Temperament: Difference between revisions

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A '''temperament''' is a ~~[[tuning system]] that slightly compromises the pure [[interval]]s~~ of ~~[[just intonation]] (or~~, ~~more generally, of any [[target tuning]]) to meet other requirements~~.

The term '''temperament''' is used in a number of distinct but related senses, depending on context.

In regular temperament theory, the term ''temperament'' usually refers to a [[regular temperament]].

During the {{w|common practice period}}, the term ''temperament'' was used to describe a [[tuning system]] that slightly compromised the pure [[interval]]s of [[low-complexity just intonation]] to meet other requirements. Nowadays, a temperament in this sense can also be called a '''tempered tuning system''' (often shortened to '''tempered tuning''') to avoid any ambiguity, and it can be designed to approximate any set of pitches.

In regular temperament theory, the term ''temperament'' usually refers to a [[regular temperament]], an abstract mathematical structure from which tempered tuning systems can be derived.

Specific kinds of temperaments, such as [[equal temperament]]s and [[well temperament]]s, can alternatively be viewed as standalone tuning systems or analyzed as specific tunings of regular temperaments.

== History ==

In Western music history, the first ~~temperaments~~ to be described by theorists ~~were~~ [[meantone]] ~~temperaments~~, in the beginning of the 16th century. ~~These were~~ developed in an attempt to solve some of the issues of the [[Pythagorean tuning]], the most commonly used tuning system until then. In particular, the pure fifths ([[3/2]]) are slightly compromised in order to obtain either pure major thirds ([[5/4]]), in [[quarter-comma meantone]], or slightly compromised major thirds in other meantone ~~temperaments~~. The linear structure of meantone ~~temperaments~~ has laid the foundations for the development of [[regular temperament theory]].

In Western music history, the first temperament to be described by theorists was the [[meantone]] temperament, in the beginning of the 16th century. It was developed in an attempt to solve some of the issues of the [[Pythagorean tuning]], the most commonly used tuning system until then. In particular, the pure fifths ([[3/2]]) are slightly compromised in order to obtain either pure major thirds ([[5/4]]), in [[quarter-comma meantone]], or slightly compromised major thirds in other meantone tunings. The linear structure of meantone has laid the foundations for the development of [[regular temperament theory]].

Later in the 16th century, other theorists proposed several [[equal temperament]]s, including [[12edo|12-tone equal temperament]] (12-TET), [[19edo|19-tone equal temperament]] (19-TET) and [[31edo|31-tone equal temperament]] (31-TET). Equal temperaments are now often called [[equal divisions of the octave]] (EDO or edo) in order to distinguish them from other [[equal tuning]]s with the same number of notes spanning an interval other than the [[octave]] ([[nonoctave]] tunings).

Because ~~meantone temperaments~~ have their own issues, a new kind of temperaments appeared in the 17th century: [[well ~~temperament]]s~~. ~~These have an~~ irregular structure ~~that~~ allow for more flexibility in the way each note is tuned, and thus how each interval is compromised. As a result, most scales sound different when they are transposed to a different key.

Because the previous systems have their own issues, a new kind of temperaments appeared in the 17th century: well temperaments. Their irregular structure allow for more flexibility in the way each note is tuned, and thus how each interval is compromised. As a result, most scales sound different when they are transposed to a different key.

== See also ==

* [[Historical temperaments]]

[[Category:~~Theory~~]]

[[Category:Tuning]]

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 {{Wikipedia|Musical temperament}}
-A '''temperament''' is a [[tuning system]] that slightly compromises the pure [[interval]]s of [[just intonation]] (or, more generally, of any [[target tuning]]) to meet other requirements.
+The term '''temperament''' is used in a number of distinct but related senses, depending on context.
-In regular temperament theory, the term ''temperament'' usually refers to a [[regular temperament]].
+During the {{w|common practice period}}, the term ''temperament'' was used to describe a [[tuning system]] that slightly compromised the pure [[interval]]s of [[low-complexity just intonation]] to meet other requirements. Nowadays, a temperament in this sense can also be called a '''tempered tuning system''' (often shortened to '''tempered tuning''') to avoid any ambiguity, and it can be designed to approximate any set of pitches.
+In regular temperament theory, the term ''temperament'' usually refers to a [[regular temperament]], an abstract mathematical structure from which tempered tuning systems can be derived.
+Specific kinds of temperaments, such as [[equal temperament]]s and [[well temperament]]s, can alternatively be viewed as standalone tuning systems or analyzed as specific tunings of regular temperaments.
 == History ==
-In Western music history, the first temperaments to be described by theorists were [[meantone]] temperaments, in the beginning of the 16th century. These were developed in an attempt to solve some of the issues of the [[Pythagorean tuning]], the most commonly used tuning system until then. In particular, the pure fifths ([[3/2]]) are slightly compromised in order to obtain either pure major thirds ([[5/4]]), in [[quarter-comma meantone]], or slightly compromised major thirds in other meantone temperaments. The linear structure of meantone temperaments has laid the foundations for the development of [[regular temperament theory]].
+In Western music history, the first temperament to be described by theorists was the [[meantone]] temperament, in the beginning of the 16th century. It was developed in an attempt to solve some of the issues of the [[Pythagorean tuning]], the most commonly used tuning system until then. In particular, the pure fifths ([[3/2]]) are slightly compromised in order to obtain either pure major thirds ([[5/4]]), in [[quarter-comma meantone]], or slightly compromised major thirds in other meantone tunings. The linear structure of meantone has laid the foundations for the development of [[regular temperament theory]].
+Later in the 16th century, other theorists proposed several [[equal temperament]]s, including [[12edo|12-tone equal temperament]] (12-TET), [[19edo|19-tone equal temperament]] (19-TET) and [[31edo|31-tone equal temperament]] (31-TET). Equal temperaments are now often called [[equal divisions of the octave]] (EDO or edo) in order to distinguish them from other [[equal tuning]]s with the same number of notes spanning an interval other than the [[octave]] ([[nonoctave]] tunings).
-Because meantone temperaments have their own issues, a new kind of temperaments appeared in the 17th century: [[well temperament]]s. These have an irregular structure that allow for more flexibility in the way each note is tuned, and thus how each interval is compromised. As a result, most scales sound different when they are transposed to a different key.
+Because the previous systems have their own issues, a new kind of temperaments appeared in the 17th century: well temperaments. Their irregular structure allow for more flexibility in the way each note is tuned, and thus how each interval is compromised. As a result, most scales sound different when they are transposed to a different key.
 == See also ==
 * [[Historical temperaments]]
-[[Category:Theory]]
+[[Category:Tuning]]