Editing Well temperament

{{Short description|A musical tuning system}}
{{Use dmy dates|date=November 2019}}
'''Well temperament''' (also '''good temperament''', '''circular''' or '''circulating''' temperament) is a type of [[musical temperament|tempered]] [[musical tuning|tuning]] described in 20th-century [[music theory]]. The term is modeled on the German word ''wohltemperiert''. This word also appears in the title of [[Johann Sebastian Bach|J. S. Bach]]'s famous composition "Das wohltemperierte Klavier", ''[[The Well-Tempered Clavier]]''.<!--If Werckmeister had already used the term in 1691, why should Bach be credited with the expression some thirty years later?-->

==Origins==
[[File:Orgelprobe 1681 3 gemerkt 2.jpg|thumb|upright=1.5|300px|Cover of ''Orgelprobe'' (1681)|alt=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 and minor|major]] or [[Major and minor|minor]] [[key (music)|keys]] that were commonly in use, without sounding perceptibly out of tune.{{sfn|Duffin|2007||p=37}}

One of the first attestations of the concept of "well tempered" is found in a treatise in German by the music theorist [[Andreas Werckmeister]].<ref name="Ledbetter2002">{{cite book |last1=Ledbetter |first1=David |title=Bach's Well-tempered clavier : the 48 preludes and fugues |date=2002 |publisher=Yale University Press |location=New Haven |isbn=978-0-300-12898-7 |url=https://books.google.com/books?id=02rmCC1MgvoC}}</ref>{{rp|37}} In the subtitle of his ''Orgelprobe'', from 1681, he writes:<ref name="Norrback2002">{{cite journal |last1=Norrback |first1=Johan |title=A Passable and Good Temperament. A New Methodology for Studying Tuning and Temperament in Organ Music |journal=Studies from the Department of Musicology |date=27 September 2002 |volume=70 |hdl=2077/15641 |url=http://hdl.handle.net/2077/15641 |access-date=22 December 2020}}</ref>
{{blockquote|{{lang|de|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.|italic=no}}}}

The words {{lang|de|wohl}} and {{lang|de|temperieren}} were subsequently combined into {{lang|de|Wohltemperiert}}. A modern definition of "well temperament", from [[Herbert Kelletat]], is given below:{{sfn|Kelletat|1981–82/94|p=9}}
{{clear}}
:{| style="padding: 0 1em"
|style="vertical-align: top;"|{{lang|de|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.|italic=no}}
|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 [[Just intonation|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 [[perfect fifth|fifths]] were narrowed so as to maximize the number of pure [[major third]]s. [[Syntonic comma]]s were distributed across most sequences of four narrowed fifths, with one remaining correction accommodated usually in the diminished sixth [[G♯ (musical note)|G{{music|sharp}}]] to [[E♭ (musical note)|E{{music|flat}}]],{{sfn|Lindley|1990}} which expands to almost a justly tuned [[minor sixth]]. It is this interval that is usually called the "[[wolf interval|wolf]]", because it is so far from [[Consonance and dissonance|consonance]].<ref name="Cyr1992">{{cite book |last1=Cyr |first1=Mary |title=Performing baroque music |date=1992 |publisher=Scolar Press |location=Aldershot, England |isbn=978-0-85967-960-2}}</ref>{{rp|65}}

The wolf was not a problem if music was played in a small number of keys (or to be more precise, transposed [[mode (music)|modes]]) with few [[accidental (music)|accidentals]], but it prevented players from [[transposition (music)|transposing]] and [[modulation (music)|modulating]] freely. Some instrument-makers sought to remedy the problem by introducing more than twelve notes per octave, producing [[enharmonic keyboard]]s which could provide, for example, a D{{music|sharp}} and an E{{music|flat}} with different pitches so that the thirds B–D{{music|sharp}} and E{{music|flat}}–G could both be euphonious. These solutions could include [[split sharp|split keys]] and multiple [[manual (music)|manuals]]; one such solution, the [[archicembalo]], was mentioned by [[Nicola Vicentino]] in 1555.<ref>{{cite journal |last1=Kaufmann |first1=Henry W. |title=More on the Tuning of the Archicembalo |journal=Journal of the American Musicological Society |date=1 April 1970 |volume=23 |issue=1 |pages=84–94 |doi=10.2307/830349|jstor=830349 }}</ref>

However, Werckmeister realised that split keys, or "subsemitonia" as he called them, were unnecessary, and even counterproductive in music with [[chromatic scale|chromatic]] progressions and extensive [[modulation (music)|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{{music|flat}} and D{{music|sharp}}, 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.{{r|Ledbetter2002|p=37}} This is also the source of the terms "circular temperament" or "circulating temperament".<ref>{{cite book |title=Harpsichord and clavichord : an encyclopedia |date=2007 |publisher=Routledge |location=New York |isbn=978-1-135-94978-5 |page=68}}</ref><ref name="Campbell2004">{{cite book |last1=Campbell |first1=Murray |title=Musical instruments : history, technology, and performance of instruments of western music |date=2004 |publisher=Oxford University Press |location=Oxford |isbn=978-0-19-816504-0 |page=341}}</ref>

