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Well temperament
In Western music theory, a well temperament (also good temperament, circular or circulating temperament) is a type of tempered tuning used for keyboard instruments of the seventeenth and eighteenth centuries. 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.
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.
One of the first attestations of the concept of "well tempered" is found in a treatise in German by the music theorist Andreas Werckmeister. In the subtitle of his Orgelprobe, from 1681, he writes:
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:
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. Syntonic commas were distributed across most sequences of four narrowed fifths, with one remaining correction accommodated usually in the diminished sixth G♯ to E♭, 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.
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.
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. This is also the source of the terms "circular temperament" or "circulating temperament".
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Well temperament
In Western music theory, a well temperament (also good temperament, circular or circulating temperament) is a type of tempered tuning used for keyboard instruments of the seventeenth and eighteenth centuries. 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.
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.
One of the first attestations of the concept of "well tempered" is found in a treatise in German by the music theorist Andreas Werckmeister. In the subtitle of his Orgelprobe, from 1681, he writes:
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:
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. Syntonic commas were distributed across most sequences of four narrowed fifths, with one remaining correction accommodated usually in the diminished sixth G♯ to E♭, 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.
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.
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. This is also the source of the terms "circular temperament" or "circulating temperament".