<< Back to main.

Equal Tempered 12-Tone System

As was pointed out in the sections about Pythagorean Tuning and Quarter Comma Meantone , these temperaments suffer from the lack of transposability. As a rescue, in the late 17th and beginning 18th centuries J.S. Bach and contemporaries established a different tuning scheme named Equal Temperament, which not only remedied these inadequacies, but also simplified tuning instruments and composing musics. While the scheme has existed probably since the 16th century, with J.S. Bach it bacame so popular that it actually replaced most of the other tuning systems. It is until now the most often used tuning system.

In the Equal Temperament the octave is divided into 12 perfectly equal steps. Compared to the Meantone Temperament the triads sound less pure in equal temperament than the first-rate triads in Meantone, but they sound exacly the same on each note of the series, giving free transposability and a new realm of compositional freedom.

A comparison of the three temperaments is given here:

Note Pythagorean cents Meantone cents Cents in
Equ. Temp.
Ab 0 0 0
Eb 701.955 696.58 700
Bb 203.910 193.16 200
F 905.865 889.74 900
C 407.820 386.31 400
G 1109.775 1082.89 1100
D 611.730 579.47 600
A 113.685 76.05 100
E 815.640 772.63 800
B 317.595 269.21 300
F# 1019.550 965.78 1000
C# 521.505 462.36 500
G# 23.460 1158.94 0 or 1200

(a cent is the 100th part of a an Equal Temperament small second, on a logarithmic scale). As you can see, all intervals in the Equal Temperament lie somewhere between their counterparts in the Pythagorean and Meantone system.