About Q scale....100+ years ago, Marklin in Germany offered electric trains in track gauges from IIRC Numbers 1 through 4, with No.1 gauge (1.75", today's "G gauge") being the smallest(!). When they created an even smaller size, 1.25" gauge, they had to call it 0 (zero) gauge, which we call O (like the letter) gauge.
If you divide it out, the correct scale for O is 1:45, or 17/64th" = 1 foot. Virtually no one liked that; too hard to work with. In the U.S., we decided to use 1/4" = 1 foot, or 1:48 scale. So US O scale trains are running on 5' gauge track instead of 4'-8-1/2" like the real standard gauge. In Britain and Europe, they were more familiar with the metric system than us, so they went with 7mm = 1 foot, or 1:43.55 scale. That's why there are all those "O scale" automobiles from Europe that are 1:43 scale. It's also why HO ("Half-O") scale is 1:87.1 - it was developed in Europe, so is 1/2 of European O scale.
A few hardy souls in the 1930's, like Minton Chronkite, built layouts using 1.25" O gauge track, but with trains (mostly scratch)built to the correct 1:45 scale. That's what came to be called "Q scale". Later O "fine scale" developed, which is 1:48 scale trains but using the corrected narrower track gauge.