Although [[equal temperament]] is discussed by Werckmeister in his treatises,<ref name="Bartel2015">{{cite journal |last1=Bartel |first1=Dietrich |title=Andreas Werckmeister's final tuning: the path to equal temperament: 1 |journal=Early Music |date=25 June 2015 |volume=43 |issue=3 |pages=503–512 |doi=10.1093/em/cav047 |access-date=22 December 2020 |url=https://academic.oup.com/em/article-abstract/43/3/503/414311}}</ref> it is distinguished from non-equal well temperaments.{{r|Cyr1992|p=66}}

==Forms==
The term "well temperament" or "good temperament"{{sfn|Barbour|1951|loc=x, 221}}{{sfn|Lindley|2001}} 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 (music)|interval]] ratios, and hence different keys have distinct characters. Such "[[key coloration|key-color]]" was an essential part of much 18th- and 19th-century music and was described in treatises of the period.{{r|Campbell2004}}{{r|Cyr1992|p=66}}

One of the earliest recorded circular temperaments was described by the organist [[Arnolt Schlick]] in the early 16th century.{{sfn|Barbour|1951|p=114}} However, "well temperaments" did not become widely used until the [[Baroque music|Baroque]] period. They persisted through the [[classical music era|Classical period]], and even survived into the second half of 19th century in some areas, for example in Italy.<ref name="PianoEncyclopedia">{{cite book |last1=Palmieri |first1=Robert |title=The Piano : an Encyclopedia |date=2014 |publisher=Routledge |location=New York |isbn=978-1-135-94964-8 |edition=Secondi}}</ref>{{rp|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 [[just intonation|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 (acoustics)|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.<ref>{{cite book |title=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 |date=2006 |publisher=Peter Lang |location=Bern |isbn=978-3-03910-993-7 |page=116}}</ref>

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

* [[Werckmeister temperament|Werckmeister]] (invented by [[Andreas Werckmeister]])
* French [[Temperament ordinaire]]
* {{ill|Johann Georg Neidhardt|de|lt=Neidhardt}}
* [[Kirnberger temperament|Kirnberger]]
* [[David Kellner|Kellner]]
* [[Vallotti temperament|Vallotti]] (invented by [[Francesco Antonio Vallotti]])
* [[Young temperament|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.<ref>{{cite web| url=http://persianney.com/misc/wtemp.pdf |access-date=2023-11-04| title=Baroque temperaments| first=Kees | last=van den Doel}}</ref>

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|date=September 2016}}

==See also==
* [[Pythagorean tuning]]
* [[Just intonation]]
* [[Meantone temperament]]
* [[Regular temperament]]
* [[Equal temperament]]

==References==
<references />

'''Sources'''
* {{wikicite|ref={{harvid|Barbour|1951}}|reference=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).}}
* {{wikicite|ref={{harvid|Duffin|2007}}|reference=Duffin, Ross W. 2007. ''How Equal Temperament Ruined Harmony''. New York: W.W. Norton. {{ISBN|978-0-393-06227-4}}.}}
* {{wikicite|ref={{harvid|Kelletat|1981–82/94}}|reference=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}}).}}
* {{cite journal|last1=Lindley|first1=Mark|title=An historical survey of meantone temperaments to 1620|journal=Early Keyboard Journal|date=1990|url=https://www.academia.edu/1504088|access-date=22 December 2020}}
* {{wikicite|ref={{harvid|Lindley|2001}}|reference=Lindley, Mark. 2001. "Well-tempered clavier". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|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". ''[[Ethnomusicology (journal)|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 (journal)|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.&nbsp;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==
* [http://bach.tuning.googlepages.com/ Bach Well Temperament by John Charles Francis] {{Webarchive|url=https://web.archive.org/web/20061107205248/http://bach.tuning.googlepages.com/ |date=7 November 2006 }}
* [http://plaza.ufl.edu/wnb/baroque_temperament.htm Bach's temperament according to Herbert Anton Kellner]
* [http://www.unequaltemperament.com The Effects of Non-Equal Temperament on Chopin's Mazurkas] Dr. Willis G. Miller, III, PhD diss., University of Houston, October 2001
* [http://home.deds.nl/~broekaert/Well%20Tempering.html Well Temperaments based on the Werckmeister Definition]
* [http://www.larips.com/ Johann Sebastian Bach's tuning, according to Bradley Lehman]
* {{usurped|1=[https://web.archive.org/web/20120301105734/http://bachtuning.jencka.com/essay.htm Johann Sebastian Bach's tuning, according to Daniel Jencka]}}
*[http://www.slate.com/id/2250793 ''The Wolf at Our Heels: The centuries-old struggle to play in tune'', by Jan Swafford, 2010-04-20]
* Willem Kroesbergen, Andrew Cruickshank: "[https://www.academia.edu/5210832 18th century quotes on J.S. Bach's temperament]" 
*Dominic Eckersley: "[https://www.academia.edu/3368760 Rosetta Revisited: Bach's Very Ordinary Temperament]".
* [http://www.larips.com/ Bach Lehman Temperament]

{{Musical tuning}}

{{DEFAULTSORT:Well Temperament}}
[[Category:Musical temperaments]]