Pythagorean Tuning vs. Quarter-Comma Meantone
Compare the tuning characteristics of Pythagorean Tuning and Quarter-Comma Meantone — cent deviations per note, practical guidance, and historical context.
At a Glance
| Feature | Pythagorean Tuning | Quarter-Comma Meantone |
|---|---|---|
| Category | pythagorean | meantone |
| Formula Type | pythagorean-stacking | fractional-comma |
| Historical Era | Ancient / Medieval | Renaissance / Early Baroque |
| Key Advantage | Pure perfect fifths (3:2) — ideal for medieval polyphony and chant. | Pure major thirds (5:4) in the most common Renaissance/Baroque keys. |
| Key Limitation | Major thirds are very sharp (+22 cents) and the wolf fifth makes distant keys harsh. | A dissonant wolf fifth (between G# and Eb) makes enharmonic keys unusable. |
| Typical Use | Medieval music, chant, early polyphony, and Pythagorean theory study. | Renaissance and early Baroque keyboard music in flat-key signatures. |
Cent Deviations: All 12 Notes vs. Equal Temperament
Positive cents = sharper than equal temperament. Negative = flatter. Difference column shows Quarter-Comma Meantone minus Pythagorean Tuning: positive means Quarter-Comma Meantone is sharper.
| Note | Pythagorean Tuning (¢) | Quarter-Comma Meantone (¢) | Difference (¢) |
|---|---|---|---|
| C4 | -5.87 | +10.26 | +16.13 |
| Db4 | +7.82 | -13.69 | -21.51 |
| D4 | -1.96 | +3.42 | +5.38 |
| Eb4 | -11.73 | +20.53 | +32.26 |
| E4 | +1.96 | -3.42 | -5.38 |
| F4 | -7.82 | +13.69 | +21.51 |
| Gb4 | +5.87 | -10.26 | -16.13 |
| G4 | -3.91 | +6.85 | +10.76 |
| Ab4 | +9.78 | -17.11 | -26.89 |
| A4 | 0.00 | 0.00 | 0.00 |
| Bb4 | -9.78 | +17.11 | +26.89 |
| B4 | +3.91 | -6.85 | -10.76 |
When to Choose Each
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.
Choose Quarter-Comma Meantone when:
Choose Quarter-Comma Meantone for Renaissance and early Baroque keyboard music. Its pure major thirds (5:4) give harpsichord and organ repertoire from 1500-1650 its characteristic warm, consonant sound.
Historical Context
Pythagorean Tuning predates meantone temperament historically. Meantone (dominant 1500-1700) emerged as a practical keyboard solution that split the difference between Pythagorean fifths and just-intonation thirds, distributing the syntonic comma to achieve near-pure thirds on keyboard instruments.
- Pythagorean Tuning
- Developed by Ancient Greek theory (attributed to Pythagoras) — Ancient / Medieval era
- Quarter-Comma Meantone
- Developed by Pietro Aaron (c. 1523) — Renaissance / Early Baroque era
Compare Temperaments in Tunable — Get Tunable.
Tunable supports Pythagorean Tuning, Quarter-Comma Meantone, and 14 other tuning systems. Hear the difference in real-time as you play.
