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.
Origins
As used in the 17th century, the term "well tempered" meant that the twelve notes per octave of the standard keyboard were tuned in such a way that it was possible to play music in all major or minor keys that were commonly in use, without sounding perceptibly out of tune.[1]
One of the first attestations of the concept of "well tempered" is found in a treatise in German by the music theorist Andreas Werckmeister.[2]: 37 In the subtitle of his Orgelprobe, from 1681, he writes:[3]
Unterricht, Wie durch Anweiß und Hülffe des Monochordi ein Clavier wohl zu temperiren und zu stimmen sei, damit man nach heutiger Manier alle modos fictos in einer erträglichen und angenehmen harmoni vernehme.
The words wohl and temperieren were subsequently combined into Wohltemperiert. A modern definition of "well temperament", from Herbert Kelletat, is given below:[4]
Wohltemperierung heißt mathematisch-akustische und praktisch-musikalischen Einrichtung von Tonmaterial innerhalb der zwölfstufigen Oktavskala zum einwandfreien Gebrauch in allen Tonarten auf der Grundlage des natürlich-harmonischen Systems mit Bestreben möglichster Reinerhaltung der diatonische Intervalle. Sie tritt auf als proportionsgebundene, sparsam temperierende Lockerung und Dehnung des mitteltönigen Systems, als ungleichschwebende Semitonik und als gleichschwebende Temperatur. Well temperament means a mathematical-acoustic and musical-practical organisation of the tone system within the twelve steps of an octave, with the goal of impeccable performance in all tonalities, based on the natural-harmonic tone system [i.e., extended just intonation], while striving to keep the diatonic intervals as pure as possible. This temperament acts, while tied to given pitch ratios, as a thriftily tempered smoothing and extension of the meantone, as unequally beating half tones and as equally beating [i.e., equal] temperament.
In most tuning systems used before 1700, one or more intervals on the twelve-note keyboard were so far from any pure interval that they were unusable in harmony and were called a "wolf interval". Until about 1650 the most common keyboard temperament was quarter-comma meantone, in which the fifths were narrowed so as to maximize the number of pure major thirds. The syntonic comma was distributed between four intervals, usually with most of the comma accommodated in the diminished sixth G♯ to E♭,[5] which expands to almost a justly tuned minor sixth. It is this interval that is usually called the "wolf", because it is so far from consonance.[6]: 65
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 twelve 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. These solutions could include split keys and multiple manuals; one such solution, the archicembalo, was mentioned by Nicola Vicentino in 1555.[7]
However, Werckmeister realised that split keys, or "subsemitonia" as he called them, were unnecessary, and even counterproductive in music with
Although equal temperament is discussed by Werckmeister in his treatises,[10] it is distinguished from non-equal well temperaments.[6]: 66
Forms
The term "well temperament" or "good temperament"
One of the earliest recorded circular temperaments was described by the organist
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:
- Werckmeister (invented by Andreas Werckmeister)
- French Temperament ordinaire
- Neidhardt
- Kirnberger
- Kellner
- Vallotti (invented by Francesco Antonio Vallotti)
- Young
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.[citation needed]
See also
References
- ^ Duffin 2007, p. 37.
- ^ ISBN 978-0-300-12898-7.
- hdl:2077/15641. Retrieved 22 December 2020.
- ^ Kelletat & 1981–82/94, p. 9.
- ^ Lindley 1990.
- ^ ISBN 978-0-85967-960-2.
- JSTOR 830349.
- ISBN 978-1-135-94978-5.
- ^ ISBN 978-0-19-816504-0.
- . Retrieved 22 December 2020.
- ^ Barbour 1951, x, 221.
- ^ Lindley 2001.
- ^ Barbour 1951, p. 114.
- ISBN 978-1-135-94964-8.
- ISBN 978-3-03910-993-7.
- ^ van den Doel, Kees. "Baroque temperaments" (PDF). Retrieved 4 November 2023.
Sources
- Barbour, J. Murray. 1951. Tuning and Temperament: A Historical Survey. East Lansing: Michigan State College Press. Reprinted, Da Capo Music Reprint Series, New York: Da Capo Press, 1972. ISBN 0-486-43406-0(pbk).
- Duffin, Ross W. 2007. How Equal Temperament Ruined Harmony. New York: W.W. Norton. ISBN 978-0-393-06227-4.
- Kelletat, Herbert. 1981–82/94. Zur musikalischen Temperatur, second corrected and enlarged edition, 3 vols. Edition Merseburger 1190, 1196, 1538. Kassel: Merseburger. Vol I: Johann Sebastian Bach und seine Zeit (ISBN 3-87537-239-5).
- Lindley, Mark (1990). "An historical survey of meantone temperaments to 1620". Early Keyboard Journal. Retrieved 22 December 2020.
- Lindley, Mark. 2001. "Well-tempered clavier". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
Further reading
- Kuttner, Fritz A. 1975. "Prince Chu Tsai-Yü's Life and Work: A Re-Evaluation of His Contribution to Equal Temperament Theory". Ethnomusicology19, no. 2 (May): 163–206.
- Padgham, Charles A. 1986. "The Well-Tempered Organ". Oxford: Positif Press. ISBN 0-906894-13-1(pbk).
- Swich, Luigi. 2011. "Further thoughts on Bach's 1722 temperament". Early Music 39, no. 3 (August): 401–407.
- Temple, Robert K. G. 1986. 2007. The Genius of China: 3,000 Years of Science, Discovery, and Invention. New York: Simon and Schuster. ISBN 978-1-59477-217-7(pbk).
- Robinson, Kenneth G., and Joseph Needham. 1962. "Physics and Physical Technology". In Science and Civilisation in China, vol. 4: "Physics and Physical Technology", Part 1: "Physics", edited by Joseph Needham, pp. 212–228. Cambridge: University Press.
- Robinson, Kenneth. 1980. A Critical Study of Chu Tsai-yü's Contribution to the Theory of Equal Temperament in Chinese Music. Sinologica Coloniensia 9. Wiesbaden: Franz Steiner Verlag.
- Stevin, Simon. 1884. Vande Spiegeling der Singconst, et Vande Molens. Deux traites inédits, edited by D. Bierens de Haan. Amsterdam: D. Bierens de Haan.
External links
- Bach Well Temperament by John Charles Francis Archived 7 November 2006 at the Wayback Machine
- Bach's temperament according to Herbert Anton Kellner
- The Effects of Non-Equal Temperament on Chopin's Mazurkas Dr. Willis G. Miller, III, PhD diss., University of Houston, October 2001
- Well Temperaments based on the Werckmeister Definition
- Johann Sebastian Bach's tuning, according to Bradley Lehman
- Johann Sebastian Bach's tuning, according to Daniel Jencka
- The Wolf at Our Heels: The centuries-old struggle to play in tune, by Jan Swafford, 2010-04-20
- Willem Kroesbergen, Andrew Cruickshank: "18th century quotes on J.S. Bach's temperament"
- Dominic Eckersley: "Rosetta Revisited: Bach's Very Ordinary Temperament".
- Bach Lehman Temperament