Well temperament
Well temperament (also good temperament, circular or circulating temperament) is a type of tempered tuning described in 20th-century music theory. The term is modeled on the German word wohltemperiert. This word also appears in the title of J. S. Bach's famous composition "Das wohltemperierte Klavier", The Well-Tempered Clavier.
The term "well temperament" or "good temperament"[11][12] 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 thus has a slightly different pattern of interval ratios, and hence different keys have distinct characters. Such "key-color" was an essential part of much 18th- and 19th-century music and was described in treatises of the period.[9][6]: 66
One of the earliest recorded circular temperaments was described by the organist Arnolt Schlick in the early 16th century.[13] However, "well temperaments" did not become widely used until the Baroque period. They persisted through the Classical period, and even survived into the second half of 19th century in some areas, for example in Italy.[14]: 393–394
There are many well temperament schemes, some nearer meantone temperament, others nearer 12-tone equal temperament. Although such tunings have no wolf fifth, keys with many sharps or flats still do not sound very pure, due to their thirds. This can create contrast between chords in which vibrations are concordant with others where the vibrations are not harmonically related and thus beat.
Some modern theorists such as Owen Jorgensen have sought to define "well temperament" more narrowly to exclude fifths wider than pure, which rules out many such schemes.[15]
Some well-known well temperaments go by the following names:
Some temperament schemes feature numbers of perfect, pure fifths and these give enhanced harmonic resonance to instruments and music on which they are played so that music moves into and out of focus between keys as vibrations lock together or not. Werckmeister features 8 perfect fifths, Kellner 7 and Vallotti 6. Alternatively, "Reverse Lehman-Bach 14," a system by Kees Van Den Doel, features only 3 pure perfect fifths in exchange for optimal major thirds, with none wider than a Pythagorean Third.[16]
The contemporary composer Douglas Leedy has written several works for harpsichord or organ in which the use of a well temperament is required.
Sources