The first DIN standard for instance gave only the gamma to be processed to (0.8).
The ASA standard started also from a level above fog but instead of precribing a certain gamm it characterized a certain point with a given position with respect to that point above fog.
That is not my understanding. In fact, it's pretty much the exact opposite of my understanding.
The original DIN standard was, I believe, for processing to gamma infinity (the maximum gamma obtainable before fog started to bring the contrast down again) with a fixed density speed point.
The original ASA standard was based on the Kodak fractional gradient criterion, which greatly reduced the importance of development time. The speed point was taken as a point where the tangent of the slope of the D/log E curve was 0.3x that of the tangent of the slope between the speed point and another point 1.5 log units to the right.
This was theoretically superb but hard to determine so the later (post-1959) ASA standard and the current ISO standard are based on a fixed density with a gamma criterion that looks a bit odd but approximates surprisingly well to the fractional gradient point. This is 0.8 log density at a point 1.3 log units to the right on the exposure axis.
For those who want lots of theory on this, read Perfect Exposure, which I co-wrote with my wife Frances Schultz (David & Charles/Amphoto 1999). The text was checked by a member of the ISO film speed committee so it's reasonably accurate -- though all errors are ours, not his.
Finally, the ISO arothmetic standard for 1/3 stop speeds seems to me to be based on common sense. You're going to want round numbers such as 100, and the smallest meaningful variations are 1/3 stop (which is also the interval of the DIN log standard), so it all flows from there.
Yes, you could have ISO 73 or ISO 140, and indeed ISO testing gives you those numbers on occasion; but by convention (and ISO standard) these are rounded to the nearest 1/3 stop number, usually upwards, though with monochrome, they are sometimes rounded downwards to give a fraction of a stop more latitude for under-exposure. For example, I'd expect more FP4 Plus (ISO 125) to be ISO 130-140 than ISO 110-120. Do not forget batch variations, which are much smaller today than they used to be but which were commonly +/- 1/3 stop as recently as the 1970s.
Several film speeds don't correspond to traditional shutter speeds: you get ISO 12, 25, 64 and 80 but seldom 1/12, 1/25 (except on old shutters), 1/64 and 1/80.
Cheers,
Roger