See hed. A spinoff on current fun with numbers thread.
The sqr-root(-12)* works out to the ratio of each tone within the octave of the equal-tempered scale, the one in current use on the piano, and in theory the one everyone uses on post-Bach tuning systems (==temperaments).
For millennia people have been screwing around with the ineffable meaning of other tuning systems based on divvying up of rational numbers, which unfortunately doesn’t get you 11 nice notes to play around with if you want to keep the 2:1 “octave” ratio (the etymology of “octave” is itself is laden with historical baggage irrelevant at this point).
If only 3:2 were commensurate with 2:1. Sorry Pythagoras.
*In case the symbol doesn’t display right in the hed.