A4 in Werckmeister IV

A4 is 440.000 Hz in all tuning systems that use A=440 as their reference. In Werckmeister IV, the surrounding chromatic notes are tuned according to an unequal circulating temperament using a different distribution of comma-narrowed fifths than Werckmeister III, producing stronger key contrasts.

This system was used for Baroque keyboard music with strong key-affect emphasis and German harpsichord literature.

Chromatic Scale at A4=440 Hz in Werckmeister IV

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 Werckmeister IV tunes each interval relative to A4.

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

Werckmeister IV: Mathematical Formula

Werckmeister IV (also called "Septenarius" in some sources) uses a more complex distribution of narrowed and widened fifths than Werckmeister III. The temperament employs a combination of 1/3 and 2/3 comma adjustments across selected fifths, producing more extreme key contrasts. Near keys have noticeably purer major thirds than in Werckmeister III, while remote keys have wider, more dissonant thirds that give them strong tonal character. The system circulates through all 24 keys, but the variation in interval quality is larger than in Werckmeister III. This stronger differentiation was intended to highlight the "affects" (emotional characters) of different keys more vividly.

Formula type: Cent offsets from equal temperament

How Werckmeister IV Sounds

Werckmeister IV creates an even more pronounced palette of key colors than Werckmeister III. C major and G major feel particularly smooth and settled, with major thirds approaching meantone quality. The transition to sharper or flatter key signatures is more dramatic — Ab major and F# major sound distinctly edgier and more brilliant. For composers who wanted to exploit key-specific emotional characters in the Baroque affective tradition, this strong differentiation was a feature rather than a defect. Modern players using Werckmeister IV for late Baroque music report that the system brings a vividness to key changes that equal temperament cannot replicate.

Historical Context

Werckmeister introduced this temperament alongside Werckmeister III in his 1691 Musicalische Temperatur, presenting multiple options for keyboard tuning. Werckmeister IV attracted less practical adoption than Werckmeister III, possibly because the stronger key contrasts made it less versatile for general use. However, it influenced subsequent theorists exploring the relationship between temperament and key character. The system represents part of the broader late 17th-century project of solving the meantone wolf problem while preserving meaningful tonal differentiation. Contemporary interest in the temperament has grown among performers seeking more extreme historical key colors for Baroque repertoire.

Other Tuning Systems for A4

See A4 in all temperaments →

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