Equal Temperament
All 12 keys are equally in-tune — transpose freely without re-tuning.
Quick Facts
- Creator
- Theoretical development (12-TET standardized c. 1900)
- Historical Era
- Modern
- Formula Type
- equal-division
- Key Advantage
- All 12 keys are equally in-tune — transpose freely without re-tuning.
- Key Limitation
- Pure fifths (2 cents flat) and major thirds (14 cents sharp) are slightly impure in every key.
- Typical Use
- Standard tuning for all modern Western instruments since the 20th century.
Mathematical Basis
Equal temperament divides the octave into 12 identical semitones. Each semitone = 2^(1/12) ≈ 1.05946, giving exactly 100 cents per semitone. Every interval is equally tempered.
Sound Character
Equal temperament sounds bright and uniform: all 12 keys are equally in-tune and all intervals are equally tempered. There is no key color — C major and F# major sound identical in character. This uniformity makes it ideal for chromatic music, free modulation, and all fixed-pitch instruments.
Equal Temperament Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | Equal Temperament (Hz) | Cents from Equal |
|---|---|---|---|
| C4 | 261.626 | 261.626 | 0.00 |
| Db4 | 277.183 | 277.183 | 0.00 |
| D4 | 293.665 | 293.665 | 0.00 |
| Eb4 | 311.127 | 311.127 | 0.00 |
| E4 | 329.628 | 329.628 | 0.00 |
| F4 | 349.228 | 349.228 | 0.00 |
| Gb4 | 369.994 | 369.994 | 0.00 |
| G4 | 391.995 | 391.995 | 0.00 |
| Ab4 | 415.305 | 415.305 | 0.00 |
| A4 | 440.000 | 440.000 | 0.00 |
| Bb4 | 466.164 | 466.164 | 0.00 |
| B4 | 493.883 | 493.883 | 0.00 |
Frequencies in Hz at A4=440Hz. Positive cents = sharper than equal temperament. Negative = flatter. Formula: f = f_equal × 2(cents/1200)
Historical Context
Equal Temperament originates from the Modern era, developed by Theoretical development (12-TET standardized c. 1900). It was primarily used for Standard tuning for all modern Western instruments since the 20th century..
Equal temperament became the universal standard in the 20th century, adopted for piano, organ, and all fixed-pitch instruments. It enables free modulation across all 24 major and minor keys.
Who Uses Equal Temperament Today
Equal temperament is used by virtually all modern ensembles and instruments: string orchestras, pianos, guitars, woodwinds, brass, and electronic instruments. It is the default tuning for all modern Western music.
Tune with Equal Temperament — Get Tunable.
Tunable supports Equal Temperament and 15 other tuning systems including equal temperament, Pythagorean, just intonation, and well temperaments. See exact Hz values in real-time as you play.