Equal Temperament

Equal temperament - commonly used today - divides the octave into 12 semitones of equal size. It was proposed since the sixteenth century:

However it was not until the nineteenth century that it begins to be used with the reluctance of some:

(from Musique et témperaments, Pierre-Yves Asselin)

The equal temperament semitone

How do we calculate the size of the semitone that divides an octave into twelve equal parts? If we were able to split the third in two tones of equal size using the square root, then we can divide the octave into 12 equal parts by calculating the twelve root of 2 (octave):

The following table shows that we can use this number to calculate the frequency of each semitone:

C 262
C# 277.6 262 x 1.0594630943593
D 294.1 277.6 x 1.0594630943593
D# 311.6 294.1 x 1.0594630943593
E 330.1 311.6 x 1.0594630943593
F 349.7 330.1 x 1.0594630943593
F# 370.5 349.7 x 1.0594630943593
G 392.6 370.5 x 1.0594630943593
G# 415.9 392.6 x 1.0594630943593
A 440.6 415.9 x 1.0594630943593
A# 466.8 440.6 x 1.0594630943593
B 494.6 466.8 x 1.0594630943593
C 524 494.6 x 1.0594630943593



    
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José Rodríguez Alvira.