One of the most frustrating things is trying to make a long rope out of all sorts of short pieces, especially when they are different thickness. So here is the splicing knot for different sized ropes.
Make a loop with the larger rope. Run the end of the smaller rope through the loop. Wrap it around the base. Now comes the unexpected part -- thread the end of the smaller rope just under itself, not back through the larger loop. Pull that tight. If you tape the ends together it will last forever.
On TV, I showed you the trucker's hitch again for cinching down a load on the top of the car. Since I did it a couple of years ago and have all the images already in the database, check here for the trucker's hitch.