A4 in Vallotti

A4 is 440.000 Hz in all tuning systems that use A=440 as their reference. In Vallotti, the surrounding chromatic notes are tuned according to six fifths from F to B are each narrowed by 1/6 of the Pythagorean comma, while the remaining six fifths are pure — distributing the comma evenly across half the circle.

This system was used for Baroque Italian keyboard music and orchestral Baroque and Classical period works.

Chromatic Scale at A4=440 Hz in Vallotti

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 Vallotti tunes each interval relative to A4.

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

Vallotti: Mathematical Formula

Vallotti's temperament divides the 12-note circle into two equal halves: the six fifths spanning F-C-G-D-A-E-B are each narrowed by 1/6 of the Pythagorean comma (approximately 3.91 cents), while the six fifths on the flat side (Bb-F, Eb-Bb, Ab-Eb, Db-Ab, Gb-Db, B-F#) are pure 3:2 intervals. The result is a smooth gradient from well-tuned near keys to purer-fifths remote keys. Major thirds in C, G, D, A, and E major range from approximately 390 to 402 cents — all better than equal temperament. Flat-key thirds are wider, approaching Pythagorean quality near Gb major.

Formula type: Cent offsets from equal temperament

How Vallotti Sounds

Vallotti has a balanced, easy-listening quality that avoids the strong key-color contrasts of Werckmeister temperaments while still providing noticeable improvement over equal temperament in common keys. C major and G major sound warm and slightly sweet, with major thirds noticeably purer than equal temperament. The transition across the circle of fifths is gradual rather than sudden — no key sounds dramatically bad, and the variation in key color has a pleasing regularity. Vallotti is often described as the most practical historical temperament for modern early music ensembles because it sounds natural without requiring dramatic adjustments from players accustomed to equal temperament.

Historical Context

Francesco Antonio Vallotti, a Franciscan monk and maestro di cappella at the Basilica of Sant'Antonio in Padua, developed this temperament around 1754 and published it in his Della scienza teorica e pratica della moderna musica. Vallotti composed extensively and used his own temperament for the organs at Sant'Antonio, making it one of the best-documented historical temperaments in terms of its creator's practical application. The system was later popularized by Thomas Young (1799), who described an identical or near-identical arrangement. Vallotti's temperament is frequently used today in recordings of Baroque Italian keyboard and orchestral music.

Other Tuning Systems for A4

See A4 in all temperaments →

For a full deep dive into Vallotti, see the Tunable guide to Vallotti.