Michael, lets assume an equal-tempered chromatic scale, the one mostly used in the west. The twelfth root of two is an algebraic irrational number, it represents the frequency ratio of a semitone in equal temperament.
So, you have the frequency ratio of a semitone = 106%
These days, they use pitch shifters in recording studios.
Back in the days, reel-to-reel magnetic tape recorders typically had a pitch adjustments of up to 6%..
To step even further, the 6♭ and the 6♯ scales are not identical.. (even though they are on the piano keyboard) the ♭ scales are one Pythagorean comma lower.

In parts of the world, where they wanted to be as close to the real thing as possible, they tied their scales to harmonic series, so the intervals are complementary values of the harmonic overtones series and so on.