Well temperament
Encyclopedia
Well temperament is a type of tempered 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, The Well-Tempered Clavier
. The phrase wohl temperiert also occurs in the works of Bach's predecessor, the organ tuner and music theorist Andreas Werckmeister
.
of the standard keyboard are tuned in such a way that it is possible to play music in most major
or minor
keys
and it will not sound perceptibly out of tune. 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
". Until about 1650 the most common keyboard temperament was quarter-comma meantone
, in which the fifths
were narrowed to the extent that they were just usable, and would thereby produce justly tuned thirds. The syntonic comma
was distributed between four intervals, with most of the comma accommodated in the sol
to mi
diminished sixth, which expands to nearly a minor sixth. It is this interval that is usually called the "wolf", because it is so far out of consonance. The term "mean tone", the basis for meantone temperament
, refers to the mathematical averaging of thirds, in which the middle note (for example the D between C and E) is in the "mean" position between the notes making the third. Another example of this is equal temperament
(which is actually eleventh-comma meantone if seen in the perspective as to how to divide the comma between the fifths).
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 keyboard
s 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.
According to Sinologist Robert K. G. Temple
, the well temperament was first invented by the Chinese prince of the Ming dynasty Chu Tsai-Yü in 1584 and came in contact with Western culture during exchange fairs organized by the Cantonese viceroy in that time. How exactly it travelled to Europe is not documented, but it is likely that Jesuits in China brought the knowledge over to Europe (Temple 2007). Other scholars, however, state that Prince Chu accurately calculated not a well temperament but equal temperament
—though only in his second treatise, Lii Lu Ching I, written in 1595–96 and probably first published in 1606 did he achieve the full chromatic complement of 12 notes (Kutter 1975, 166–67). However, at just the same time, the Flemish mathematician Simon Stevin
(1548–1620) wrote an essay containing the correct mathematical formulation of equal temperament for the first time in Western musical theory, though his manuscript remained unpublished until long after the author's death (Kutter 1975, 167–68; Stevin 1884).
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 19th century in some areas.
There are many well temperament schemes, some nearer meantone temperament
, others nearer equal temperament. 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:
The contemporary composer Douglas Leedy
has written several works for harpsichord or organ in which the use of a well temperament is required.
Musical tuning
In music, there are two common meanings for tuning:* Tuning practice, the act of tuning an instrument or voice.* Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases.-Tuning practice:...
described in 20th-century music theory
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach's
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...
famous composition, The Well-Tempered Clavier
The Well-Tempered Clavier
The Well-Tempered Clavier , BWV 846–893, is a collection of solo keyboard music composed by Johann Sebastian Bach...
. The phrase wohl temperiert also occurs in the works of Bach's predecessor, the organ tuner and music theorist Andreas Werckmeister
Andreas Werckmeister
Andreas Werckmeister was an organist, music theorist, and composer of the Baroque era.-Life:Born in Benneckenstein, Germany, Werckmeister attended schools in Nordhausen and Quedlinburg. He received his musical training from his uncles Heinrich Christian Werckmeister and Heinrich Victor Werckmeister...
.
Origins
"Well tempered" means that the twelve notes per octaveOctave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
of the standard keyboard are tuned in such a way that it is possible to play music in most major
Major and minor
In Western music, the adjectives major and minor can describe a musical composition, movement, section, scale, key, chord, or interval.Major and minor are frequently referred to in the titles of classical compositions, especially in reference to the key of a piece.-Intervals and chords:With regard...
or minor
Major and minor
In Western music, the adjectives major and minor can describe a musical composition, movement, section, scale, key, chord, or interval.Major and minor are frequently referred to in the titles of classical compositions, especially in reference to the key of a piece.-Intervals and chords:With regard...
keys
Key (music)
In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...
and it will not sound perceptibly out of tune. 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
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
and were called a "wolf
Wolf interval
In music theory, the wolf fifth is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament...
". Until about 1650 the most common keyboard temperament was quarter-comma meantone
Quarter-comma meantone
Quarter-comma meantone, or 1/4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. This method is a variant of Pythagorean tuning...
, in which the fifths
Perfect fifth
In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
were narrowed to the extent that they were just usable, and would thereby produce justly tuned thirds. The syntonic comma
Syntonic comma
In music theory, the syntonic comma, also known as the chromatic diesis, the comma of Didymus, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 cents...
was distributed between four intervals, with most of the comma accommodated in the sol
Solfege
In music, solfège is a pedagogical solmization technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solfège syllable...
to mi
Solfege
In music, solfège is a pedagogical solmization technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solfège syllable...
diminished sixth, which expands to nearly a minor sixth. It is this interval that is usually called the "wolf", because it is so far out of consonance. The term "mean tone", the basis for meantone temperament
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
, refers to the mathematical averaging of thirds, in which the middle note (for example the D between C and E) is in the "mean" position between the notes making the third. Another example of this is equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
(which is actually eleventh-comma meantone if seen in the perspective as to how to divide the comma between the fifths).
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
Accidental (music)
In music, an accidental is a note whose pitch is not a member of a scale or mode indicated by the most recently applied key signature. In musical notation, the symbols used to mark such notes, sharps , flats , and naturals , may also be called accidentals...
