Twelfth root of two

The twelfth root of two or ${\displaystyle {\sqrt[{12}]{2}}}$ (or equivalently${\displaystyle 2^{1/12}}$) is an algebraicirrational number approximately equal to 1.0594631. It is important in Western music theory, where it represents the frequencyratio (musical interval) of a semitone (Play) in 12-tone equal temperament. This number was first proposed in relation to musical tuning in the 16th and 17th centuries. It allows measurement and comparison of different intervals (frequency ratios) as consisting of different numbers of a single interval, the equal-tempered semitone (for example, a minor third is 3 semitones, a major third is 4 semitones, and a perfect fifth is 7 semitones). Semitones are divided into 100 cents (1 cent = ${\displaystyle {\sqrt[{1200}]{2}}=2^{1/1200}}$).