Equal Temperament vs. Pythagorean Tuning
Compare the tuning characteristics of Equal Temperament and Pythagorean Tuning — cent deviations per note, practical guidance, and historical context.
At a Glance
| Feature | Equal Temperament | Pythagorean Tuning |
|---|---|---|
| Category | equal | pythagorean |
| Formula Type | equal-division | pythagorean-stacking |
| Historical Era | Modern | Ancient / Medieval |
| Key Advantage | All 12 keys are equally in-tune — transpose freely without re-tuning. | Pure perfect fifths (3:2) — ideal for medieval polyphony and chant. |
| Key Limitation | Pure fifths (2 cents flat) and major thirds (14 cents sharp) are slightly impure in every key. | Major thirds are very sharp (+22 cents) and the wolf fifth makes distant keys harsh. |
| Typical Use | Standard tuning for all modern Western instruments since the 20th century. | Medieval music, chant, early polyphony, and Pythagorean theory study. |
Cent Deviations: All 12 Notes vs. Equal Temperament
Positive cents = sharper than equal temperament. Negative = flatter. Difference column shows Pythagorean Tuning minus Equal Temperament: positive means Pythagorean Tuning is sharper.
| Note | Equal Temperament (¢) | Pythagorean Tuning (¢) | Difference (¢) |
|---|---|---|---|
| C4 | 0.00 | -5.87 | -5.87 |
| Db4 | 0.00 | +7.82 | +7.82 |
| D4 | 0.00 | -1.96 | -1.96 |
| Eb4 | 0.00 | -11.73 | -11.73 |
| E4 | 0.00 | +1.96 | +1.96 |
| F4 | 0.00 | -7.82 | -7.82 |
| Gb4 | 0.00 | +5.87 | +5.87 |
| G4 | 0.00 | -3.91 | -3.91 |
| Ab4 | 0.00 | +9.78 | +9.78 |
| A4 | 0.00 | 0.00 | 0.00 |
| Bb4 | 0.00 | -9.78 | -9.78 |
| B4 | 0.00 | +3.91 | +3.91 |
When to Choose Each
Choose Equal Temperament when:
Choose Equal Temperament for modern ensembles, fixed-pitch instruments (piano, guitar, wind instruments), and any music that modulates freely across all 24 keys. It is the universal standard for contemporary Western music.
Choose Pythagorean Tuning when:
Choose Pythagorean tuning for medieval ensemble music, plainchant, early polyphony, and Pythagorean melodic writing where pure open fifths are the primary consonances. String players often gravitate naturally toward this intonation for melodic lines.
Historical Context
Pythagorean tuning was the standard throughout the Medieval period (c. 500-1400 CE), while Equal Temperament only became universal in the 20th century. For more than 1,500 years these two systems represent opposite poles: one optimized for pure fifths and medieval polyphony, the other for chromatic freedom and modern fixed-pitch instruments.
- Equal Temperament
- Developed by Theoretical development (12-TET standardized c. 1900) — Modern era
- Pythagorean Tuning
- Developed by Ancient Greek theory (attributed to Pythagoras) — Ancient / Medieval era
Compare Temperaments in Tunable — Get Tunable.
Tunable supports Equal Temperament, Pythagorean Tuning, and 14 other tuning systems. Hear the difference in real-time as you play.
