E5 in Third-Comma Meantone

In Third-Comma Meantone, E5 is tuned to 657.954 Hz (-3.42 cents from equal temperament). The surrounding chromatic notes at octave 5 are tuned according to each perfect fifth is narrowed by 1/3 of the syntonic comma, producing pure minor thirds (6:5) at the cost of impure major thirds.

This system was used for Renaissance minor-key keyboard music and modal vocal polyphony.

Chromatic Scale at Octave 5 in Third-Comma Meantone

The table below shows all 12 chromatic notes at octave 5 in Third-Comma Meantone. Frequencies use A=440 Hz as the concert pitch reference.

Positive cents = sharper than equal temperament. Negative = flatter. 100 cents = 1 semitone.

Third-Comma Meantone: Mathematical Formula

Third-comma meantone flattens each fifth by 1/3 of the syntonic comma — approximately 7.168 cents — far more than the quarter-comma version. This aggressive narrowing produces pure 6:5 minor thirds rather than pure 5:4 major thirds. Three stacked minor thirds arrive at an exact 6:5 ratio (315.64 cents), making minor triads acoustically pure while major thirds are widened to approximately 401.95 cents. The wolf fifth is smaller than in quarter-comma meantone (approximately 722 cents) but still clearly audible and unusable for harmony. The fifths measure 694.79 cents each, noticeably narrower than equal-tempered fifths.

Formula type: Cent offsets from equal temperament

How Third-Comma Meantone Sounds

Third-comma meantone has a characteristically dark, rich timbre in the minor mode. Minor chords achieve the same purity that quarter-comma meantone brings to major chords — the minor third snaps into beatless resonance. Major chords, conversely, sound slightly hard and wide, which some performers find gives them a strong, declarative character. The system creates a tonal world where minor tonality feels settled and major tonality feels energetic. It suits music in modal minor contexts: Dorian, Phrygian, and Aeolian pieces from the late Renaissance benefit from the system's preference for minor-third purity.

Note: Third-Comma Meantone contains a wolf fifth — an interval significantly wider than a pure fifth. Avoid chromatic passages that cross this interval.

Historical Context

Third-comma meantone appears in the theoretical literature of the late Renaissance as a variant designed for music dominated by minor harmony. Theorists including Zarlino discussed it as a natural extension of the meantone principle toward minor-third purity. The system was less widely used on historical instruments than quarter-comma meantone, but it found a niche in regions and ensembles where modal minor music predominated. Some luthiers and organ builders experimented with this tuning for instruments built specifically for minor-key repertoire. Modern early music scholars sometimes use third-comma meantone for ensemble readings of 16th-century Italian madrigals in minor modes.

Other Tuning Systems for E5

See E5 in all temperaments →

For a full deep dive into Third-Comma Meantone, see the Tunable guide to Third-Comma Meantone.