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by jacobolus 2556 days ago
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.