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Equal Temperament

One of the methods of addressing the discrepancy in Just Temperament now most widely adopted as the means of tuning western instruments. 

A method of tuning such that each and every semitone is an equal interval from those above and below. Since an octave is composed chromatically of 12 semitones, the equal temperament is the 12th root of 2 times the frequency or 1.05946309435929 .. 

Hence starting with A = 440Hz, Bb would be 466.16 Hz (440 x 1.05946 ..)
B would be 493.88 Hz (466.16 x 1.05946 ..) and so on. Every interval is equal and eventually it brings one to the Octave A at 880Hz.

 

The differences between Just Temperament and Equal Temperament are shown in the table below:


Note

Just Scale

Equal Temperament

Difference

C4

261.63

261.63

0

C4#

272.54

277.18

+4.64

D4

294.33

293.66

-0.67

E4b

313.96

311.13

-2.84

E4

327.03

329.63

+2.60

F4

348.83

349.23

+0.40

F4#

367.92

369.99

+2.07

G4

392.44

392.00

-0.44

A4b

418.60

415.30

-3.30

A4

436.05

440.00

+3.94

B4b

470.93

466.16

-4.77

B4

490.55

493.88

+3.33

C5

523.25

523.25

0

This shows that the equal tempering actually sharpens some notes and flattens others. The Fifth (G) and the Fourth (F) are the least affected notes other than the octave which is of course precise.