adunaic is the mixture of quenya and the tongues of man so I don't know if it would count as its own language.