That difference is best represented as 1/2-stop, whether or not the settings of the camera result in that complete 1/2-stop being used.
Still not correct.
With a 1/2 stop setting f1.2 is actually f1.1892.
With a 1/3 stop setting f1.2 is actually f1.2599.
With both a 1/2 & 1/3 stop setting f1.4 is actually f1.4142.
This difference is why the 1/2 stop setting between f1.4 & f2.0 is f1.7 not f1.6 or f1.8 as it is less confusing due to larger numbers allowing better numeric distinction between settings.
On a side note,
Is a f1.2 lens actually 1/6 stop wider when set to 1/2 stop increments when shot wide open???
Who are you, DxOMark, unable to consider a lens independent of a camera?
Forget about the camera for a moment. Compare an f/1.4 lens vs. an f/1.2 lens, just the lens - how much faster is the f/1.2 lens? Well, neither exactly 1/2 nor exactly 1/3 stop, but 1/2 stop is a better approximation.
To answer your question, 1D X with 85mm f/1.2L II, illumination constant, camera locked down, VF shutter closed, AV mode, ISO 100:
1/3 stop increments: f/1.2, f/1.4, f/1.6, f/1.8, f/2, metered shutter speed 1/50, 1/40, 1/30, 1/25, 1/20 s
1/2 stop increments: f/1.2, f/1.4, f/1.8, f/2, metered shutter speeds 1/45, 1/45 (no change from wide open), 1/30, 1/20 s
1 stop increments: f/1.2, f/1.4, f/2, metered shutter speeds 1/60 s, 1/30 s, 1/15 s