Twelfth root of two
Note Standard interval name ( s ) relating to A 440 Frequency ( Hz ) Multiplier Coefficient ( to six places ) Just intonation ratio
A Unison 440.00 2 1.000 000 1
A ♯ /B ♭ Minor second/Half step/Semitone 466.16 2 1.059 463 ≈ ​ ⁄ 15
B Major second/Full step/Whole tone 493.88 2 1.122 462 ≈ ​ ⁄ 8
C Minor third 523.25 2 1.189 207 ≈ ​ ⁄ 5
C ♯ /D ♭ Major third 554.37 2 1.259 921 ≈ ​ ⁄ 4
D Perfect fourth 587.33 2 1.334 839 ≈ ​ ⁄ 3
D ♯ /E ♭ Augmented fourth/Diminished fifth/Tritone 622.25 2 1.414 213 ≈ ​ ⁄ 5
E Perfect fifth 659.26 2 1.498 307 ≈ ​ ⁄ 2
F Minor sixth 698.46 2 1.587 401 ≈ ​ ⁄ 5
F ♯ /G ♭ Major sixth 739.99 2 1.681 792 ≈ ​ ⁄ 3
G Minor seventh 783.99 2 1.781 797 ≈ ​ ⁄ 5
G ♯ /A ♭ Major seventh 830.61 2 1.887 748 ≈ ​ ⁄ 8
A Octave 880.00 2 2.000 000 2
The equal-tempered chromatic scale
A musical interval is a ratio of frequencies and the equal-tempered chromatic scale divides the octave ( which has a ratio of 2:1 ) into twelve parts . Applying this value successively to the tones of a chromatic scale , starting from A above middle C ( known as A4 ) with a frequency of 440 Hz , produces the following sequence of pitches :
The twelfth root of two or formula_1 (or equivalently formula_2) is an algebraic irrational number. It is most important in Western music theory, where it represents the frequency ratio (musical interval) of a semitone () in twelve-tone equal temperament. This number was proposed for the first time in relationship to musical tuning in the sixteenth and seventeenth 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 perfect fifth is 7 semitones). A semitone itself is divided into 100 cents (1 cent = formula_3).