Temperament - Revision history

Kili: equal temparemnt

2026-05-26T18:29:16Z

equal temparemnt

← Older revision		Revision as of 18:29, 26 May 2026
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	'''Temperament''' is a method of tuning musical instruments based on approximating harmonic targets (almost always [[Just intonation\|just intervals]]) with other intervals, in order to maintain the desired harmony between sounds while simultaneously simplifying melodic structure. For example, in standard tuning, we approximate the harmonic target of 3/2 with the 7-semitone interval, and the target of 5/4 with the 4-semitone interval. The process of application of temperament is called '''tempering'''.		'''Temperament''' is a method of tuning musical instruments based on approximating harmonic targets (almost always [[Just intonation\|just intervals]]) with other intervals, in order to maintain the desired harmony between sounds while simultaneously simplifying melodic structure. For example, in standard tuning, we approximate the harmonic target of 3/2 with the 7-semitone interval, and the target of 5/4 with the 4-semitone interval. The process of application of temperament is called '''tempering'''.

	Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly-used temperaments can be divided into [[Irregular temperament\|well temperaments]] and [[regular temperament]]s. [[Equal temperament\|Equal temperaments]], a very popular tuning approach, are a subset of regular temperaments.		Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly-used temperaments can be divided into [[Irregular temperament\|well temperaments]] and [[regular temperament]]s. [[Equal temperament\|Equal temperaments]], a very popular tuning approach, are a subset of regular temperaments which chop a given interval (such as the octave) into any number of equally large morsels.

	== History ==		== History ==

Hkm at 03:34, 23 March 2026

2026-03-23T03:34:06Z

← Older revision		Revision as of 03:34, 23 March 2026
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	'''Temperament''' is a method of tuning musical instruments based on approximating harmonic targets (almost always [[Just intonation\|just intervals]]) with other intervals, in order to maintain the desired harmony between sounds while simultaneously simplifying melodic structure. The process of application of temperament is called '''tempering'''.		'''Temperament''' is a method of tuning musical instruments based on approximating harmonic targets (almost always [[Just intonation\|just intervals]]) with other intervals, in order to maintain the desired harmony between sounds while simultaneously simplifying melodic structure. For example, in standard tuning, we approximate the harmonic target of 3/2 with the 7-semitone interval, and the target of 5/4 with the 4-semitone interval. The process of application of temperament is called '''tempering'''.

	Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly used temperaments can be divided into ~~[[EDO\|equal temperaments]],~~ [[Irregular temperament\|well temperaments]], and [[regular temperament]]s.		Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly-used temperaments can be divided into [[Irregular temperament\|well temperaments]] and [[regular temperament]]s. [[Equal temperament\|Equal temperaments]], a very popular tuning approach, are a subset of regular temperaments.

	== History ==		== History ==

Lériendil at 09:05, 14 December 2025

2025-12-14T09:05:16Z

← Older revision		Revision as of 09:05, 14 December 2025
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	'''Temperament''' is a method of tuning musical instruments based on approximating ~~certain~~ [[Just intonation\|just intervals]] with other intervals, in order to maintain the desired harmony between sounds. The process of application of temperament is called '''tempering'''.		'''Temperament''' is a method of tuning musical instruments based on approximating harmonic targets (almost always [[Just intonation\|just intervals]]) with other intervals, in order to maintain the desired harmony between sounds while simultaneously simplifying melodic structure. The process of application of temperament is called '''tempering'''.

	Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly used temperaments can be divided into [[EDO\|equal temperaments]], [[Irregular temperament\|well temperaments]], and [[~~Regular~~ temperament~~\|regular temperaments~~]].		Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly used temperaments can be divided into [[EDO\|equal temperaments]], [[Irregular temperament\|well temperaments]], and [[regular temperament]]s.

	== History ==		== History ==

	In Medieval Western Europe, [[Pythagorean tuning]] was the most widely used, in which fifths and fourths are tuned to just intonation. At the time, thirds were omitted and considered a dissonance, which followed from the characteristics of Pythagorean tuning (the [[diatonic major third]] is rather complex). Instrumental music was based on two-part voice leading. To overcome these limitations, a compromise solution was sought that would allow the use of just thirds without sacrificing the purity of fifths.		In Medieval Western Europe, [[Pythagorean tuning]] was the most widely used, in which fifths and fourths are tuned to just intonation. At the time, thirds were omitted and considered a dissonance, which followed from the characteristics of Pythagorean tuning (the [[diatonic major third]] is rather complex). Instrumental music was based on two-part voice leading. To overcome these limitations, a compromise solution was sought that would allow the use of just thirds without sacrificing the purity of fifths.

Inthar at 05:16, 13 December 2025

2025-12-13T05:16:01Z

← Older revision		Revision as of 05:16, 13 December 2025
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	[[~~index.php?title=~~Category:Core knowledge]]		[[Category:Core knowledge]]

Vector: what in god's name is the "tempering zone"

2025-12-13T02:56:54Z

what in god's name is the "tempering zone"

← Older revision		Revision as of 02:56, 13 December 2025
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	'''Temperament''' is a method of tuning musical instruments based on approximating certain [[~~just~~ intonation\|just intervals]] with ~~others~~, in order to maintain the desired harmony between sounds. ~~Process~~ of application of temperament is called '''tempering'''~~, and it is performed in the '''tempering zone''', usually twelve notes within one octave, which is subsequently repeated in remaining octaves~~.		'''Temperament''' is a method of tuning musical instruments based on approximating certain [[Just intonation\|just intervals]] with other intervals, in order to maintain the desired harmony between sounds. The process of application of temperament is called '''tempering'''.

	Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly used can be divided into [[EDO\|equal temperaments]], [[~~well~~ temperament\|well temperaments]] and [[~~regular~~ temperament\|regular temperaments]].		Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly used temperaments can be divided into [[EDO\|equal temperaments]], [[Irregular temperament\|well temperaments]], and [[Regular temperament\|regular temperaments]].

	== History ==		== History ==

	In Medieval Western Europe [[Pythagorean tuning]] was the most widely used, in which fifths and fourths are just. At the time, thirds were omitted and considered a dissonance which followed from characteristics of Pythagorean tuning. Instrumental music was based on two-part voice leading ~~- a majestic bourdon and melodic descant~~. To overcome these limitations, a compromise solution was sought that would allow the use of just thirds without sacrificing the purity of fifths.		In Medieval Western Europe, [[Pythagorean tuning]] was the most widely used, in which fifths and fourths are tuned to just intonation. At the time, thirds were omitted and considered a dissonance, which followed from the characteristics of Pythagorean tuning (the [[diatonic major third]] is rather complex). Instrumental music was based on two-part voice leading. To overcome these limitations, a compromise solution was sought that would allow the use of just thirds without sacrificing the purity of fifths.

	That lead to adoption of [[meantone temperament]] ~~(meantone tuning)~~ in the end of the 15th century. Fifths began to be narrowed, which led to the complete disappearance of just fifth, instead impression of purity of harmony was achieved by just ~~thirds; differently than before when the pure fifths could not compensate for wide major~~ thirds. This enabled introduction of third-based chords and development of [[tertian harmony]].		That lead to the adoption of [[Meantone\|meantone temperament]] in the end of the 15th century. Fifths began to be narrowed, which led to the complete disappearance of the just fifth, and instead the impression of purity of harmony was achieved by just thirds. This enabled the introduction of third-based chords and development of [[tertian harmony]].

	The downside of meantone was that not every diatonic scale known in European music in that time could be played in tune on tempered instruments. In practice, meantone was being modified in a various ~~way~~ by tuners to reduce dissonance created by [[~~wolf~~ interval\|wolf intervals]]. Some theoreticians since 16th century proposed to resolve the problem by use of equal temperaments like 12, ~~19 or 31 edo~~.		The downside of meantone was that not every diatonic scale known in European music in that time could be played in tune on tempered instruments. In practice, meantone was being modified in various ways by tuners to reduce the dissonance created by [[Wolf interval\|wolf intervals]]. Some theoreticians since the 16th century proposed to resolve the problem by the use of equal temperaments like [[12edo]], [[19edo]], and [[31edo]].

	~~Adoption of~~ 12-tone equal temperament became widely accepted practice ~~already in~~ the ~~beginnings~~ of 18th century.		12-tone equal temperament became widely accepted practice by the beginning of the 18th century.


	[[Category:Core knowledge]]		[[index.php?title=Category:Core knowledge]]

Calvera: stub for temperament article

2025-12-13T02:20:39Z

stub for temperament article

New page

'''Temperament''' is a method of tuning musical instruments based on approximating certain [[just intonation|just intervals]] with others, in order to maintain the desired harmony between sounds. Process of application of temperament is called '''tempering''', and it is performed in the '''tempering zone''', usually twelve notes within one octave, which is subsequently repeated in remaining octaves.

Temperaments can be defined as sequences of operations or more formally as mathematical functions. Most commonly used can be divided into [[EDO|equal temperaments]], [[well temperament|well temperaments]] and [[regular temperament|regular temperaments]].

== History ==

In Medieval Western Europe [[Pythagorean tuning]] was the most widely used, in which fifths and fourths are just. At the time, thirds were omitted and considered a dissonance which followed from characteristics of Pythagorean tuning. Instrumental music was based on two-part voice leading - a majestic bourdon and melodic descant. To overcome these limitations, a compromise solution was sought that would allow the use of just thirds without sacrificing the purity of fifths.

That lead to adoption of [[meantone temperament]] (meantone tuning) in the end of the 15th century. Fifths began to be narrowed, which led to the complete disappearance of just fifth, instead impression of purity of harmony was achieved by just thirds; differently than before when the pure fifths could not compensate for wide major thirds. This enabled introduction of third-based chords and development of [[tertian harmony]].

The downside of meantone was that not every diatonic scale known in European music in that time could be played in tune on tempered instruments. In practice, meantone was being modified in a various way by tuners to reduce dissonance created by [[wolf interval|wolf intervals]]. Some theoreticians since 16th century proposed to resolve the problem by use of equal temperaments like 12, 19 or 31 edo.

Adoption of 12-tone equal temperament became widely accepted practice already in the beginnings of 18th century.

[[Category:Core knowledge]]