Meantone 1/3 Comma
Pure minor thirds (6:5) — better suited to minor-mode Renaissance music.
Quick Facts
- Creator
- Francisco de Salinas (1577)
- Historical Era
- Renaissance / Baroque
- Formula Type
- fractional-comma
- Key Advantage
- Pure minor thirds (6:5) — better suited to minor-mode Renaissance music.
- Key Limitation
- Wider wolf fifth and less pure major thirds than quarter-comma meantone.
- Typical Use
- Renaissance music with emphasis on minor thirds and minor-key tonality.
Mathematical Basis
Meantone temperament distributes a fraction of the syntonic comma (81:80) across the fifths. Meantone 1/3 Comma distributes one sixth of the comma, flattening each fifth slightly to produce pure (or near-pure) major thirds.
Wolf Fifth Warning
Meantone temperaments produce a "wolf fifth" — an extremely dissonant fifth between the last note in the chain of fifths and the first. In Meantone 1/3 Comma, the wolf fifth occurs between G# and Eb (or Ab and D#). This interval sounds severely out of tune and limits modulation to distant keys. Meantone temperaments work best in keys with few accidentals.
Sound Character
Meantone temperament produces smooth, resonant major thirds that are purer than equal temperament and give Renaissance and early Baroque music its characteristic warm, consonant sound. The wolf fifth — an extremely dissonant fifth between the end and start of the chain of fifths — is the trade-off for this purity in the common keys.
Meantone 1/3 Comma Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | Meantone 1/3 Comma (Hz) | Cents from Equal | Tunable Offset |
|---|---|---|---|---|
| C4 | 261.626 | 264.001 | +15.64 | 0 |
| Db4 | 277.183 | 273.864 | -20.86 | -36.498 |
| D4 | 293.665 | 294.551 | +5.21 | -10.428 |
| Eb4 | 311.127 | 316.800 | +31.28 | 15.642 |
| E4 | 329.628 | 328.637 | -5.21 | -20.856 |
| F4 | 349.228 | 353.461 | +20.86 | 5.214 |
| Gb4 | 369.994 | 366.666 | -15.64 | -31.284 |
| G4 | 391.995 | 394.363 | +10.43 | -5.214 |
| Ab4 | 415.305 | 409.098 | -26.07 | -41.712 |
| A4 | 440.000 | 440.000 | 0.00 | -15.642 |
| Bb4 | 466.164 | 473.237 | +26.07 | 10.428 |
| B4 | 493.883 | 490.917 | -10.43 | -26.07 |
Frequencies in Hz at A4=440Hz. Positive cents = sharper than equal temperament. Negative = flatter. Formula: f = f_equal × 2(cents/1200)
Tunable Offset shows the cent values in Tunable's custom temperament format (C=0 reference). To enter this temperament manually: Settings → Tuner → Alternate Temperament → Add → enter these 12 values.
Historical Context
Meantone 1/3 Comma originates from the Renaissance / Baroque era, developed by Francisco de Salinas (1577). It was primarily used for Renaissance music with emphasis on minor thirds and minor-key tonality..
Meantone temperaments dominated keyboard music from roughly 1500–1700. Composers including William Byrd, Girolamo Frescobaldi, and early Bach likely worked with meantone-tuned instruments.
Who Uses Meantone 1/3 Comma Today
Meantone temperaments are used today by historically-informed performance groups, harpsichordists, and organists specializing in Renaissance and early Baroque music. Period instrument ensembles frequently employ meantone to restore the original sound world of this repertoire.
Tune with Meantone 1/3 Comma — Get Tunable.
Tunable supports Meantone 1/3 Comma and 17 other tuning systems including equal temperament, Pythagorean, just intonation, and well temperaments. See exact Hz values in real-time as you play.
