A4 in Sixth-Comma Meantone

A4 is 440.000 Hz in all tuning systems that use A=440 as their reference. In Sixth-Comma Meantone, the surrounding chromatic notes are tuned according to each perfect fifth is narrowed by 1/6 of the syntonic comma, splitting the difference between pure fifths and pure major thirds.

This system was used for Baroque orchestral ensemble tuning and French Baroque string writing.

Chromatic Scale at A4=440 Hz in Sixth-Comma Meantone

The table below shows all 12 chromatic notes at octave 4. A4 is the tuning reference — its frequency is 440.000 Hz in all temperaments at this concert pitch. The other notes show how Sixth-Comma Meantone tunes each interval relative to A4.

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

Sixth-Comma Meantone: Mathematical Formula

Sixth-comma meantone narrows each fifth by 1/6 of the syntonic comma — approximately 3.584 cents — producing a compromise midway between Pythagorean tuning (0 comma narrowing) and quarter-comma meantone (1/4 comma narrowing). Major thirds measure approximately 393.48 cents (6.83 cents from pure) and minor thirds measure approximately 306.52 cents — better than Pythagorean thirds but not as pure as quarter-comma meantone. The wolf fifth is significantly smaller than in quarter-comma or third-comma meantone (approximately 726 cents), making the system more practical in musical contexts requiring occasional accidentals. Fifths measure 698.37 cents, very close to the 700-cent equal-tempered fifth.

Formula type: Cent offsets from equal temperament

How Sixth-Comma Meantone Sounds

Sixth-comma meantone occupies an aesthetic middle ground — major thirds are noticeably purer than equal temperament but not quite as luminous as quarter-comma meantone. The system has a pleasing, slightly warm quality without the strong key-color contrasts of its more extreme meantone cousins. For Baroque orchestral music, where ensemble instruments naturally drift toward pure intervals, sixth-comma meantone provides a workable framework. The smaller wolf fifth is less disruptive, allowing composers more freedom to explore accidentals. The system is often described as sounding "civilized" — balanced and pleasing without being as startling as quarter-comma in either its best or worst keys.

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

Historical Context

Sixth-comma meantone emerged as a practical compromise for Baroque ensemble contexts where both the purity of meantone and the flexibility of well temperament were desired. Giuseppe Tartini and other 18th-century theorists explored similar compromise systems for string ensemble tuning. The system is particularly associated with French Baroque practice, where orchestral violinists were known to tune their open strings to nearly pure fifths while favoring pure thirds in stopped positions — a practical approximation of sixth-comma meantone. The system fell out of use as equal temperament standardized ensemble tuning in the 19th century, but it remains of interest to historically-informed practitioners.

Other Tuning Systems for A4

See A4 in all temperaments →

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