Toothed belt == timing belts.
The normally accepted max transmission with belts is about 1:3 or 1:4.
Ie You need 14 teeth in HTD to get good belt wrap.
(12 teeth) is not good, although they are sold.
A 50 teeth pulley at 1:3.57 is already about 10 cm in diameter, and 30€ each.
You need good belt wrap (so small size cannot be too small) and as good a rigidity as practically possible (shorter belt is better).
E.g.
If your big pulley is say 140 teeth (for 1:10) the belt becomes very long, as you wont get good wrap near the small pulley.
And thus you have a lot of space between the pulleys, which reduces rigidity.
So for 1:10. you would get 238 mm between centers, a very long distance.
Here is a calculator.
http://www.sdp-si.com/cd/default.htmA 72 teeth pulley is 40$.
https://sdp-si.com/eStore/Catalog/Group/346#140 will be about 100$++. (Very little production).