Equal Temperament vs. Just / Pure
Compare the tuning characteristics of Equal Temperament and Just / Pure — cent deviations per note, practical guidance, and historical context.
At a Glance
| Feature | Equal Temperament | Just / Pure |
|---|---|---|
| Category | equal | just-intonation |
| Formula Type | equal-division | just-ratios |
| Historical Era | Modern | Renaissance / Theory |
| Key Advantage | All 12 keys are equally in-tune — transpose freely without re-tuning. | Perfectly pure major thirds (5:4) and fifths (3:2) in the home key. |
| Key Limitation | Pure fifths (2 cents flat) and major thirds (14 cents sharp) are slightly impure in every key. | Fixed tonal center — modulating to other keys produces out-of-tune intervals. |
| Typical Use | Standard tuning for all modern Western instruments since the 20th century. | A cappella choral music, theoretical analysis, and tuning reference for pure intervals. |
Cent Deviations: All 12 Notes vs. Equal Temperament
Positive cents = sharper than equal temperament. Negative = flatter. Difference column shows Just / Pure minus Equal Temperament: positive means Just / Pure is sharper.
| Note | Equal Temperament (¢) | Just / Pure (¢) | Difference (¢) |
|---|---|---|---|
| C4 | 0.00 | +15.64 | +15.64 |
| Db4 | 0.00 | +27.37 | +27.37 |
| D4 | 0.00 | +19.55 | +19.55 |
| Eb4 | 0.00 | +31.28 | +31.28 |
| E4 | 0.00 | -2.04 | -2.04 |
| F4 | 0.00 | +13.69 | +13.69 |
| Gb4 | 0.00 | +5.87 | +5.87 |
| G4 | 0.00 | +17.60 | +17.60 |
| Ab4 | 0.00 | +29.33 | +29.33 |
| A4 | 0.00 | 0.00 | 0.00 |
| Bb4 | 0.00 | +11.73 | +11.73 |
| 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 Just / Pure when:
Choose Just / Pure for a cappella choirs, string quartets, and any ensemble exploring pure intonation in the home key. Best suited to music that stays near one tonal center rather than modulating widely.
Historical Context
Just intonation was championed by Gioseffo Zarlino in the 16th century as the ideal for vocal polyphony, while Equal Temperament became universal in the 20th century. The transition from pure-ratio tuning to equal division represents one of the most significant shifts in Western musical practice.
- Equal Temperament
- Developed by Theoretical development (12-TET standardized c. 1900) — Modern era
- Just / Pure
- Developed by Gioseffo Zarlino and Renaissance theorists — Renaissance / Theory era
Compare Temperaments in Tunable — Get Tunable.
Tunable supports Equal Temperament, Just / Pure, and 16 other tuning systems. Hear the difference in real-time as you play.
