Well temperament

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Well temperament (or circular temperament) is a type of tuning described in 20th-century music theory. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach's famous composition, Well-Tempered Clavier. The phrase wohl temperiert also occurs in the works of Bach's predecessor, the organ tuner and music theorist Andreas Werckmeister. The German usage is gute Temperatur "good temperament", but "well temperament" has become ingrained, despite its perceived ungrammaticality and hence avoidance by some authors.

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Origins

"Well tempered" means that the 12 notes per octave of the standard keyboard are tuned in such a way that it is possible to play music in any major or minor key and it will not sound perceptibly out of tune. In most tuning systems used before 1700, one or more intervals on the 12-note keyboard were so far from any pure interval that they were unusable in harmony and were called a "wolf". The most used system immediately before Werckmeister was meantone in which one fifth (usually E♭–G♯) was nearly two commas wider than pure, and four major thirds were also very wide.

The wolf was not a problem if music was played in a small number of keys (or to be more precise, transposed modes) with few accidentals but it prevented players from transposing and modulating freely. Some instrument-makers sought to remedy the problem by introducing more than 12 notes per octave, producing enharmonic keyboards which could provide, for example, a D♯ and an E♭ with different pitches so that the thirds B–D♯ and E♭–G could both be euphonious.

However, Werckmeister realised that these "subsemitonia", as he called them, were unnecessary, and even counterproductive in music with chromatic progressions and extensive modulations. He described a series of tunings where enharmonic notes had the same pitch: in other words, the same note was used as both (say) E♭ and D♯, thereby "bringing the keyboard into the form of a circle". This refers to the fact that the notes or keys may be arranged in a circle of fifths and it is possible to modulate from one key to another unrestrictedly.

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Forms of well temperament

Equal temperament is the simplest example of "well temperament", but is not usually referred to as such. The term usually means some sort of irregular temperament in which the tempered fifths are of different sizes but no key has very impure intervals. Historical irregular temperaments usually have the narrowest fifths between the diatonic notes ("naturals") producing purer thirds, and wider fifths among the chromatic notes ("sharps and flats"). Each key then has a slightly different intonation, hence different keys have distinct characters. Such "key-colour" was an essential part of much 18th-century music and was described in treatises of the period.

The first circular temperament was described by the organist Arnolt Schlick in the early 16th century, but "well temperaments" did not become widely used until the baroque period. They persisted through the classical period, and even survived into the late nineteenth century in some areas.

There are many well temperament schemes, some nearer meantone temperament, others nearer equal temperament. Some of the schemes closer to meantone, in particular temperament ordinaire, are debatable. Although such tunings have no wolf fifth, keys with many sharps or flats still do not sound very well in tune (due to their thirds), and can only be used fleetingly. Some theorists have sought to define "well temperament" more narrowly to exclude fifths wider than pure, which rules out many such schemes.

Some well-known well temperaments go by the following names:

Werckmeister temperament (invented by Andreas Werckmeister)
French Temperament Ordinaire
Neidhardt
Kirnberger
Vallotti
Young

For guitars and similar instruments, inventor Buzz Feiten patented and commercialized a method, Feitenizing, for getting guitars resonably well tempered.

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