Well temperament (also circular or circulating temperament) is a type of tempered tuning described in twentieth-century music theory. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach's famous composition, Well-Tempered Clavier. The phrase wohl temperiert also occurs in the works of Bach's predecessor, the organ tuner and music theorist Andreas Werckmeister. In musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system. ... In music, there are two common meanings for tuning: Tuning practice The act of tuning an instrument or voice. ... Music Theory is a field of study that investigates the nature or mechanics of music. ... Bach in a 1748 portrait by Haussmann Places in which Bach resided throughout his life Johann Sebastian Bach (pronounced ) (21 March 1685 O.S. – 28 July 1750 N.S.) was a prolific German composer and organist whose sacred and secular works for choir, orchestra and solo instruments drew together the... Title-page of Das wohltemperirte Clavier A flat major (As-dur) fugue from the second part of Das wohltemperirte Clavier (manuscript) The Well-Tempered Clavier (in the original German: Das wohltemperierte Clavier[1]) is a collection of solo keyboard music composed by Johann Sebastian Bach. ... Music Theory is a field of study that investigates the nature or mechanics of music. ... Andreas Werckmeister (November 30, 1645 – October 26, 1706) was a musician and music theorist of the Baroque era. ...

Origins

"Well tempered" means that the twelve notes per octave of the standard keyboard are tuned in such a way that it is possible to play music in any major or minor key 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". The most used system immediately before Werckmeister was meantone in which one fifth was nearly two commas wider than pure, and four major thirds were also very wide. In music, an octave (sometimes abbreviated 8ve) is the interval between one musical note and another with half or double its frequency. ... In music theory, the key identifies the tonic triad, the chord, major or minor, which represents the final point of rest for a piece, or the focal point of a section. ... Harmony is the use and study of pitch simultaneity, and therefore chords, actual or implied, in music. ... When the twelve notes within the octave are tuned using meantone temperament, one of the fifths will be much sharper than the rest. ... Meantone temperament is a system of musical tuning. ... In music theory, a comma is a small or very small interval between two enharmonic notes tuned in different ways. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ...

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. This article is about modes as used in music. ... An accidental is a musical notation symbol used to raise or lower the pitch of a note from that indicated by the key signature. ... In music transposition is moving a note or collection of notes (or pitches) up or down in pitch by a constant interval. ... In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ... Enharmonic Keyboard The piano is an enharmonic keyboard. ... Euphony describes flowing and aesthetically pleasing speech. ...

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. The chromatic scale is the scale that contains all twelve pitches of the Western tempered scale. ... In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... In music theory, the circle of fifths (or cycle of fifths) is an imaginary geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ...

Forms of well temperament

Equal temperament is the simplest example of "well temperament", but is not usually referred to as such. The term 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-colour" was an essential part of much eighteenth-century music and was described in treatises of the period. An equal temperament is a musical temperament -- that is, a system of tuning intended to approximate some form of just intonation -- in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... In music theory, the circle of fifths is a model of pitch space. ... In Music theory, the diatonic major scale (also known as the Guido scale), from the Greek diatonikos or to stretch out, is a fundamental building block of the European-influenced musical tradition. ...

The first circular temperament was described by the organist Arnolt Schlick in the early sixteenth 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 nineteenth century in some areas. Arnolt Schlick (c1460 - after 1521) was a German organist and composer of the Renaissance. ... Baroque music describes an era and a set of styles of European classical music which were in widespread use between approximately 1600 and 1750 (see Dates of classical music eras for a discussion of the problems inherent in defining the beginning and end points). ... The Classical period in Western music occurred from about 1730 through 1820, despite considerable overlap at both ends with preceding and following periods, as is true for all musical eras. ...

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. Meantone temperament is a system of musical tuning. ...

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

• Werckmeister temperament (invented by Andreas Werckmeister)
• French Temperament Ordinaire
• Neidhardt
• Kirnberger
• Vallotti (invented by Francesco Antonio Vallotti)
• Young

The contemporary composer Douglas Leedy has written several works for harpsichord or organ in which the use of a well temperament is required. Werckmeister temperament refers to any of the tuning systems described by Andreas Werckmeister in his writings [1] and [2]. The tuning systems are confusingly numbered in two different ways. ... Andreas Werckmeister (November 30, 1645 – October 26, 1706) was a musician and music theorist of the Baroque era. ... Origin Kirnberger temperament is an irregular temperament which was developed in the second half of the eighteenth century by Johann Kirnberger. ... Francesco Antonio Vallotti Francesco Antonio Vallotti (1697 - 1780) was an Italian composer, music theorist, and organist. ... Thomas Young (1773 - 1829) devised a form of musical tuning known as a well temperament which he included in a letter to the Royal Society of London written July 9, 1799. ... Douglas (Harry) Leedy, born March 3rd, 1938 in Portland, Oregon is an American composer. ...

For guitars and similar instruments, inventor/guitarist Buzz Feiten patented and commercialized a method, Feitenizing, for getting guitars very well-tempered. It is marketed under the name "Buzz Feiten Tuning System^TM". Howard Buzz Feiten is a session guitar player who once played with Mr Mister. ... A patent is a set of exclusive rights granted by a state to a patentee (the inventor or assignee) for a fixed period of time in exchange for the regulated, public disclosure of certain details of a device, method, process or composition of matter (substance) (known as an invention) which...

Scales have been constructed which circulate in numbers of intervals to the octave other than twelve, but these do not seem to have had much, perhaps not any, actual use as yet in Western music. Other music systems have divided the octave much more finely; in Indian music, for example, the octave is divided as many as 31 times.

See also: Pythagorean tuning, just intonation, meantone temperament, regular temperament, equal temperament. Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. ... Meantone temperament is a system of musical tuning. ... Regular temperament is a 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. ... An equal temperament is a musical temperament -- that is, a system of tuning intended to approximate some form of just intonation -- in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ...

External links

• Tonalsoft Encyclopaedia of Tuning
• Bach's Tuning by Bradley Lehman
• Bach Well Temperament by John Charles Francis