Tool
Temperament comparator
The same note in different tunings, in cents and in sound: what equal temperament costs and what it buys.
A pure major third, at the ratio 5:4, and the piano's major third, at a hundred cents per semitone, are not the same thing: the piano's is fourteen cents wider, and the difference is heard as a beat. Choose two temperaments and a sound, and hear one after the other from the same C. The table shows where each note falls in each tuning, and how far it sits from equal temperament.
Equal temperament. Twelve equal semitones of a hundred cents. No fifth is pure, no third is pure, and everything works in every key. It is the modern piano's.
Just intonation. Every note in a simple ratio with the tonic. The major third is pure, 5:4, and the tonic chord sounds without beating; other degrees pay for it.
| Semitones | Equal temperament | Just intonation |
|---|---|---|
| 0 | C 0.0 (0) | C 0.0 (0) |
| 1 | C♯/D♭ 100.0 (0) | D♭ 111.7 (+11.7) |
| 2 | D 200.0 (0) | D 203.9 (+3.9) |
| 3 | D♯/E♭ 300.0 (0) | E♭ 315.6 (+15.6) |
| 4 | E 400.0 (0) | E 386.3 (−13.7) |
| 5 | F 500.0 (0) | F 498.0 (−2.0) |
| 6 | F♯/G♭ 600.0 (0) | F♯ 590.2 (−9.8) |
| 7 | G 700.0 (0) | G 702.0 (+2.0) |
| 8 | G♯/A♭ 800.0 (0) | A♭ 813.7 (+13.7) |
| 9 | A 900.0 (0) | A 884.4 (−15.6) |
| 10 | A♯/B♭ 1000.0 (0) | B♭ 996.1 (−3.9) |
| 11 | B 1100.0 (0) | B 1088.3 (−11.7) |
