Well Temperament

Well temperament—also called good temperament, circular temperament or circulating temperament—is a family of tuning systems developed principally between the 16th and 19th centuries to make all major and minor keys usable on fixed-pitch keyboard instruments. The term is modelled on the German wohltemperiert, familiar from the title of Johann Sebastian Bach’s Das wohltemperierte Klavier. Although Bach popularised the term through his compositions, the concept and the terminology appear earlier, particularly in the writings of Andreas Werckmeister in the late 17th century. Well temperament represents a major stage in the evolution from meantone systems to the later adoption of twelve-tone equal temperament.

Origins and Historical Context

In the 17th century well tempered referred to any tuning that enabled performance in all the commonly used keys without producing strongly dissonant, unusable intervals. In earlier systems—especially quarter-comma meantone—one interval within the octave became so wide and harsh that it was known as the wolf interval. This unavoidable compromise restricted the available key range and prevented free modulation. Until around 1650, meantone temperament dominated keyboard practice, and although it delivered many pure major thirds, it rendered certain fifths intolerably wide.
Some instrument makers attempted to overcome these limitations by constructing enharmonic keyboards with more than twelve pitches per octave and split sharps that distinguished, for example, D♯ from E♭. Others added multiple manuals. Nicola Vicentino’s 16th-century archicembalo is an early example of such a solution. However, Werckmeister argued that these refinements were unnecessary in music with extensive chromaticism. He proposed temperaments in which enharmonic notes were tuned identically, thereby producing a circular system of fifths in which modulation could proceed freely. This theoretical circularity is the basis for the designation “circular” or “circulating” temperament.
Although Werckmeister also discussed equal temperament in his treatises, he regarded it as distinct from the nonequal tunings he promoted. His principal aim was not uniformity but usability of all keys with varying degrees of colouration.

Principles of Well Temperament

Well temperament normally signifies an irregular tuning system in which the twelve fifths are tempered unequally but to degrees that avoid producing any wolf intervals. The most characteristic feature of these temperaments is that different keys possess subtly different sonorities. Keys with few accidentals tend to contain purer thirds and narrower fifths, while remote keys include sharper tensions owing to wider fifths and less consonant intervals.
This key-specific colouration was an important expressive resource for composers of the Baroque, Classical and early Romantic eras. Treatises from the 18th and 19th centuries frequently describe the emotional affects associated with particular keys, interpretations that depend on the uneven distribution of tempered intervals.
Well temperaments vary widely. Some are closer to meantone, preserving many pure or near-pure thirds, while others approximate equal temperament. Despite eliminating the wolf fifth, these systems do not make all intervals uniform, and thus keys with numerous sharps or flats may still sound less just than central keys. Nevertheless, the absence of severely impure intervals allows unrestricted modulation.

Examples of Historical Well Temperaments

Many circulating temperaments were introduced across Europe from the 16th century onwards. Arnolt Schlick described an early circular scheme in the early 1500s, though such tunings did not become widespread until the late Baroque period. By the Classical era, well temperaments were commonly in use, and some persisted regionally into the late 19th century, particularly in Italy.
Notable systems include:

• Werckmeister temperaments, introduced by Andreas Werckmeister, featuring tempered fifths arranged to balance consonance and modulatory freedom. Some variants incorporate up to eight pure fifths.
• Temperament ordinaire, a French tradition that influenced harpsichord tuning in the 17th and 18th centuries.
• Vallotti temperament, a scheme by Francesco Antonio Vallotti using six pure fifths and distributing the requisite tempering across the remainder.
• Kellner temperament, with seven pure fifths, emphasising harmonic clarity in central keys.
• Reverse Lehman–Bach 1/4, a modern system by Kees van den Doel that sacrifices the number of pure fifths for highly refined major thirds.

Modern theorists occasionally attempt more restrictive definitions. Owen Jorgensen, for example, has described well temperament in a way that excludes systems containing fifths wider than the pure interval, thereby narrowing the category.

Musical and Acoustic Implications

Well temperaments retain some variance among interval sizes, influencing the acoustic character of each key. Chords with more consonant interval relationships produce stable, slow-beating sonorities, whereas keys relying on wider fifths or less pure thirds produce faster beating, creating tension. Musically, this results in progressions that appear to move into and out of acoustic focus, a property valued for expressive contrast in composition.
Because the fifths in these systems are unequal, enharmonic equivalence (e.g., G♯ = A♭) holds in pitch but not necessarily in acoustic effect. Keys that sit far around the circle of fifths exhibit distinctive brightness or sharpness, while central keys remain smoother.