Tuning & Temperament
Equal Temperament: What It Costs and What It Buys
Twelve equal semitones solve the problem pure intervals create. The cost is small in fifths, large in thirds, and paid by every fixed-pitch instrument.
Equal temperament
A tuning that divides the octave into twelve equal semitones of 100 cents, so every key sounds alike and no interval is pure.
Also called: 12-tone equal temperament, 12-TET, equal tuning
Equal temperament divides the octave into twelve semitones of equal size. Each semitone has a frequency ratio of the twelfth root of two, about 1.05946, so twelve semitones make exactly one octave of 1200 cents. Every key uses the same intervals, which lets a piano play in any key without retuning. The price is that no interval except the octave is pure. The equal fifth is 700 cents, about 2 cents narrower than the pure 3:2 fifth at 701.96 cents. The equal major third is 400 cents, about 14 cents wider than the pure 5:4 third at 386.3 cents. Most modern pianos and other fixed-pitch instruments use this tuning.
Related terms
- CentA unit for small pitch differences: 1/100 of an equal-tempered semitone, so an octave is 1200 cents.
- Just intonationA tuning built from simple whole-number frequency ratios, so intervals ring clean but the sizes of steps vary by key.
- Well temperamentA family of unequal tunings in which every key is usable and each key has its own character, with some keys purer than others.
- Meantone temperamentA temperament that narrows the fifths so that major thirds are close to pure, at the cost of several unusable keys.