Originally Posted by
LesterOfPuppets
It's not odd numbers but prime numbers. It's a consideration for fixed gear. Having prime numbers increases the number of skid patches.
I knew that part of it, but there is also a part that has to do with chain wear. On fixed gear ratio (not fixed freewheel, but fixed gear ratio), chain wear all falls on the roller units or pin link units with even number sums, and it gets balanced between them with odd numbers. It has been a lifetime since I worked with chain drives in power transmission applications, but I kind of recall that same rule in specifying power transmission systems.