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Well temperament

January 01, 1970

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 edit

 
Cover of Orgelprobe (1681)

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 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 without restriction.[2]: 37  This is also the source of the terms "circular temperament" or "circulating temperament".[8][9]

Although equal temperament is discussed by Werckmeister in his treatises,[10] it is distinguished from non-equal well temperaments.[6]: 66 

Forms edit

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.[citation needed]

See also edit

References edit

  1. ^ Duffin 2007, p. 37.
  2. ^ a b Ledbetter, David (2002). Bach's Well-tempered clavier : the 48 preludes and fugues. New Haven: Yale University Press. ISBN 978-0-300-12898-7.
  3. ^ Norrback, Johan (27 September 2002). "A Passable and Good Temperament. A New Methodology for Studying Tuning and Temperament in Organ Music". Studies from the Department of Musicology. 70. hdl:2077/15641. Retrieved 22 December 2020.
  4. ^ Kelletat & 1981–82/94, p. 9.
  5. ^ Lindley 1990.
  6. ^ a b c Cyr, Mary (1992). Performing baroque music. Aldershot, England: Scolar Press. ISBN 978-0-85967-960-2.
  7. ^ Kaufmann, Henry W. (1 April 1970). "More on the Tuning of the Archicembalo". Journal of the American Musicological Society. 23 (1): 84–94. doi:10.2307/830349. JSTOR 830349.
  8. ^ Harpsichord and clavichord : an encyclopedia. New York: Routledge. 2007. p. 68. ISBN 978-1-135-94978-5.
  9. ^ a b Campbell, Murray (2004). Musical instruments : history, technology, and performance of instruments of western music. Oxford: Oxford University Press. p. 341. ISBN 978-0-19-816504-0.
  10. ^ Bartel, Dietrich (25 June 2015). "Andreas Werckmeister's final tuning: the path to equal temperament: 1". Early Music. 43 (3): 503–512. doi:10.1093/em/cav047. Retrieved 22 December 2020.
  11. ^ Barbour 1951, x, 221.
  12. ^ Lindley 2001.
  13. ^ Barbour 1951, p. 114.
  14. ^ Palmieri, Robert (2014). The Piano : an Encyclopedia (Secondi ed.). New York: Routledge. ISBN 978-1-135-94964-8.
  15. ^ Musique ancienne, instruments et imagination : actes des Rencontres Internationales harmoniques, Lausanne 2004 = Music of the past, instruments and imagination : proceedings of the harmoniques International Congress, Lausanne 2004. Bern: Peter Lang. 2006. p. 116. ISBN 978-3-03910-993-7.
  16. ^ 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 0-306-70422-6. Reprinted, Mineola, New York: Dover Publications, 2004. 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 3-87537-156-9); Vol. 2: Wiener Klassik (ISBN 3-87537-187-9); Vol. 3: Franz Schubert (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 edit

  • Kuttner, Fritz A. 1975. "Prince Chu Tsai-Yü's Life and Work: A Re-Evaluation of His Contribution to Equal Temperament Theory". Ethnomusicology 19, 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 0-671-62028-2. Reprint London: Prion. 1991, ISBN 1-85375-078-6, and paperback, 1998. ISBN 1-85375-292-4. Third edition, introduction by Joseph Needham. London: Andre Deutsch; Rochester, Vermont: Inner Traditions 2007. ISBN 978-0-233-00202-6 (cloth); 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 edit

  • Bach Well Temperament by John Charles Francis 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
  • 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

January 01, 1970
well, temperament, also, good, temperament, circular, circulating, temperament, type, tempered, tuning, described, 20th, century, music, theory, term, modeled, german, word, wohltemperiert, this, word, also, appears, title, bach, famous, composition, wohltempe. 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 Contents 1 Origins 2 Forms 3 See also 4 References 5 Further reading 6 External linksOrigins edit nbsp Cover of Orgelprobe 1681 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 Hulffe des Monochordi ein Clavier wohl zu temperiren und zu stimmen sei damit man nach heutiger Manier alle modos fictos in einer ertraglichen 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 zwolfstufigen Oktavskala zum einwandfreien Gebrauch in allen Tonarten auf der Grundlage des naturlich harmonischen Systems mit Bestreben moglichster Reinerhaltung der diatonische Intervalle Sie tritt auf als proportionsgebundene sparsam temperierende Lockerung und Dehnung des mitteltonigen 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 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 without restriction 2 37 This is also the source of the terms circular temperament or circulating temperament 8 9 Although equal temperament is discussed by Werckmeister in his treatises 10 it is distinguished from non equal well temperaments 6 66 Forms editThe 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 Werckmeister invented by Andreas Werckmeister French Temperament ordinaire Neidhardt de 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 editPythagorean tuning Just intonation Meantone temperament Regular temperament Equal temperamentReferences edit Duffin 2007 p 37 a b Ledbetter David 2002 Bach s Well tempered clavier the 48 preludes and fugues New Haven Yale University Press ISBN 978 0 300 12898 7 Norrback Johan 27 September 2002 A Passable and Good Temperament A New Methodology for Studying Tuning and Temperament in Organ Music Studies from the Department of Musicology 70 hdl 2077 15641 Retrieved 22 December 2020 Kelletat amp 1981 82 94 p 9 Lindley 1990 a b c Cyr Mary 1992 Performing baroque music Aldershot England Scolar Press ISBN 978 0 85967 960 2 Kaufmann Henry W 1 April 1970 More on the Tuning of the Archicembalo Journal of the American Musicological Society 23 1 84 94 doi 10 2307 830349 JSTOR 830349 Harpsichord and clavichord an encyclopedia New York Routledge 2007 p 68 ISBN 978 1 135 94978 5 a b Campbell Murray 2004 Musical instruments history technology and performance of instruments of western music Oxford Oxford University Press p 341 ISBN 978 0 19 816504 0 Bartel Dietrich 25 June 2015 Andreas Werckmeister s final tuning the path to equal temperament 1 Early Music 43 3 503 512 doi 10 1093 em cav047 Retrieved 22 December 2020 Barbour 1951 x 221 Lindley 2001 Barbour 1951 p 114 Palmieri Robert 2014 The Piano an Encyclopedia Secondi ed New York Routledge ISBN 978 1 135 94964 8 Musique ancienne instruments et imagination actes des Rencontres Internationales harmoniques Lausanne 2004 Music of the past instruments and imagination proceedings of the harmoniques International Congress Lausanne 2004 Bern Peter Lang 2006 p 116 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 0 306 70422 6 Reprinted Mineola New York Dover Publications 2004 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 156 9 Vol 2 Wiener Klassik ISBN 3 87537 187 9 Vol 3 Franz Schubert 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 editKuttner Fritz A 1975 Prince Chu Tsai Yu s Life and Work A Re Evaluation of His Contribution to Equal Temperament Theory Ethnomusicology 19 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 0 671 62028 2 Reprint London Prion 1991 ISBN 1 85375 078 6 and paperback 1998 ISBN 1 85375 292 4 Third edition introduction by Joseph Needham London Andre Deutsch Rochester Vermont Inner Traditions 2007 ISBN 978 0 233 00202 6 cloth 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 yu 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 inedits edited by D Bierens de Haan Amsterdam D Bierens de Haan External links editBach 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 Retrieved from https en wikipedia org w index php title Well temperament amp oldid 1203585142, wikipedia, wiki, book, books, library,

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