In reply to:

ataharre: Correa de cuero que sujeta la silla, y rodea los ijares y ancas de la caballería para impedir que el aparejo se corre hacia adelante-Pequeño Larousse Ilustrado

Sounds to me like the ataharre is the cinch and maybe something more. It is a leather strap that attaches to the saddle, runs between the ribs and the hips of the horse, goes around the rump (presumably the strap that goes under the horse's tail) that prevents the saddle from sliding forward. I'm not up on the terminology in English. Anyone know what it's called?