Regarding your other question, the smallest difference, once upon a time (early 1970's and earlier) a common "racing" gearing was the so-called "half step" gearing. A typical set up would be 49/52 chainrings and something like a 14-16-18-21-24 freewheel. The gear ratios on the smaller chainring were half way between those of the larger, so lowest to highest gears would be 1 6 2 7 3 8 4 9 5 10. You probably wouldn't use gears 6 and 5 very often. As straight block freewheels and more gears became more common 42/52 and 13-14-15-16-17-19(-21) became the standard. A touring set-up would be "half step plus granny" - an example being 36/49/52 with a 14-16-18-21-24-28.

I really liked the half step gearing. You could have the "fine tuning" gear change - just change chainrings, or a slightly wider gear change by switching freewheel cogs. The front derailleurs always shifted really smoothly with only the 3 tooth difference. Nowadays brifters, indexing, many more cogs, and freehubs are all great improvements, but with the technology and parts of that era half step gearing worked well. I can just imaging using it today - since they probably wouldn't remember it or understand the reasoning or principle behind it, I can just imaging my cycling buddies reaction to my having a 3 tooth difference in my chainrings. Maybe I'll set a bike up that way sometime just to see their reaction.