Equal Temperament

Twelve equal semitones let every key work on one instrument and made free modulation normal.

Related

BaroqueTonalityKey SignatureHarpsichord

Dividing the octave into twelve equal semitones sounds mathematical. In practice it let every key appear freely on one instrument, and Bach made the change audible in two books of preludes and fugues.

Time and place

Eighteenth-century Europe, Leipzig in 1722. Bach published Book I of the Well-Tempered Clavier, with a prelude and fugue in all twenty-four keys. Strict equal temperament spread only in the nineteenth century, with piano manufacture and standardised tuning.

What happened

Equal temperament divides the octave by the twelfth root of two, so every semitone has the same ratio. Fifths are slightly narrow and major thirds slightly wide; in return, no key needs retuning, and modulation works everywhere. Bach's well-tempered tuning was not strict equal temperament but a circulating system that made all keys usable. It proved that remote keys could be written and heard as naturally as C major.

What changed

The network of keys became an even map. Composers could start anywhere and stay anywhere, and guitars, organs and pianos were tuned accordingly. Modern modulation, chromaticism and enharmonic relations rest on this base. The price was the pure third of just intonation; the gain was the freedom of all twelve keys.

Listen for the turn

Begin with the C major prelude, then hear the fugues in C sharp major, F sharp major and A flat major. Remote keys no longer carry the tension of being out of tune; the subject holds in five or six sharps or flats. The versions are piano; listen for stable intonation, not old instruments' tuning differences.

Related

This turn belongs to Baroque and connects Tonality, Key Signature and Harpsichord.

Sources

• The New Grove Dictionary of Music and Musicians, 2nd ed., entry "Temperaments" — mathematics and dates checked, not quoted
• Richard Taruskin, The Oxford History of Western Music (Oxford University Press) — narrative checked, not quoted

Used for fact-checking only; all prose is original.