Up into the 1960's the model railroad magazines and literature sometimes referred to "Q scale".
John Armstrong's book "Track Planning for Realistic Operation" (1963 version) mentioned Q scale as using 1.177" track gauge for 1:48 scale, so it was accurate for standard gauge. However, I just saw in Wikipedia the explanation that Q scale used 1.25" track gauge and 1:45 scale. Their info came from another model railroad forum, but the forum does also mention Q as 1.177" gauge. But the forum responses aren't necessarily complete and accurate. There is also mention of "O17" scale, using 17/64"=12" with 1.25" track gauge.
https://en.wikipedia.org/wiki/...ort_modelling_scales
In any case, the Q scale label seems to have fallen by the wayside in the 1960's. Modifying the track gauge would make the trains incompatible with mainstream O scale/O gauge, and was probably only used by diehard scratch-builders in the earlier years of the hobby.
Maybe some of the collectors of old O-scale equipment have run across rolling stock gauged for 1-3/16" ?