, but it prevented players from transposing
Transposition (music)
In music transposition refers to the process, or operation, of moving a collection of notes up or down in pitch by a constant interval.For example, one might transpose an entire piece of music into another key...
and modulating
Modulation (music)
In music, modulation is most commonly the act or process of changing from one key to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest...
freely. Some instrument-makers sought to remedy the problem by introducing more than twelve notes per octave, producing enharmonic keyboard
Enharmonic keyboard
An enharmonic keyboard is a musical keyboard based on an enharmonic scale. At the very least such keyboards will have 17 keys per octave, and enharmonically equivalent notes will have different pitches. A typical keyboard will have one key for, for instance, C sharp and D flat, but a basic 17 key...
s 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
Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
progressions and extensive modulations
Modulation (music)
In music, modulation is most commonly the act or process of changing from one key to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest...
. He described a series of tunings where enharmonic
Enharmonic
In modern musical notation and tuning, an enharmonic equivalent is a note , interval , or key signature which is equivalent to some other note, interval, or key signature, but "spelled", or named, differently...
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
Circle of fifths
In music theory, the circle of fifths shows the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys...
and it is possible to modulate from one key to another unrestrictedly.
According to Sinologist Robert K. G. Temple
Robert K. G. Temple
Robert K. G. Temple is an American author best known for his controversial book, The Sirius Mystery which presents the idea that the Dogon people preserve the tradition of contact with intelligent extraterrestrial beings from the Sirius star-system...
, the well temperament was first invented by the Chinese prince of the Ming dynasty Chu Tsai-Yü in 1584 and came in contact with Western culture during exchange fairs organized by the Cantonese viceroy in that time. How exactly it travelled to Europe is not documented, but it is likely that Jesuits in China brought the knowledge over to Europe (Temple 2007). Other scholars, however, state that Prince Chu accurately calculated not a well temperament but equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
—though only in his second treatise, Lii Lu Ching I, written in 1595–96 and probably first published in 1606 did he achieve the full chromatic complement of 12 notes (Kutter 1975, 166–67). However, at just the same time, the Flemish mathematician Simon Stevin
Simon Stevin
Simon Stevin was a Flemish mathematician and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical...
(1548–1620) wrote an essay containing the correct mathematical formulation of equal temperament for the first time in Western musical theory, though his manuscript remained unpublished until long after the author's death (Kutter 1975, 167–68; Stevin 1884).
Forms
The term "well temperament" 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-color" was an essential part of much 18th- and 19th-century music and was described in treatises of the period.The first circular temperament was described by the organist Arnolt Schlick
Arnolt Schlick
Arnolt Schlick was a German organist, lutenist and composer of the Renaissance. He is grouped among the composers known as the Colorists. He was most probably born in Heidelberg and by 1482 established himself as court organist for the Electoral Palatinate...
in the early 16th century, but "well temperaments" did not become widely used until the baroque
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...
period. They persisted through the classical period, and even survived into the late 19th century in some areas.
There are many well temperament schemes, some nearer meantone temperament
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
, others nearer equal temperament. 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 temperamentWerckmeister temperamentWerckmeister temperaments are the tuning systems described by Andreas Werckmeister in his writings . The tuning systems are confusingly numbered in two different ways: the first refers to the order in which they were presented as "good temperaments" in Werckmeister's 1691 treatise, the second to...
(invented by Andreas WerckmeisterAndreas WerckmeisterAndreas Werckmeister was an organist, music theorist, and composer of the Baroque era.-Life:Born in Benneckenstein, Germany, Werckmeister attended schools in Nordhausen and Quedlinburg. He received his musical training from his uncles Heinrich Christian Werckmeister and Heinrich Victor Werckmeister...
) - French Temperament OrdinaireTemperament OrdinaireThe phrase temperament ordinaire is a term for musical intonation, particularly the tempered tuning of keyboard instruments...
- Neidhardt
- KirnbergerJohann Philipp Kirnberger temperamentKirnberger temperament is an irregular temperament developed in the second half of the 18th century by Johann Kirnberger. Kirnberger was a student of Johann Sebastian Bach, held great admiration for his teacher and was one of his principle proponents, though it is rumored that they had many...
- Vallotti (invented by Francesco Antonio VallottiFrancesco Antonio VallottiFrancesco Antonio Vallotti was an Italian composer, music theorist, and organist.- Life :He was born in Vercelli. He studied with G. A. Bissone at the church of St. Eusebius, and joined the Franciscan order in 1716. He was ordained as a priest in 1720. In 1722 he became an organist at St...
) - YoungYoung temperamentYoung temperament is a well temperament devised by Thomas Young, which he included in a letter to the Royal Society of London written July 9, 1799...
The contemporary composer Douglas Leedy
Douglas Leedy
Douglas Leedy is an American composer, performer and music scholar.-Biography:Born in Portland, Oregon, Leedy studied with Karl Kohn at Pomona College and at the University of California, Berkeley, where he was in a composition seminar with membership including La Monte Young and Terry Riley...
has written several works for harpsichord or organ in which the use of a well temperament is required.
See also
- Pythagorean tuningPythagorean tuningPythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
- Just intonationJust intonationIn music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
- Meantone temperamentMeantone temperamentMeantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
- Regular temperamentRegular temperamentRegular temperament is any tempered system of musical tuning such that each frequency ratio is obtainable as a product of powers of a finite number of generators, or generating frequency ratios...
- Equal temperamentEqual temperamentAn equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
External links
- Bach Well Temperament by John Charles Francis
- 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
- Bach- and Well Temperaments for Western Classical Music, A proposal for an objective musical definition