[masklinn]

> I do. I sleep 8 hours, wake up 2 hours before work, work 8 hours, and spend 6 hours in the evening afterwards. That's 1/3, 1/12, 1/3, and 1/4 of the day

You do realise that you use these approximations because they're the integral results of easy calculations, and you'd just use slightly different durations in a decimal time framework, right?

As in, metric countries don't use a 12.7mm wrench because that's what 1/2" is. They use a 13mm wrench (and the corresponding metric nuts). And their speed limits are 110/120/130, not 112.6/120.7/128.7.

[lifthrasiir]

But we still have preferred numbers [1] which never map neatly to the decimal or any other radixes due to their logarithmic nature. The ratios, sharing the same logarithmic nature, ARE one of the good reasons to select radixes if the decimal were not as pervasive as now.

[1] https://en.wikipedia.org/wiki/Preferred_number

[jacobolus]

The whole point of preferred numbers is fitting a rough logarithmic scale to a positional (e.g. decimal) number system.

For an alternative let me recommend just using binary logarithms written in base 12. (So that 1 corresponds to doubling, 1.7 corresponds pretty closely to tripling, and 2.4 corresponds roughly to quintupling. i.e. 0.1 (base 12) is an equal-tempered semitone.