You can pick a coarser or finer scale depending on the particular need.
For a base twelve world, I would recommend using binary logarithms written in base twelve (“dublogs”) whenever possible; 0.1 on such a scale matches one semitone in a 12-note-per-octave equal-tempered musical scale.
Traditionally various "gauge" units have been used (e.g. AWG[1]), which are more or less logarithmic. Not quite as elegant as Renard/E series, but still craftsmen and engineers of the past were not completely oblivious of the utility of such scales.
One interesting thing about E-series is how it includes rounding in its definition. If we take E192 as an example, naively thinking the 186th value should be 10^(185/192) = 9.19479 which rounds to 9.19. But instead it actually is 9.09*10^(1/192) = 9.19967 which rounds to 9.20 (!). I haven't been able to figure out how you would come to that figure without needing first to calculate all the preceding 185 numbers.
edit: I just noticed that the E-series tolerances do not actually match the series in the upper end; for example for 2% tolerance, E48 actually leaves gaps in the range and would be more suitable for 2.5% tolerance. For 2% tolerance hypothetical E60 series would make more sense (and kinda also mirror E6 ~ 20% series). Same applies for E96/1% and E192/0.5% where E120 and E240 (or 1.25% and 0.625%) should have been used instead respectively. I suppose it doesn't matter for practical engineering, but it does tarnish the elegance a bit.
In a hypothetical base twelve world, they could instead use a log scale (think decibels) explicitly, and one nice option is to use binary logarithms, since then twelfths correspond approximately to nice duodecimal fractions. This is the basis of the Western musical scale.
I'm not sure that the Old English system used sixths much. Eighths for sure though.
Fun fact: The NYSE and NASDAQ switched from fractional dollar quoting to decimal dollar quoting in the 2002-2003 time frame. The reason was to narrow the bid/ask spread, as 1/64 of a dollar rounds to 2 cents.
The side effect was that prices could no longer be represented exactly as standard IEEE 754 floating point numbers and all calculations now have some small amount of error. Or you could do decimal math and be 50x slower. Take your pick!
They should have just reduced the minimum bid to 1/128th of a dollar!