A4 in Quarter-Comma Meantone

A4 is 440.000 Hz in all tuning systems that use A=440 as their reference. In Quarter-Comma Meantone, the surrounding chromatic notes are tuned according to each perfect fifth is narrowed by 1/4 of the syntonic comma (81/80), so that four stacked fifths produce a pure major third (5:4).

This system was used for Renaissance keyboard music and early Baroque harpsichord and organ.

Chromatic Scale at A4=440 Hz in Quarter-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 Quarter-Comma Meantone tunes each interval relative to A4.

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

Quarter-Comma Meantone: Mathematical Formula

Quarter-comma meantone flattens each fifth by exactly 1/4 of the syntonic comma — approximately 5.377 cents — so that four stacked fifths arrive at a pure 5:4 major third (386.31 cents), identical to just intonation. The major second is the geometric mean of two pure major thirds, giving the system its name: "meantone" refers to this mean-tone whole step of 193.16 cents. Eleven of the twelve fifths are narrowed to 696.58 cents; the twelfth "wolf fifth" (typically between Ab and D#) is dramatically wide at approximately 737.64 cents — nearly 35 cents above a pure fifth — making it unusable as a harmonic interval.

Formula type: Cent offsets from equal temperament

How Quarter-Comma Meantone Sounds

Quarter-comma meantone is celebrated for its luminous, singing major thirds. In the eight keys well-served by the system (those without accidentals or with one or two flats/sharps), major chords have a pure, almost vocal resonance that is absent in equal temperament. The system creates strong key colors: C major feels open and settled, while Eb major is bright and E major is edgy. The wolf fifth between Ab and D# produces a jarring howl — this interval must be avoided in performance. The system was the dominant keyboard tuning for two centuries precisely because its major thirds are so convincing.

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

Historical Context

Quarter-comma meantone was the standard keyboard tuning across much of the Renaissance and Baroque periods, codified by theorist Pietro Aaron in his 1523 Toscanello in musica. Virtually all keyboard music composed between roughly 1500 and 1700 was intended for instruments tuned in this or related meantone systems. The harpsichords, virginals, and early organs of Frescobaldi, Byrd, and the early Couperin family were tuned in quarter-comma meantone, and the repertoire exploits the system's characteristic key colors. As composers began to venture more freely into remote key signatures requiring Ab, Eb, and D#, the wolf fifth became an increasing limitation, eventually motivating the development of well temperaments in the late 17th century.

Other Tuning Systems for A4

See A4 in all temperaments →

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