For the record, these are [https://groups.google.com/g/comp.sys.sinclair/c/-zCR2kxMryY Matthew (Gasman) Westcott measurements] (normalised) on its ZX Spectrum: 0, 0.0105, 0.0154, 0.0216, 0.0314, 0.0461, 0.0635, 0.1061, 0.1319, 0.2163, 0.2973, 0.3908, 0.5129, 0.6371, 0.8186, 1
ay3 manual show different values: 2 steps down = half values down. Thus, the theoretical formula is f(x) = 2 ^ ((x - 15) / 2) with x between 0 and 15.
This is the volume table used by BSC: