> It’s worth noting that instruments were being tuned to this scale well before the invention of logarithms. I assume it was done by ear or perhaps by geometry, not by algebra.
Well temperament wasn't known before 1681, there were predecessors that came close but none used the the twelfth root of two.
Logarithms were introduced by John Napier in 1614 [1], the twelfth root of two
was first calculated by Marin Mersenne in 1636 [2], well temperament was introduced by Werckmeister 1681 [3].
> Around 1600 Simon Stevin did attempt to calculate numerical values for the pitch intervals by decomposing 12th roots into combinations of square and cube roots; his results were not flawless.
Well temperament wasn't known before 1681, there were predecessors that came close but none used the the twelfth root of two. Logarithms were introduced by John Napier in 1614 [1], the twelfth root of two was first calculated by Marin Mersenne in 1636 [2], well temperament was introduced by Werckmeister 1681 [3].
> Around 1600 Simon Stevin did attempt to calculate numerical values for the pitch intervals by decomposing 12th roots into combinations of square and cube roots; his results were not flawless.
He had the right idea but not the right math.
[1] https://en.wikipedia.org/wiki/John_Napier
[2] https://en.wikipedia.org/wiki/Twelfth_root_of_two
[3] https://en.wikipedia.org/wiki/Well_temperament