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- tuning and temperament
equal temperament
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What is equal temperament in music?
In music, equal temperament is a tuning system that divides the octave into 12 equal semitones, each precisely 100 cents apart. This system allows keyboard instruments to play in all keys with minimal intonation flaws, replacing earlier systems based on acoustically pure intervals.
The frequency of each semitone increases by the twelfth root of 2 (approximately 1.059). While it sacrifices perfectly tuned intervals (except for the octave), equal temperament's consistent intervals across the chromatic scale accommodate the expanded harmonies of later music. This system was widely adopted in France and Germany by the late 18th century, and in England by the 19th.
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Why do musicians use equal temperament?
Musicians use equal temperament because it's a tuning system that divides the octave into 12 equal semitones, allowing keyboard instruments to play in all keys with minimal intonation issues. This system replaced earlier tuning methods that relied on acoustically pure intervals.
The adoption of equal temperament gained momentum in the 18th century among German musicians and theorists, becoming widespread in France and Germany by the late 18th century and in England by the 19th. Because equal temperament divides the octave into equal parts, it's called a "divisional" system.
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How does equal temperament affect the way instruments are tuned?
Equal temperament is a tuning system where each semitone equals precisely 1/12th of an octave. This system ensures that keyboard instruments can play in any key with minimal intonation flaws, which led to it replacing earlier tuning systems based on acoustically pure intervals.
With equal temperament, the intervals are identical across the chromatic scale, which accommodates the expanded harmonies of later music. On fretted instruments, equal temperament ensures properly tuned octaves and unisons when the same note is played on different strings. Though it lacks perfectly tuned intervals (except the octave), equal temperament's benefits outweigh its drawbacks for many instruments.
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What is the main difference between equal temperament and other tuning systems?
Equal temperament divides the octave into 12 equal semitones, enabling keyboard instruments to play in all keys with minimal intonation issues. Unlike earlier tuning systems like meantone temperament and just intonation, which were cyclic and based on acoustically pure intervals, equal temperament is a divisional system. This means that earlier systems accumulated intonational differences when moving to more distant keys, causing instruments to sound out of tune in those keys. Equal temperament distributes these small defects equally among the 12 tones, with only the octave remaining pure.
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How does equal temperament make it easier to play in different keys?
Equal temperament simplifies playing in different keys by dividing the octave into 12 equal semitones. This system ensures that the intervals are consistent across the chromatic scale, allowing musicians to play in any key without significant intonation flaws. Unlike earlier tuning systems, equal temperament distributes small imperfections equally among all tones, so only the octave remains acoustically pure. This uniformity accommodates the expanded harmonies of later music and provides equal steps melodically. Because the intervals are identical in all parts of the chromatic scale, the system can accommodate the expanded range of harmonies.
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What are some advantages and disadvantages of equal temperament for musicians and composers?
Equal temperament is a tuning system that divides the octave into 12 equal semitones, allowing keyboard instruments to play in all keys. It replaced earlier tuning systems based on acoustically pure intervals.
Advantages
- Accommodates a wider range of harmonies in music.
- The intervals are identical in all parts of the chromatic scale.
- Melodically fulfills the ideal of equal steps.
- Essential for fretted instruments like lutes and guitars to avoid mistuned octaves.
Disadvantages
- Results in the disappearance of perfectly tuned intervals, except for the octave.
- Some argue that on instruments with sustained tones, like the organ, the disadvantages outweigh the benefits.
- Musicians such as Samuel Sebastian Wesley opposed equal temperament as late as the mid-19th century.
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equal temperament, in music, a tuning system in which the octave is divided into 12 semitones of equal size. Because it enables keyboard instruments to play in all keys with minimal flaws in intonation, equal temperament replaced earlier tuning systems that were based on acoustically pure intervals, that is, intervals that occur naturally in the overtone series. For a more technical explanation of overtones, see sound: Standing waves.
The search for satisfactory tuning systems parallels the development of the Western tonal system, with its reliance on enharmonic equivalence (for example, having the notes F♯ and G♭ sound the same) and multiple major and minor keys. In 1581 Florentine music theorist Vincenzo Galilei (father of the astronomer Galileo) proposed a system of equal intervals for tuning the lute. Chinese prince and musicologist Zhu Zaiyu in 1596 and French philosopher and mathematician Marin Mersenne in 1636, among others, wrote of such a system. The idea of equal temperament had its most effective advocates among German musicians and theorists, beginning with Andreas Werckmeister in the early 18th century. Even before the system was widespread, equal temperament was approximated in various degrees as a practical matter, in the small adjustments made by organ tuners and harpsichordists. Equal temperament tuning was widely adopted in France and Germany by the late 18th century and in England by the 19th. Other systems are discussed in tuning and temperament.
In equal temperament, each semitone is measured at 100 cents (1 cent = 1/1,200 octave); measuring by frequency (vibrational cycles per second), each semitone step increases in frequency by a factor of the 12th root of 2, or about 1.059. The 12th semitone, which completes the octave, therefore has a multiplier of 2; for example, the standard A measures 440 hertz, the octave below 220 hertz, and the octave above 880 hertz. Because equal-tempered tuning is calculated by subdividing the octave, it is called a “divisional” system. Earlier European tuning systems—such as meantone temperament and just intonation—were “cyclic” systems, in which given intervals were calculated by adding together other “pure” intervals. Such systems accumulate intonational differences as they move to more distantly related keys (those with increasing numbers of sharps or flats in the key signature), with the result that keyboard instruments and others with fixed intonation will sound unpleasantly out of tune in those keys. In other words, music that would sound perfectly in tune in C major (with no sharps or flats) would sound wrong if transposed to B major (five sharps) because all of the intervals would actually be different in the two keys. In equal temperament, the perfect fifth, such as C–G, is narrower than the natural, or Pythagorean, fifth by 2 cents, a nearly imperceptible amount. These small intonational defects are equally distributed among the 12 tones of the chromatic scale, and only the octave remains as an acoustically pure interval.
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