The rope halter is 1/4" rope, and I don't know the size of the rope I used to add the "attachments", but it's a little smaller diameter rope. It's what I had. I wanted it to be flimsy enough so that when I tied on my mecate reins it would droop. Kinda like a slobber strap does. I tie a big enough knot with my mecate's so that when I release the pressure it drops from the weight of the mecate knot.
The knot I used to attach the smaller white rope to the halter is called a rolling hitch knot. I doubled up the white rope too. I basically held one end of the white rope in my left hand and outstretched my arm and pulled the rope into my armpit, then I doubled it back from my armpit to my hand. I tied on the top knot using the end in my left hand. I haven't cut the rope to length yet cus I wanna make sure the loops I get are big enough and it also helps to have something to grab and pull the knots tight. Then I tied on the lower knot using the free end of the measured length of rope. I cleaned up the knots and made sure the loops I created were a good size for me and then I pulled the knots tight. Cut your rope ends off and use a flame to melt the rope together at the knot.
Then do the other side. Line up your loops to make sure the left and right side of the halters loops are the same size then pull your knots tight. Cut your ends add some flame and voila. Riding rope halter. Slide your knots to where you want the pull to come from, adjust your fiador knot if needed so that the halter will fit on the horse in a good spot on the nose and you've got an excellent peice of tack.
If you have questions or want more detail I will get out the camera and possibly do a step by step.