[math-fun] Whisks

My 8-wire balloon whisk has wires that, read clockwise, follow the pattern 1 5 2 6 3 7 4 8, where 1 stands for the shortest wire, 2 stands for the second-shortest wire, etc. But Drew Lewis has an 8-wire whisk that goes 1 5 8 4 6 2 7 3. (He also has a 1 6 2 7 3 8 4 9 5 10 and a 1 4 2 5 3 and a 1 3 2, and I have a 1 2 3 4.) Is there any rhyme or reason (or math!) behind this diversity? (I personally would like to have a 1 5 3 7 2 6 4 8 whisk, since I’m a fan of the van der Corput sequence.) Jim Propp