1/6 SC - Attenuated
Compromise between equal and quarter-comma: better key flexibility with acceptable thirds.
Quick Facts
- Creator
- Baroque theorists
- Historical Era
- Baroque
- Formula Type
- fractional-comma
- Key Advantage
- Compromise between equal and quarter-comma: better key flexibility with acceptable thirds.
- Key Limitation
- Major thirds less pure than quarter-comma; wolf fifth still present but narrower.
- Typical Use
- Late Baroque keyboard music where some modulation is needed alongside pure-ish thirds.
Mathematical Basis
Meantone temperament distributes a fraction of the syntonic comma (81:80) across the fifths. 1/6 SC - Attenuated 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 1/6 SC - Attenuated, 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.
1/6 SC - Attenuated Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | 1/6 SC - Attenuated (Hz) | Cents from Equal | Tunable Offset |
|---|---|---|---|---|
| C4 | 261.626 | 262.352 | +4.80 | 0 |
| Db4 | 277.183 | 279.272 | +13.00 | 8.2 |
| D4 | 293.665 | 293.954 | +1.70 | -3.1 |
| Eb4 | 311.127 | 312.893 | +9.80 | 5 |
| E4 | 329.628 | 329.323 | -1.60 | -6.4 |
| F4 | 349.228 | 350.542 | +6.50 | 1.7 |
| Gb4 | 369.994 | 373.127 | +14.60 | 9.8 |
| G4 | 391.995 | 392.720 | +3.20 | -1.6 |
| Ab4 | 415.305 | 418.049 | +11.40 | 6.6 |
| A4 | 440.000 | 440.000 | 0.00 | -4.8 |
| Bb4 | 466.164 | 468.350 | +8.10 | 3.3 |
| B4 | 493.883 | 492.942 | -3.30 | -8.1 |
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
1/6 SC - Attenuated originates from the Baroque era, developed by Baroque theorists. It was primarily used for Late Baroque keyboard music where some modulation is needed alongside pure-ish thirds..
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 1/6 SC - Attenuated 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 1/6 SC - Attenuated — Get Tunable.
Tunable supports 1/6 SC - Attenuated and 17 other tuning systems including equal temperament, Pythagorean, just intonation, and well temperaments. See exact Hz values in real-time as you play.
