TT generally (in N. America at least) is 1/10" = 1' or 1:120. The track gauge is .471".
England adopted a scale of 3mm=1' or close to 1:100 (actually 1:101.6666) on 12mm track gauge. (nearly .471")
TT wasn't quite enough smaller than HO (compare S to O) and was zapped by N which really allowed a lot more running in cramped space.